idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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52,401 | Confidence bands in case of fitting ARIMA in R? | I've included an example below to show one method of how to calculate Bartlett's approximations and add them to a graph of the autocorrelation function.
In the example, I've done things by hand rather than rely on a particular package hence the code is longer than it perhaps need be. I don't claim the code to be effic... | Confidence bands in case of fitting ARIMA in R? | I've included an example below to show one method of how to calculate Bartlett's approximations and add them to a graph of the autocorrelation function.
In the example, I've done things by hand rathe | Confidence bands in case of fitting ARIMA in R?
I've included an example below to show one method of how to calculate Bartlett's approximations and add them to a graph of the autocorrelation function.
In the example, I've done things by hand rather than rely on a particular package hence the code is longer than it per... | Confidence bands in case of fitting ARIMA in R?
I've included an example below to show one method of how to calculate Bartlett's approximations and add them to a graph of the autocorrelation function.
In the example, I've done things by hand rathe |
52,402 | Do skewness and kurtosis uniquely determine type of distribution? | No it's not enough. These are only the third and fourth standardized moments, & distributions may differ in higher-order moments. Note also that some moments may not exist. | Do skewness and kurtosis uniquely determine type of distribution? | No it's not enough. These are only the third and fourth standardized moments, & distributions may differ in higher-order moments. Note also that some moments may not exist. | Do skewness and kurtosis uniquely determine type of distribution?
No it's not enough. These are only the third and fourth standardized moments, & distributions may differ in higher-order moments. Note also that some moments may not exist. | Do skewness and kurtosis uniquely determine type of distribution?
No it's not enough. These are only the third and fourth standardized moments, & distributions may differ in higher-order moments. Note also that some moments may not exist. |
52,403 | Do skewness and kurtosis uniquely determine type of distribution? | The general answer is no, they are just moments. To keep it simple: Does the mean (first moment) determine the type of distribution ?
This works only if you are working on a certain family of distribution. For example you can define a Gaussian with only the mean and the variance. This is what happened in your example, ... | Do skewness and kurtosis uniquely determine type of distribution? | The general answer is no, they are just moments. To keep it simple: Does the mean (first moment) determine the type of distribution ?
This works only if you are working on a certain family of distribu | Do skewness and kurtosis uniquely determine type of distribution?
The general answer is no, they are just moments. To keep it simple: Does the mean (first moment) determine the type of distribution ?
This works only if you are working on a certain family of distribution. For example you can define a Gaussian with only ... | Do skewness and kurtosis uniquely determine type of distribution?
The general answer is no, they are just moments. To keep it simple: Does the mean (first moment) determine the type of distribution ?
This works only if you are working on a certain family of distribu |
52,404 | Covariance of binary and continuous variable | This answer (and all the comments from the second comment onwards on the main question) comes from a question, now-closed as a duplicate of the one above by ophelie, from Thevesh Theva who asked for a proof of
$$\operatorname{cov}(X,Y) = E[Y\mid X=1] - E[Y\mid X=0],
\tag{1}$$ which is a false result. In fact, for $X \s... | Covariance of binary and continuous variable | This answer (and all the comments from the second comment onwards on the main question) comes from a question, now-closed as a duplicate of the one above by ophelie, from Thevesh Theva who asked for a | Covariance of binary and continuous variable
This answer (and all the comments from the second comment onwards on the main question) comes from a question, now-closed as a duplicate of the one above by ophelie, from Thevesh Theva who asked for a proof of
$$\operatorname{cov}(X,Y) = E[Y\mid X=1] - E[Y\mid X=0],
\tag{1}$... | Covariance of binary and continuous variable
This answer (and all the comments from the second comment onwards on the main question) comes from a question, now-closed as a duplicate of the one above by ophelie, from Thevesh Theva who asked for a |
52,405 | Covariance of binary and continuous variable | \begin{eqnarray}
Cov(y,d) &=& E(y \cdot d) - E(y) \cdot E(d) \\
&=& p \cdot E(y|d=1)-[p \cdot E(y|d=1) + (1-p) \cdot E(y|d=0)] \cdot p \\
&=& p \cdot (1-p) \cdot [E(y|d=1) - E(y|d=0)]
\end{eqnarray} | Covariance of binary and continuous variable | \begin{eqnarray}
Cov(y,d) &=& E(y \cdot d) - E(y) \cdot E(d) \\
&=& p \cdot E(y|d=1)-[p \cdot E(y|d=1) + (1-p) \cdot E(y|d=0)] \cdot p \\
&=& p \cdot (1-p) \cdot [E(y|d=1) - E(y|d=0)]
\end{eqnarray} | Covariance of binary and continuous variable
\begin{eqnarray}
Cov(y,d) &=& E(y \cdot d) - E(y) \cdot E(d) \\
&=& p \cdot E(y|d=1)-[p \cdot E(y|d=1) + (1-p) \cdot E(y|d=0)] \cdot p \\
&=& p \cdot (1-p) \cdot [E(y|d=1) - E(y|d=0)]
\end{eqnarray} | Covariance of binary and continuous variable
\begin{eqnarray}
Cov(y,d) &=& E(y \cdot d) - E(y) \cdot E(d) \\
&=& p \cdot E(y|d=1)-[p \cdot E(y|d=1) + (1-p) \cdot E(y|d=0)] \cdot p \\
&=& p \cdot (1-p) \cdot [E(y|d=1) - E(y|d=0)]
\end{eqnarray} |
52,406 | Analysis of variance not statistically significant... but is there still a pattern to the data? | You're thinking about your ANOVA incorrectly. It's OK, lots of people are taught ANOVA that way. The ANOVA does not mean there are any significant differences between levels of the predictor variable. None of them can be significant and yet the ANOVA is. It means that the pattern of data has meaning. Simply report... | Analysis of variance not statistically significant... but is there still a pattern to the data? | You're thinking about your ANOVA incorrectly. It's OK, lots of people are taught ANOVA that way. The ANOVA does not mean there are any significant differences between levels of the predictor variabl | Analysis of variance not statistically significant... but is there still a pattern to the data?
You're thinking about your ANOVA incorrectly. It's OK, lots of people are taught ANOVA that way. The ANOVA does not mean there are any significant differences between levels of the predictor variable. None of them can be ... | Analysis of variance not statistically significant... but is there still a pattern to the data?
You're thinking about your ANOVA incorrectly. It's OK, lots of people are taught ANOVA that way. The ANOVA does not mean there are any significant differences between levels of the predictor variabl |
52,407 | Analysis of variance not statistically significant... but is there still a pattern to the data? | You are running into one of the fundamental problems with p-values: They are partly dependent on sample sizes.
So, when you increase sample size, smaller effect sizes become significant. This accounts for both changes that you report 1) More comparisons become significant because smaller effect sizes are (this seems li... | Analysis of variance not statistically significant... but is there still a pattern to the data? | You are running into one of the fundamental problems with p-values: They are partly dependent on sample sizes.
So, when you increase sample size, smaller effect sizes become significant. This accounts | Analysis of variance not statistically significant... but is there still a pattern to the data?
You are running into one of the fundamental problems with p-values: They are partly dependent on sample sizes.
So, when you increase sample size, smaller effect sizes become significant. This accounts for both changes that y... | Analysis of variance not statistically significant... but is there still a pattern to the data?
You are running into one of the fundamental problems with p-values: They are partly dependent on sample sizes.
So, when you increase sample size, smaller effect sizes become significant. This accounts |
52,408 | Formal definition of random assignment | While Michael Chernick gave a good answer, I do not think that the people who are involved in treatment effect estimation think in terms of finite populations and randomization-based inference. Economists (Angrist and Imbens are well-known econometricians) usually don't; if the OP comes from the same tradition, that is... | Formal definition of random assignment | While Michael Chernick gave a good answer, I do not think that the people who are involved in treatment effect estimation think in terms of finite populations and randomization-based inference. Econom | Formal definition of random assignment
While Michael Chernick gave a good answer, I do not think that the people who are involved in treatment effect estimation think in terms of finite populations and randomization-based inference. Economists (Angrist and Imbens are well-known econometricians) usually don't; if the OP... | Formal definition of random assignment
While Michael Chernick gave a good answer, I do not think that the people who are involved in treatment effect estimation think in terms of finite populations and randomization-based inference. Econom |
52,409 | Formal definition of random assignment | This definition of random assignment seems to be assigning with equal probability. To assign 0 weight any of the possible assignments could create bias and should be considered a nonrandom assignemnt by any definition. However sampling with unequal nonzero weights can be an acceptable procedure (e.g. sampling randoml... | Formal definition of random assignment | This definition of random assignment seems to be assigning with equal probability. To assign 0 weight any of the possible assignments could create bias and should be considered a nonrandom assignemnt | Formal definition of random assignment
This definition of random assignment seems to be assigning with equal probability. To assign 0 weight any of the possible assignments could create bias and should be considered a nonrandom assignemnt by any definition. However sampling with unequal nonzero weights can be an acce... | Formal definition of random assignment
This definition of random assignment seems to be assigning with equal probability. To assign 0 weight any of the possible assignments could create bias and should be considered a nonrandom assignemnt |
52,410 | Formal definition of random assignment | One thing that you'll notice in the AIR paper is that they do not condition on covariates $X$. You can generalize the AIR exposition by doing so.
Let $X$ be an indicator for whether a subject is male. Also suppose that you want men to be more likely to receive treatment than women. You can have $$
\begin{equation*}\Pr... | Formal definition of random assignment | One thing that you'll notice in the AIR paper is that they do not condition on covariates $X$. You can generalize the AIR exposition by doing so.
Let $X$ be an indicator for whether a subject is male | Formal definition of random assignment
One thing that you'll notice in the AIR paper is that they do not condition on covariates $X$. You can generalize the AIR exposition by doing so.
Let $X$ be an indicator for whether a subject is male. Also suppose that you want men to be more likely to receive treatment than wome... | Formal definition of random assignment
One thing that you'll notice in the AIR paper is that they do not condition on covariates $X$. You can generalize the AIR exposition by doing so.
Let $X$ be an indicator for whether a subject is male |
52,411 | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA | Regarding Bonferroni (and multiple comparisons issues in general) Jacob Cohen, in his book on regression, said "this is a subject on which reasonable people can differ". There are arguments for not doing such corrections at all (see, e.g., this piece by Andrew Gelman). I find such arguments persuasive.
If you reduce c... | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA | Regarding Bonferroni (and multiple comparisons issues in general) Jacob Cohen, in his book on regression, said "this is a subject on which reasonable people can differ". There are arguments for not do | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA
Regarding Bonferroni (and multiple comparisons issues in general) Jacob Cohen, in his book on regression, said "this is a subject on which reasonable people can differ". There are arguments for not doing such corrections at all (see, e.g., this ... | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA
Regarding Bonferroni (and multiple comparisons issues in general) Jacob Cohen, in his book on regression, said "this is a subject on which reasonable people can differ". There are arguments for not do |
52,412 | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA | A couple of points - too long for a comment:
If you are protecting your pre-planned tests with Bonferroni correction, than there is no need to run the original ANOVA. The "double protection" only looses power.
Most of the standard "post-hoc" tests for ANOVA do not need the protection of the original F-test. Essentiall... | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA | A couple of points - too long for a comment:
If you are protecting your pre-planned tests with Bonferroni correction, than there is no need to run the original ANOVA. The "double protection" only loo | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA
A couple of points - too long for a comment:
If you are protecting your pre-planned tests with Bonferroni correction, than there is no need to run the original ANOVA. The "double protection" only looses power.
Most of the standard "post-hoc" te... | Bonferroni and Greenhouse-Geisser corrections with repeated-measures ANOVA
A couple of points - too long for a comment:
If you are protecting your pre-planned tests with Bonferroni correction, than there is no need to run the original ANOVA. The "double protection" only loo |
52,413 | What can I do if my logistic regression model doesn't predict anything? | What do you mean by doesn't predict? Are you implying the model is doing the same as randomly guessing?
Maybe your cutoff (for predicting a 'positive' result) is not adequate? You may way want to try producing some ROC curves based on data you currently have to choose an appropriate cutoff. You would want take into ... | What can I do if my logistic regression model doesn't predict anything? | What do you mean by doesn't predict? Are you implying the model is doing the same as randomly guessing?
Maybe your cutoff (for predicting a 'positive' result) is not adequate? You may way want to tr | What can I do if my logistic regression model doesn't predict anything?
What do you mean by doesn't predict? Are you implying the model is doing the same as randomly guessing?
Maybe your cutoff (for predicting a 'positive' result) is not adequate? You may way want to try producing some ROC curves based on data you cu... | What can I do if my logistic regression model doesn't predict anything?
What do you mean by doesn't predict? Are you implying the model is doing the same as randomly guessing?
Maybe your cutoff (for predicting a 'positive' result) is not adequate? You may way want to tr |
52,414 | What can I do if my logistic regression model doesn't predict anything? | A general strategy when a model has no predictive power is to start over.
But does it really have no predictive power? That is does it do no better than flipping a coin?
In general, and with only rare exceptions, models will do better on the data they were trained on then on new data.
Beyond that, some more context ... | What can I do if my logistic regression model doesn't predict anything? | A general strategy when a model has no predictive power is to start over.
But does it really have no predictive power? That is does it do no better than flipping a coin?
In general, and with only ra | What can I do if my logistic regression model doesn't predict anything?
A general strategy when a model has no predictive power is to start over.
But does it really have no predictive power? That is does it do no better than flipping a coin?
In general, and with only rare exceptions, models will do better on the data... | What can I do if my logistic regression model doesn't predict anything?
A general strategy when a model has no predictive power is to start over.
But does it really have no predictive power? That is does it do no better than flipping a coin?
In general, and with only ra |
52,415 | What can I do if my logistic regression model doesn't predict anything? | What were you plotting for predicted values and actual values? The model predicts either log-odds, or some other value depending on what you ask predict to return. It could be probability. Actual values are just 0,1. One way around this is to bin your actual values over subranges of the predictor and get the means ... | What can I do if my logistic regression model doesn't predict anything? | What were you plotting for predicted values and actual values? The model predicts either log-odds, or some other value depending on what you ask predict to return. It could be probability. Actual v | What can I do if my logistic regression model doesn't predict anything?
What were you plotting for predicted values and actual values? The model predicts either log-odds, or some other value depending on what you ask predict to return. It could be probability. Actual values are just 0,1. One way around this is to b... | What can I do if my logistic regression model doesn't predict anything?
What were you plotting for predicted values and actual values? The model predicts either log-odds, or some other value depending on what you ask predict to return. It could be probability. Actual v |
52,416 | Analyze and visualize participants response towards particular condition | For two, avoid dynamite plots (see Drummond & Vowler, 2011), and utilize dot plots since you only have 15 participants. You can super-impose confidence lines over the dot plots, and you can create a category axis label to label the dots/bars/lines, foregoing the need to differentiate between categories using color, poi... | Analyze and visualize participants response towards particular condition | For two, avoid dynamite plots (see Drummond & Vowler, 2011), and utilize dot plots since you only have 15 participants. You can super-impose confidence lines over the dot plots, and you can create a c | Analyze and visualize participants response towards particular condition
For two, avoid dynamite plots (see Drummond & Vowler, 2011), and utilize dot plots since you only have 15 participants. You can super-impose confidence lines over the dot plots, and you can create a category axis label to label the dots/bars/lines... | Analyze and visualize participants response towards particular condition
For two, avoid dynamite plots (see Drummond & Vowler, 2011), and utilize dot plots since you only have 15 participants. You can super-impose confidence lines over the dot plots, and you can create a c |
52,417 | Analyze and visualize participants response towards particular condition | @AndyW has a good answer. I think dot plots, or even box plots are good approaches, although I think bar graphs are OK. One thing I would recommend is that you rotate your figure 90 degrees. Then, more visual would go to the right, and more auditory would go to the left. The advantage of this is that you could drop... | Analyze and visualize participants response towards particular condition | @AndyW has a good answer. I think dot plots, or even box plots are good approaches, although I think bar graphs are OK. One thing I would recommend is that you rotate your figure 90 degrees. Then, | Analyze and visualize participants response towards particular condition
@AndyW has a good answer. I think dot plots, or even box plots are good approaches, although I think bar graphs are OK. One thing I would recommend is that you rotate your figure 90 degrees. Then, more visual would go to the right, and more aud... | Analyze and visualize participants response towards particular condition
@AndyW has a good answer. I think dot plots, or even box plots are good approaches, although I think bar graphs are OK. One thing I would recommend is that you rotate your figure 90 degrees. Then, |
52,418 | What is the variance-covariance matrix of the OLS residual vector? | First and foremost, your model is typically referred to as "general" instead of "generalised".
I show you the calculation for $\textrm{Var} ( \hat{\beta} )$ so that you can continue it for $\textrm{Var}(\hat{\epsilon}) = \textrm{Var} ( Y - X\hat{\beta})$.
The OLS estimator of your vector $\beta$ is
$\hat{\beta} = (X'X... | What is the variance-covariance matrix of the OLS residual vector? | First and foremost, your model is typically referred to as "general" instead of "generalised".
I show you the calculation for $\textrm{Var} ( \hat{\beta} )$ so that you can continue it for $\textrm{V | What is the variance-covariance matrix of the OLS residual vector?
First and foremost, your model is typically referred to as "general" instead of "generalised".
I show you the calculation for $\textrm{Var} ( \hat{\beta} )$ so that you can continue it for $\textrm{Var}(\hat{\epsilon}) = \textrm{Var} ( Y - X\hat{\beta}... | What is the variance-covariance matrix of the OLS residual vector?
First and foremost, your model is typically referred to as "general" instead of "generalised".
I show you the calculation for $\textrm{Var} ( \hat{\beta} )$ so that you can continue it for $\textrm{V |
52,419 | What is the variance-covariance matrix of the OLS residual vector? | See Wikipedia under Studentized residual#How to studentize for the variance of a single residual:
$$\mbox{var}(\widehat{\varepsilon}_i)=\sigma^2(1-h_{ii})$$
where $h_{ii}$ is the ith diagonal entry in the hat matrix $H=X(X^T X)^{-1}X^T$.
And Hat matrix#Uncorrelated errors for the variance-covariance matrix of the resid... | What is the variance-covariance matrix of the OLS residual vector? | See Wikipedia under Studentized residual#How to studentize for the variance of a single residual:
$$\mbox{var}(\widehat{\varepsilon}_i)=\sigma^2(1-h_{ii})$$
where $h_{ii}$ is the ith diagonal entry in | What is the variance-covariance matrix of the OLS residual vector?
See Wikipedia under Studentized residual#How to studentize for the variance of a single residual:
$$\mbox{var}(\widehat{\varepsilon}_i)=\sigma^2(1-h_{ii})$$
where $h_{ii}$ is the ith diagonal entry in the hat matrix $H=X(X^T X)^{-1}X^T$.
And Hat matrix#... | What is the variance-covariance matrix of the OLS residual vector?
See Wikipedia under Studentized residual#How to studentize for the variance of a single residual:
$$\mbox{var}(\widehat{\varepsilon}_i)=\sigma^2(1-h_{ii})$$
where $h_{ii}$ is the ith diagonal entry in |
52,420 | Likelihood ratio test | For logistic regression you use the asymptotic distribution of the log of likelihood ratio test statistic for variable selection (testing hypotheses or model selection). In the case of linear regression, due to the assumed normality for the error distribution, there is no need to use asymptotics, and the likelihood ra... | Likelihood ratio test | For logistic regression you use the asymptotic distribution of the log of likelihood ratio test statistic for variable selection (testing hypotheses or model selection). In the case of linear regress | Likelihood ratio test
For logistic regression you use the asymptotic distribution of the log of likelihood ratio test statistic for variable selection (testing hypotheses or model selection). In the case of linear regression, due to the assumed normality for the error distribution, there is no need to use asymptotics,... | Likelihood ratio test
For logistic regression you use the asymptotic distribution of the log of likelihood ratio test statistic for variable selection (testing hypotheses or model selection). In the case of linear regress |
52,421 | Difference between experimental data and observational data? | wow, that's a tough one :-)
That question is far more widely relevant than just in data mining. It comes up in medicine and in the social sciences including psychology all the time.
The distinction is necessary when it comes to drawing conclusions about causality, that is, when you want to know if something (e.g. a me... | Difference between experimental data and observational data? | wow, that's a tough one :-)
That question is far more widely relevant than just in data mining. It comes up in medicine and in the social sciences including psychology all the time.
The distinction i | Difference between experimental data and observational data?
wow, that's a tough one :-)
That question is far more widely relevant than just in data mining. It comes up in medicine and in the social sciences including psychology all the time.
The distinction is necessary when it comes to drawing conclusions about caus... | Difference between experimental data and observational data?
wow, that's a tough one :-)
That question is far more widely relevant than just in data mining. It comes up in medicine and in the social sciences including psychology all the time.
The distinction i |
52,422 | Difference between experimental data and observational data? | Very much in a nutshell: only data for which you have all covariates under control, and have either randomization over possible confounders or enough information on them to properly account for them, can be truly called experimental. This could e.g. be the case in plant research where genetically identical and similarl... | Difference between experimental data and observational data? | Very much in a nutshell: only data for which you have all covariates under control, and have either randomization over possible confounders or enough information on them to properly account for them, | Difference between experimental data and observational data?
Very much in a nutshell: only data for which you have all covariates under control, and have either randomization over possible confounders or enough information on them to properly account for them, can be truly called experimental. This could e.g. be the ca... | Difference between experimental data and observational data?
Very much in a nutshell: only data for which you have all covariates under control, and have either randomization over possible confounders or enough information on them to properly account for them, |
52,423 | How to test the predictive power of a model? | ROC, sensitivity, specificity, and cutoffs have gotten in the way, unfortunately. Assuming there is nothing between "good" and "bad" and that the success of the experiment was not based on an underlying continuum that should have instead formed the dependent variable, a probability model such as logistic regression wou... | How to test the predictive power of a model? | ROC, sensitivity, specificity, and cutoffs have gotten in the way, unfortunately. Assuming there is nothing between "good" and "bad" and that the success of the experiment was not based on an underlyi | How to test the predictive power of a model?
ROC, sensitivity, specificity, and cutoffs have gotten in the way, unfortunately. Assuming there is nothing between "good" and "bad" and that the success of the experiment was not based on an underlying continuum that should have instead formed the dependent variable, a prob... | How to test the predictive power of a model?
ROC, sensitivity, specificity, and cutoffs have gotten in the way, unfortunately. Assuming there is nothing between "good" and "bad" and that the success of the experiment was not based on an underlyi |
52,424 | How to test the predictive power of a model? | AUC is a good start. You can also calculate what percent of observations were correctly classified, and you can make a confusion matrix.
However, the best single thing you can do is calculate these values using a "test" dataset, who's observations were not used to train the model. This is the only true test of a pred... | How to test the predictive power of a model? | AUC is a good start. You can also calculate what percent of observations were correctly classified, and you can make a confusion matrix.
However, the best single thing you can do is calculate these v | How to test the predictive power of a model?
AUC is a good start. You can also calculate what percent of observations were correctly classified, and you can make a confusion matrix.
However, the best single thing you can do is calculate these values using a "test" dataset, who's observations were not used to train the... | How to test the predictive power of a model?
AUC is a good start. You can also calculate what percent of observations were correctly classified, and you can make a confusion matrix.
However, the best single thing you can do is calculate these v |
52,425 | Help with data analysis of small datasets | One could use a non-parametric version of ANOVA: this is called the Kruskal-Wallis test. It is based on ranking all 17 results and computing the mean ranks within each group. The mean rank of 2.0 among the controls is obviously smaller than any other mean rank (which range from 7 to 12). However, the test p-value is... | Help with data analysis of small datasets | One could use a non-parametric version of ANOVA: this is called the Kruskal-Wallis test. It is based on ranking all 17 results and computing the mean ranks within each group. The mean rank of 2.0 am | Help with data analysis of small datasets
One could use a non-parametric version of ANOVA: this is called the Kruskal-Wallis test. It is based on ranking all 17 results and computing the mean ranks within each group. The mean rank of 2.0 among the controls is obviously smaller than any other mean rank (which range fr... | Help with data analysis of small datasets
One could use a non-parametric version of ANOVA: this is called the Kruskal-Wallis test. It is based on ranking all 17 results and computing the mean ranks within each group. The mean rank of 2.0 am |
52,426 | Help with data analysis of small datasets | There is a time to make formal statistical inferences from sample to population, and a time to simply report on your descriptive results and let your audience make informal inferences--or not, as they see fit. This looks like the latter. With two control values, you are one step away from having no variation on which... | Help with data analysis of small datasets | There is a time to make formal statistical inferences from sample to population, and a time to simply report on your descriptive results and let your audience make informal inferences--or not, as they | Help with data analysis of small datasets
There is a time to make formal statistical inferences from sample to population, and a time to simply report on your descriptive results and let your audience make informal inferences--or not, as they see fit. This looks like the latter. With two control values, you are one s... | Help with data analysis of small datasets
There is a time to make formal statistical inferences from sample to population, and a time to simply report on your descriptive results and let your audience make informal inferences--or not, as they |
52,427 | Help with data analysis of small datasets | This is an interesting data set. It seems like a good idea to follow @whuber's advice and do the analysis on the log scale. However, there is more than one hypothesis here. For you could have the hypothesis
$$H_{0}:\text{samples 1-5 have the same mean and variance on the log scale,}$$
$$\text{and this is different f... | Help with data analysis of small datasets | This is an interesting data set. It seems like a good idea to follow @whuber's advice and do the analysis on the log scale. However, there is more than one hypothesis here. For you could have the h | Help with data analysis of small datasets
This is an interesting data set. It seems like a good idea to follow @whuber's advice and do the analysis on the log scale. However, there is more than one hypothesis here. For you could have the hypothesis
$$H_{0}:\text{samples 1-5 have the same mean and variance on the log... | Help with data analysis of small datasets
This is an interesting data set. It seems like a good idea to follow @whuber's advice and do the analysis on the log scale. However, there is more than one hypothesis here. For you could have the h |
52,428 | Multidimensional scaling pseudo-code | There are different kind of MDS (e.g., see this brief review). Here are two pointers:
the smacof R package, developed by Jan de Leeuw and Patrick Mair has a nice vignette, Multidimensional Scaling Using Majorization: SMACOF in R (or see, the Journal of Statistical Software (2009) 31(3)) -- R code is available, of cour... | Multidimensional scaling pseudo-code | There are different kind of MDS (e.g., see this brief review). Here are two pointers:
the smacof R package, developed by Jan de Leeuw and Patrick Mair has a nice vignette, Multidimensional Scaling Us | Multidimensional scaling pseudo-code
There are different kind of MDS (e.g., see this brief review). Here are two pointers:
the smacof R package, developed by Jan de Leeuw and Patrick Mair has a nice vignette, Multidimensional Scaling Using Majorization: SMACOF in R (or see, the Journal of Statistical Software (2009) 3... | Multidimensional scaling pseudo-code
There are different kind of MDS (e.g., see this brief review). Here are two pointers:
the smacof R package, developed by Jan de Leeuw and Patrick Mair has a nice vignette, Multidimensional Scaling Us |
52,429 | Multidimensional scaling pseudo-code | If you have the Statistics Toolbox in MATLAB you can read the source code of mdscale.m. While it's not pseudocode, it will definitely help you understand MDS better and gives you one approach to coding it.
In MATLAB you can type
edit mdscale
and that will open up an editor window that shows you the mdscale.m script t... | Multidimensional scaling pseudo-code | If you have the Statistics Toolbox in MATLAB you can read the source code of mdscale.m. While it's not pseudocode, it will definitely help you understand MDS better and gives you one approach to codin | Multidimensional scaling pseudo-code
If you have the Statistics Toolbox in MATLAB you can read the source code of mdscale.m. While it's not pseudocode, it will definitely help you understand MDS better and gives you one approach to coding it.
In MATLAB you can type
edit mdscale
and that will open up an editor window ... | Multidimensional scaling pseudo-code
If you have the Statistics Toolbox in MATLAB you can read the source code of mdscale.m. While it's not pseudocode, it will definitely help you understand MDS better and gives you one approach to codin |
52,430 | Should percentages be reported with decimal places? | It depends on the size of the differences between classes. In most applications, saying the 73% prefer option A and 27% prefer option B is perfectly acceptable. But if you're dealing in an election where candidate X has 50.15% of votes and candidate Y has 49.86%, the decimal places are very much necessary.
Of course, y... | Should percentages be reported with decimal places? | It depends on the size of the differences between classes. In most applications, saying the 73% prefer option A and 27% prefer option B is perfectly acceptable. But if you're dealing in an election wh | Should percentages be reported with decimal places?
It depends on the size of the differences between classes. In most applications, saying the 73% prefer option A and 27% prefer option B is perfectly acceptable. But if you're dealing in an election where candidate X has 50.15% of votes and candidate Y has 49.86%, the ... | Should percentages be reported with decimal places?
It depends on the size of the differences between classes. In most applications, saying the 73% prefer option A and 27% prefer option B is perfectly acceptable. But if you're dealing in an election wh |
52,431 | Should percentages be reported with decimal places? | Different organisations often have conflicting rules for the precision in reporting of results. Ultimately there is a trade-off between when seeing the extra digits is useful, versus cases where unnecessary and excessive precision "can swamp the reader, overcomplicate the story and obscure the message" — a subject expl... | Should percentages be reported with decimal places? | Different organisations often have conflicting rules for the precision in reporting of results. Ultimately there is a trade-off between when seeing the extra digits is useful, versus cases where unnec | Should percentages be reported with decimal places?
Different organisations often have conflicting rules for the precision in reporting of results. Ultimately there is a trade-off between when seeing the extra digits is useful, versus cases where unnecessary and excessive precision "can swamp the reader, overcomplicate... | Should percentages be reported with decimal places?
Different organisations often have conflicting rules for the precision in reporting of results. Ultimately there is a trade-off between when seeing the extra digits is useful, versus cases where unnec |
52,432 | Should percentages be reported with decimal places? | This is a significant figures issue, and is dependent upon the precision of the numbers underlying the percentages. The technically correct number of significant figures is not dependent upon downstream use or the differences between percentage values.
If you're trying to express a percentage describing 5 items out of ... | Should percentages be reported with decimal places? | This is a significant figures issue, and is dependent upon the precision of the numbers underlying the percentages. The technically correct number of significant figures is not dependent upon downstre | Should percentages be reported with decimal places?
This is a significant figures issue, and is dependent upon the precision of the numbers underlying the percentages. The technically correct number of significant figures is not dependent upon downstream use or the differences between percentage values.
If you're tryin... | Should percentages be reported with decimal places?
This is a significant figures issue, and is dependent upon the precision of the numbers underlying the percentages. The technically correct number of significant figures is not dependent upon downstre |
52,433 | Should percentages be reported with decimal places? | The goal is to make it easy for the reader to understand the important differences. Too many digits obscures the meaningful difference between values in a table. Too few leaves out important information. Here's a great discussion: https://newmr.org/blog/how-many-significant-digits-should-you-display-in-your-presentatio... | Should percentages be reported with decimal places? | The goal is to make it easy for the reader to understand the important differences. Too many digits obscures the meaningful difference between values in a table. Too few leaves out important informati | Should percentages be reported with decimal places?
The goal is to make it easy for the reader to understand the important differences. Too many digits obscures the meaningful difference between values in a table. Too few leaves out important information. Here's a great discussion: https://newmr.org/blog/how-many-signi... | Should percentages be reported with decimal places?
The goal is to make it easy for the reader to understand the important differences. Too many digits obscures the meaningful difference between values in a table. Too few leaves out important informati |
52,434 | Subsets not significantly different but superset is | It seems to be a question of test power. If you only look at a subset you have a lot less participants and therefore a lot less power to find an effect of similar size.
With a reduced sample size you can only find a much bigger effect. So it is NOT recommended to only look at the subsets in this case. Unless there is a... | Subsets not significantly different but superset is | It seems to be a question of test power. If you only look at a subset you have a lot less participants and therefore a lot less power to find an effect of similar size.
With a reduced sample size you | Subsets not significantly different but superset is
It seems to be a question of test power. If you only look at a subset you have a lot less participants and therefore a lot less power to find an effect of similar size.
With a reduced sample size you can only find a much bigger effect. So it is NOT recommended to only... | Subsets not significantly different but superset is
It seems to be a question of test power. If you only look at a subset you have a lot less participants and therefore a lot less power to find an effect of similar size.
With a reduced sample size you |
52,435 | Subsets not significantly different but superset is | This is not necessarily an issue of statistical power; it could also be an example of confounding.
Example:
One category of $O$ is more common in males but the other is more common in females
The distribution of $A$ differs between males and females
Within each sex separately, the distribution of $A$ is exact... | Subsets not significantly different but superset is | This is not necessarily an issue of statistical power; it could also be an example of confounding.
Example:
One category of $O$ is more common in males but the other is more common in females
T | Subsets not significantly different but superset is
This is not necessarily an issue of statistical power; it could also be an example of confounding.
Example:
One category of $O$ is more common in males but the other is more common in females
The distribution of $A$ differs between males and females
Within e... | Subsets not significantly different but superset is
This is not necessarily an issue of statistical power; it could also be an example of confounding.
Example:
One category of $O$ is more common in males but the other is more common in females
T |
52,436 | What to do about ties in voting results? | To give some context, I don't view this as a "statistical" question as much of a "group preference" question. Economists and policy wonks do a lot of thinking about questions of how to convert individual preferences into a "will of the people." You will find lots of interesting reading if you search the web for "politi... | What to do about ties in voting results? | To give some context, I don't view this as a "statistical" question as much of a "group preference" question. Economists and policy wonks do a lot of thinking about questions of how to convert individ | What to do about ties in voting results?
To give some context, I don't view this as a "statistical" question as much of a "group preference" question. Economists and policy wonks do a lot of thinking about questions of how to convert individual preferences into a "will of the people." You will find lots of interesting ... | What to do about ties in voting results?
To give some context, I don't view this as a "statistical" question as much of a "group preference" question. Economists and policy wonks do a lot of thinking about questions of how to convert individ |
52,437 | What to do about ties in voting results? | You're asking an intriguing question. I agree with the comments that are showing some apprehension at the "one-man-one-vote" system. I also agree that knowing the basic statistics (like standard deviation and mean) will not give you an insight into the will of the voters.
I would like to play off of David James's answe... | What to do about ties in voting results? | You're asking an intriguing question. I agree with the comments that are showing some apprehension at the "one-man-one-vote" system. I also agree that knowing the basic statistics (like standard devia | What to do about ties in voting results?
You're asking an intriguing question. I agree with the comments that are showing some apprehension at the "one-man-one-vote" system. I also agree that knowing the basic statistics (like standard deviation and mean) will not give you an insight into the will of the voters.
I woul... | What to do about ties in voting results?
You're asking an intriguing question. I agree with the comments that are showing some apprehension at the "one-man-one-vote" system. I also agree that knowing the basic statistics (like standard devia |
52,438 | What to do about ties in voting results? | A little OT, but one of my favourite nuggets of science is Arrow's theorem, so in case you're not familiar here's the wikipedia page:
http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem
And all from a PhD thesis, too. Quite inspiring really. Mine was rubbish. | What to do about ties in voting results? | A little OT, but one of my favourite nuggets of science is Arrow's theorem, so in case you're not familiar here's the wikipedia page:
http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem
And all | What to do about ties in voting results?
A little OT, but one of my favourite nuggets of science is Arrow's theorem, so in case you're not familiar here's the wikipedia page:
http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem
And all from a PhD thesis, too. Quite inspiring really. Mine was rubbish. | What to do about ties in voting results?
A little OT, but one of my favourite nuggets of science is Arrow's theorem, so in case you're not familiar here's the wikipedia page:
http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem
And all |
52,439 | Are these equivalent representations of the same hierarchical Bayesian model? | Updated Response: You still don't have a full specification for model #2. However, I can sort of guess what you mean -- correct me if I'm wrong. The trouble is that the statements $Y = \beta_1 X$ & $Y = \beta_0 + \beta_1 X$ are not probabilistic.
[ Aside: In a mathematical sense, you're defining a set of linear equ... | Are these equivalent representations of the same hierarchical Bayesian model? | Updated Response: You still don't have a full specification for model #2. However, I can sort of guess what you mean -- correct me if I'm wrong. The trouble is that the statements $Y = \beta_1 X$ & | Are these equivalent representations of the same hierarchical Bayesian model?
Updated Response: You still don't have a full specification for model #2. However, I can sort of guess what you mean -- correct me if I'm wrong. The trouble is that the statements $Y = \beta_1 X$ & $Y = \beta_0 + \beta_1 X$ are not probabil... | Are these equivalent representations of the same hierarchical Bayesian model?
Updated Response: You still don't have a full specification for model #2. However, I can sort of guess what you mean -- correct me if I'm wrong. The trouble is that the statements $Y = \beta_1 X$ & |
52,440 | Are these equivalent representations of the same hierarchical Bayesian model? | The only similarity in the two models is the general type of models they belong to, otherwise they are not similar in general as pointed out by M. Tibbits.
Both these models belong the class of hierarchical models with varying slope (cf Gelman and Hill 2006 for detailed treatment)
The answer for "why not" are many and ... | Are these equivalent representations of the same hierarchical Bayesian model? | The only similarity in the two models is the general type of models they belong to, otherwise they are not similar in general as pointed out by M. Tibbits.
Both these models belong the class of hierar | Are these equivalent representations of the same hierarchical Bayesian model?
The only similarity in the two models is the general type of models they belong to, otherwise they are not similar in general as pointed out by M. Tibbits.
Both these models belong the class of hierarchical models with varying slope (cf Gelma... | Are these equivalent representations of the same hierarchical Bayesian model?
The only similarity in the two models is the general type of models they belong to, otherwise they are not similar in general as pointed out by M. Tibbits.
Both these models belong the class of hierar |
52,441 | Are these equivalent representations of the same hierarchical Bayesian model? | You already have good answers and have accepted one, but I'm not sure anyone's put it plainly enough for even me to intuit. At the core, your two models are:
[1] $Y=\beta_0 + \beta_1X_1 + \epsilon$
[2] $Y=(\beta_0 + \beta_1)X_1 + \epsilon$ = $\beta_0X_1 + \beta_1X_1 + \epsilon$
Yes, the $\beta$'s (and $\epsilon$) have ... | Are these equivalent representations of the same hierarchical Bayesian model? | You already have good answers and have accepted one, but I'm not sure anyone's put it plainly enough for even me to intuit. At the core, your two models are:
[1] $Y=\beta_0 + \beta_1X_1 + \epsilon$
[2 | Are these equivalent representations of the same hierarchical Bayesian model?
You already have good answers and have accepted one, but I'm not sure anyone's put it plainly enough for even me to intuit. At the core, your two models are:
[1] $Y=\beta_0 + \beta_1X_1 + \epsilon$
[2] $Y=(\beta_0 + \beta_1)X_1 + \epsilon$ = ... | Are these equivalent representations of the same hierarchical Bayesian model?
You already have good answers and have accepted one, but I'm not sure anyone's put it plainly enough for even me to intuit. At the core, your two models are:
[1] $Y=\beta_0 + \beta_1X_1 + \epsilon$
[2 |
52,442 | Are these equivalent representations of the same hierarchical Bayesian model? | If $x_1=0$, then $Y$~$(\beta_0,\sigma^2)$ in model 1 and $Y$~$(0,\sigma^2)$ in model 2.
If $x_1=1$, then $Y$~$(\beta_0+\beta_1,\sigma^2)$ in model 1 and $Y$~$(\beta_1,\sigma^2)$ in model 2.
Look for example at the first line: is $\beta_0$ a random variable or is a zero constant? | Are these equivalent representations of the same hierarchical Bayesian model? | If $x_1=0$, then $Y$~$(\beta_0,\sigma^2)$ in model 1 and $Y$~$(0,\sigma^2)$ in model 2.
If $x_1=1$, then $Y$~$(\beta_0+\beta_1,\sigma^2)$ in model 1 and $Y$~$(\beta_1,\sigma^2)$ in model 2.
Look for e | Are these equivalent representations of the same hierarchical Bayesian model?
If $x_1=0$, then $Y$~$(\beta_0,\sigma^2)$ in model 1 and $Y$~$(0,\sigma^2)$ in model 2.
If $x_1=1$, then $Y$~$(\beta_0+\beta_1,\sigma^2)$ in model 1 and $Y$~$(\beta_1,\sigma^2)$ in model 2.
Look for example at the first line: is $\beta_0$ a r... | Are these equivalent representations of the same hierarchical Bayesian model?
If $x_1=0$, then $Y$~$(\beta_0,\sigma^2)$ in model 1 and $Y$~$(0,\sigma^2)$ in model 2.
If $x_1=1$, then $Y$~$(\beta_0+\beta_1,\sigma^2)$ in model 1 and $Y$~$(\beta_1,\sigma^2)$ in model 2.
Look for e |
52,443 | Is there an analytical expression for the distribution of the max of a normal k sample? | Properly normalized, it's closely approximated by a Gumbel distribution as shown by Extreme value theory. Alternative names are provided in the links. | Is there an analytical expression for the distribution of the max of a normal k sample? | Properly normalized, it's closely approximated by a Gumbel distribution as shown by Extreme value theory. Alternative names are provided in the links. | Is there an analytical expression for the distribution of the max of a normal k sample?
Properly normalized, it's closely approximated by a Gumbel distribution as shown by Extreme value theory. Alternative names are provided in the links. | Is there an analytical expression for the distribution of the max of a normal k sample?
Properly normalized, it's closely approximated by a Gumbel distribution as shown by Extreme value theory. Alternative names are provided in the links. |
52,444 | Is there an analytical expression for the distribution of the max of a normal k sample? | You will find exact expressions for the full pdf of the $n^{th}$ order statistics (as a function of $n$, the sample size) in the following paper:
Percentage Points and Modes of Order Statistics from the Normal Distribution
Shanti S. Gupta
Source: Ann. Math. Statist. Volume 32, Number 3 (1961), 888-893.
Also includes e... | Is there an analytical expression for the distribution of the max of a normal k sample? | You will find exact expressions for the full pdf of the $n^{th}$ order statistics (as a function of $n$, the sample size) in the following paper:
Percentage Points and Modes of Order Statistics from | Is there an analytical expression for the distribution of the max of a normal k sample?
You will find exact expressions for the full pdf of the $n^{th}$ order statistics (as a function of $n$, the sample size) in the following paper:
Percentage Points and Modes of Order Statistics from the Normal Distribution
Shanti S... | Is there an analytical expression for the distribution of the max of a normal k sample?
You will find exact expressions for the full pdf of the $n^{th}$ order statistics (as a function of $n$, the sample size) in the following paper:
Percentage Points and Modes of Order Statistics from |
52,445 | Classification after factor analysis | One solution to your 1. question is to use cross-validation. You compute classification accuracy for models with different number of components and then pick one with the highest classification accuracy. You can check the references below:
PLS Dimension Reduction for Classification with Microarray Data
Rasch-based high... | Classification after factor analysis | One solution to your 1. question is to use cross-validation. You compute classification accuracy for models with different number of components and then pick one with the highest classification accura | Classification after factor analysis
One solution to your 1. question is to use cross-validation. You compute classification accuracy for models with different number of components and then pick one with the highest classification accuracy. You can check the references below:
PLS Dimension Reduction for Classification ... | Classification after factor analysis
One solution to your 1. question is to use cross-validation. You compute classification accuracy for models with different number of components and then pick one with the highest classification accura |
52,446 | Classification after factor analysis | Caution: I'm assuming that when you said "classification", you are rather referring to cluster analysis (as understood in French), that is an unsupervised method for allocating individuals in homogeneous groups without any prior information/label. It's not obvious to me how class membership might come into play in your... | Classification after factor analysis | Caution: I'm assuming that when you said "classification", you are rather referring to cluster analysis (as understood in French), that is an unsupervised method for allocating individuals in homogene | Classification after factor analysis
Caution: I'm assuming that when you said "classification", you are rather referring to cluster analysis (as understood in French), that is an unsupervised method for allocating individuals in homogeneous groups without any prior information/label. It's not obvious to me how class me... | Classification after factor analysis
Caution: I'm assuming that when you said "classification", you are rather referring to cluster analysis (as understood in French), that is an unsupervised method for allocating individuals in homogene |
52,447 | Classification after factor analysis | One approach that side-steps cross-validation to determine the optimal number of factors is to use the nonparametric Bayesian approaches for factor analysis. These approaches let the number of factors to be unbounded and eventually decided by the data. See this paper that uses such an approach for classification based ... | Classification after factor analysis | One approach that side-steps cross-validation to determine the optimal number of factors is to use the nonparametric Bayesian approaches for factor analysis. These approaches let the number of factors | Classification after factor analysis
One approach that side-steps cross-validation to determine the optimal number of factors is to use the nonparametric Bayesian approaches for factor analysis. These approaches let the number of factors to be unbounded and eventually decided by the data. See this paper that uses such ... | Classification after factor analysis
One approach that side-steps cross-validation to determine the optimal number of factors is to use the nonparametric Bayesian approaches for factor analysis. These approaches let the number of factors |
52,448 | What is numerical overflow? | It means that the algorithm generated a variable that is greater than the maximum allowed for that type of variable. That is due to the fact that computers use a finite number of bits to represent numbers, so it is not possible to represent ANY number, but only a limited subset of them.
The actual value depends on the ... | What is numerical overflow? | It means that the algorithm generated a variable that is greater than the maximum allowed for that type of variable. That is due to the fact that computers use a finite number of bits to represent num | What is numerical overflow?
It means that the algorithm generated a variable that is greater than the maximum allowed for that type of variable. That is due to the fact that computers use a finite number of bits to represent numbers, so it is not possible to represent ANY number, but only a limited subset of them.
The ... | What is numerical overflow?
It means that the algorithm generated a variable that is greater than the maximum allowed for that type of variable. That is due to the fact that computers use a finite number of bits to represent num |
52,449 | What is numerical overflow? | You can probably avoid your overflow problems by working with the log of the likelihood function rather than the likelihood function itself. Both have the same maximum. | What is numerical overflow? | You can probably avoid your overflow problems by working with the log of the likelihood function rather than the likelihood function itself. Both have the same maximum. | What is numerical overflow?
You can probably avoid your overflow problems by working with the log of the likelihood function rather than the likelihood function itself. Both have the same maximum. | What is numerical overflow?
You can probably avoid your overflow problems by working with the log of the likelihood function rather than the likelihood function itself. Both have the same maximum. |
52,450 | What is numerical overflow? | As stated by nico, numerical overflow is when computation finds a number that is too great for the limited number of bits allocated by software to store the number. For example, if your software uses 32 bits to store integers, then computing an integer that is greater than 2,147,483,648 (or smaller than -2,147,483,648)... | What is numerical overflow? | As stated by nico, numerical overflow is when computation finds a number that is too great for the limited number of bits allocated by software to store the number. For example, if your software uses | What is numerical overflow?
As stated by nico, numerical overflow is when computation finds a number that is too great for the limited number of bits allocated by software to store the number. For example, if your software uses 32 bits to store integers, then computing an integer that is greater than 2,147,483,648 (or ... | What is numerical overflow?
As stated by nico, numerical overflow is when computation finds a number that is too great for the limited number of bits allocated by software to store the number. For example, if your software uses |
52,451 | Basic question regarding variance and stdev of a sample | The second question seems to ask for a prediction interval for one future observation. Such an interval is readily calculated under the assumptions that (a) the future observation is from the same distribution and (b) is independent of the previous sample. When the underlying distribution is Normal, we just have to e... | Basic question regarding variance and stdev of a sample | The second question seems to ask for a prediction interval for one future observation. Such an interval is readily calculated under the assumptions that (a) the future observation is from the same di | Basic question regarding variance and stdev of a sample
The second question seems to ask for a prediction interval for one future observation. Such an interval is readily calculated under the assumptions that (a) the future observation is from the same distribution and (b) is independent of the previous sample. When ... | Basic question regarding variance and stdev of a sample
The second question seems to ask for a prediction interval for one future observation. Such an interval is readily calculated under the assumptions that (a) the future observation is from the same di |
52,452 | Basic question regarding variance and stdev of a sample | I'm finding it rather tricky to see what you are asking:
If you want to know whether the Var(S) is different from the population variance, then see this previous answer.
If you want to determine whether the mean(S) and the mean(X) are the same, then look at Independent two-sample t-tests.
If you want to test whether m... | Basic question regarding variance and stdev of a sample | I'm finding it rather tricky to see what you are asking:
If you want to know whether the Var(S) is different from the population variance, then see this previous answer.
If you want to determine whet | Basic question regarding variance and stdev of a sample
I'm finding it rather tricky to see what you are asking:
If you want to know whether the Var(S) is different from the population variance, then see this previous answer.
If you want to determine whether the mean(S) and the mean(X) are the same, then look at Indep... | Basic question regarding variance and stdev of a sample
I'm finding it rather tricky to see what you are asking:
If you want to know whether the Var(S) is different from the population variance, then see this previous answer.
If you want to determine whet |
52,453 | Basic question regarding variance and stdev of a sample | My first answer was full of errors. Here is a corrected version:
The correct way to test is as follows:
z = (mean(S) - mu) / (stdev(S) / sqrt(n) )
See: Student's t-test
Note the following:
The sample size is accounted for when you divide the standard deviation by the square root of the sample size.
You should also not... | Basic question regarding variance and stdev of a sample | My first answer was full of errors. Here is a corrected version:
The correct way to test is as follows:
z = (mean(S) - mu) / (stdev(S) / sqrt(n) )
See: Student's t-test
Note the following:
The sample | Basic question regarding variance and stdev of a sample
My first answer was full of errors. Here is a corrected version:
The correct way to test is as follows:
z = (mean(S) - mu) / (stdev(S) / sqrt(n) )
See: Student's t-test
Note the following:
The sample size is accounted for when you divide the standard deviation by... | Basic question regarding variance and stdev of a sample
My first answer was full of errors. Here is a corrected version:
The correct way to test is as follows:
z = (mean(S) - mu) / (stdev(S) / sqrt(n) )
See: Student's t-test
Note the following:
The sample |
52,454 | Basic question regarding variance and stdev of a sample | I think you need to nail down the question you are asking, before you can compute an answer. I think this question is way too vague to answer: "test whether it is an vis-a-vis the general population".
The only question I think you can answer is this one: If the new value came from the same population as the others, wh... | Basic question regarding variance and stdev of a sample | I think you need to nail down the question you are asking, before you can compute an answer. I think this question is way too vague to answer: "test whether it is an vis-a-vis the general population". | Basic question regarding variance and stdev of a sample
I think you need to nail down the question you are asking, before you can compute an answer. I think this question is way too vague to answer: "test whether it is an vis-a-vis the general population".
The only question I think you can answer is this one: If the n... | Basic question regarding variance and stdev of a sample
I think you need to nail down the question you are asking, before you can compute an answer. I think this question is way too vague to answer: "test whether it is an vis-a-vis the general population". |
52,455 | Basic question regarding variance and stdev of a sample | 1) The standard deviation of the sample (stdev(S)) is an unbiased estimate of the standard deviation of the population.
2) Given we have estimated both the population mean and variance we need to take this into account when we evaluate whether a new observation x is a member of this population.
We don't use Z = (x - me... | Basic question regarding variance and stdev of a sample | 1) The standard deviation of the sample (stdev(S)) is an unbiased estimate of the standard deviation of the population.
2) Given we have estimated both the population mean and variance we need to take | Basic question regarding variance and stdev of a sample
1) The standard deviation of the sample (stdev(S)) is an unbiased estimate of the standard deviation of the population.
2) Given we have estimated both the population mean and variance we need to take this into account when we evaluate whether a new observation x ... | Basic question regarding variance and stdev of a sample
1) The standard deviation of the sample (stdev(S)) is an unbiased estimate of the standard deviation of the population.
2) Given we have estimated both the population mean and variance we need to take |
52,456 | Basic question regarding variance and stdev of a sample | "how is stdev(S) related to the standard deviation of the entire population?"
I don't know if the "Confidence Interval" concept might be what you are looking for?
Stdev(S) is an Estimate of the standard deviation of the entire population. To see how good an estimate, confidence intervals could be computed, and these w... | Basic question regarding variance and stdev of a sample | "how is stdev(S) related to the standard deviation of the entire population?"
I don't know if the "Confidence Interval" concept might be what you are looking for?
Stdev(S) is an Estimate of the stand | Basic question regarding variance and stdev of a sample
"how is stdev(S) related to the standard deviation of the entire population?"
I don't know if the "Confidence Interval" concept might be what you are looking for?
Stdev(S) is an Estimate of the standard deviation of the entire population. To see how good an estim... | Basic question regarding variance and stdev of a sample
"how is stdev(S) related to the standard deviation of the entire population?"
I don't know if the "Confidence Interval" concept might be what you are looking for?
Stdev(S) is an Estimate of the stand |
52,457 | Is density estimation the same as parameter estimation? | I understand this argument and can buy it as being technically true. However, the goal of language is to communicate ideas, and statistics has decided that “density estimation”, for better or for worse, refers to doing density estimation with minimal assumptions about the density as to keep from being restricted to a p... | Is density estimation the same as parameter estimation? | I understand this argument and can buy it as being technically true. However, the goal of language is to communicate ideas, and statistics has decided that “density estimation”, for better or for wors | Is density estimation the same as parameter estimation?
I understand this argument and can buy it as being technically true. However, the goal of language is to communicate ideas, and statistics has decided that “density estimation”, for better or for worse, refers to doing density estimation with minimal assumptions a... | Is density estimation the same as parameter estimation?
I understand this argument and can buy it as being technically true. However, the goal of language is to communicate ideas, and statistics has decided that “density estimation”, for better or for wors |
52,458 | Is density estimation the same as parameter estimation? | No, it's not the same. Density estimation is about estimating the distribution of the data. This can be achieved with a parametric model, for example, fitting a Gaussian mixture to the data. In such a case, to find the distribution means to estimate its parameters since the distribution is defined by its parameters. Bu... | Is density estimation the same as parameter estimation? | No, it's not the same. Density estimation is about estimating the distribution of the data. This can be achieved with a parametric model, for example, fitting a Gaussian mixture to the data. In such a | Is density estimation the same as parameter estimation?
No, it's not the same. Density estimation is about estimating the distribution of the data. This can be achieved with a parametric model, for example, fitting a Gaussian mixture to the data. In such a case, to find the distribution means to estimate its parameters... | Is density estimation the same as parameter estimation?
No, it's not the same. Density estimation is about estimating the distribution of the data. This can be achieved with a parametric model, for example, fitting a Gaussian mixture to the data. In such a |
52,459 | Help with a proof regarding empirical CDF | Define $$Y_i(x)=\mathbb I_{\{X_i\leq x\}}$$ $\forall i\in\{1, 2,\ldots, n\}.$
Notice $$Y_i(x) \overset{\text{iid}}{\sim}\mathcal{Ber}(\theta)\tag 1\label 1$$ where $\theta := F(x) . $
Now express (how?) $$n \hat F_n(x) =\sum_{i=1}^n Y_i(x) ;\tag 2$$
Use $\eqref 1$ above to yield $\operatorname{Var}(F_n(x)). $ | Help with a proof regarding empirical CDF | Define $$Y_i(x)=\mathbb I_{\{X_i\leq x\}}$$ $\forall i\in\{1, 2,\ldots, n\}.$
Notice $$Y_i(x) \overset{\text{iid}}{\sim}\mathcal{Ber}(\theta)\tag 1\label 1$$ where $\theta := F(x) . $
Now express (how | Help with a proof regarding empirical CDF
Define $$Y_i(x)=\mathbb I_{\{X_i\leq x\}}$$ $\forall i\in\{1, 2,\ldots, n\}.$
Notice $$Y_i(x) \overset{\text{iid}}{\sim}\mathcal{Ber}(\theta)\tag 1\label 1$$ where $\theta := F(x) . $
Now express (how?) $$n \hat F_n(x) =\sum_{i=1}^n Y_i(x) ;\tag 2$$
Use $\eqref 1$ above to yiel... | Help with a proof regarding empirical CDF
Define $$Y_i(x)=\mathbb I_{\{X_i\leq x\}}$$ $\forall i\in\{1, 2,\ldots, n\}.$
Notice $$Y_i(x) \overset{\text{iid}}{\sim}\mathcal{Ber}(\theta)\tag 1\label 1$$ where $\theta := F(x) . $
Now express (how |
52,460 | Help with a proof regarding empirical CDF | Note that you can write $\mathop{\hat{F}_n}\left(x\right)$ as $\mathop{\hat{F}_n}\left(x\right) = \mathop{R_n}\left(x\right)/n$, where $\mathop{R_n}\left(x\right) \sim \mathop{\text{Binomial}}\left(n, \mathop{F}\left(x\right)\right)$.
Proof.
$\mathop{R_n}\left(x\right) \mathrel{:=}\sum_{i=1}^n \mathop{\mathbf{1}_{\lef... | Help with a proof regarding empirical CDF | Note that you can write $\mathop{\hat{F}_n}\left(x\right)$ as $\mathop{\hat{F}_n}\left(x\right) = \mathop{R_n}\left(x\right)/n$, where $\mathop{R_n}\left(x\right) \sim \mathop{\text{Binomial}}\left(n, | Help with a proof regarding empirical CDF
Note that you can write $\mathop{\hat{F}_n}\left(x\right)$ as $\mathop{\hat{F}_n}\left(x\right) = \mathop{R_n}\left(x\right)/n$, where $\mathop{R_n}\left(x\right) \sim \mathop{\text{Binomial}}\left(n, \mathop{F}\left(x\right)\right)$.
Proof.
$\mathop{R_n}\left(x\right) \mathre... | Help with a proof regarding empirical CDF
Note that you can write $\mathop{\hat{F}_n}\left(x\right)$ as $\mathop{\hat{F}_n}\left(x\right) = \mathop{R_n}\left(x\right)/n$, where $\mathop{R_n}\left(x\right) \sim \mathop{\text{Binomial}}\left(n, |
52,461 | Asymptotics of MLE without closed form solutions | I'm not sure what you mean by "asymptotics for $\hat\theta_n$", but if you are asking about the limiting distribution of the MLE, then the short answer is that a properly standardized version of $\hat\theta_n$ converges to the standard normal distribution.
More precisely, in a multidimensional parameter case with $\the... | Asymptotics of MLE without closed form solutions | I'm not sure what you mean by "asymptotics for $\hat\theta_n$", but if you are asking about the limiting distribution of the MLE, then the short answer is that a properly standardized version of $\hat | Asymptotics of MLE without closed form solutions
I'm not sure what you mean by "asymptotics for $\hat\theta_n$", but if you are asking about the limiting distribution of the MLE, then the short answer is that a properly standardized version of $\hat\theta_n$ converges to the standard normal distribution.
More precisely... | Asymptotics of MLE without closed form solutions
I'm not sure what you mean by "asymptotics for $\hat\theta_n$", but if you are asking about the limiting distribution of the MLE, then the short answer is that a properly standardized version of $\hat |
52,462 | Asymptotics of MLE without closed form solutions | You can use the fact the MLE is asymptotically unbiased, efficient (i.e. its variance converges to the inverse of the Fisher information), and Gaussian.
In summary, $\hat\theta \rightarrow \mathcal{N}(\theta,\mathcal{I}^{-1}(\theta))$ as the sample size, $n$, goes to infinity.
You can then approximate $\mathcal{I}(\the... | Asymptotics of MLE without closed form solutions | You can use the fact the MLE is asymptotically unbiased, efficient (i.e. its variance converges to the inverse of the Fisher information), and Gaussian.
In summary, $\hat\theta \rightarrow \mathcal{N} | Asymptotics of MLE without closed form solutions
You can use the fact the MLE is asymptotically unbiased, efficient (i.e. its variance converges to the inverse of the Fisher information), and Gaussian.
In summary, $\hat\theta \rightarrow \mathcal{N}(\theta,\mathcal{I}^{-1}(\theta))$ as the sample size, $n$, goes to inf... | Asymptotics of MLE without closed form solutions
You can use the fact the MLE is asymptotically unbiased, efficient (i.e. its variance converges to the inverse of the Fisher information), and Gaussian.
In summary, $\hat\theta \rightarrow \mathcal{N} |
52,463 | Help needed regarding sample size for a poll | You can calculate so called simultaneous confidence intervals for multinomial proportions, and see if they are too wide for your purposes.
In R, it can be done like this (data contains the numbers of the respondents from the 6 categories you mentioned):
if(!require(DescTools)){
install.packages("DescTools")
lib... | Help needed regarding sample size for a poll | You can calculate so called simultaneous confidence intervals for multinomial proportions, and see if they are too wide for your purposes.
In R, it can be done like this (data contains the numbers of | Help needed regarding sample size for a poll
You can calculate so called simultaneous confidence intervals for multinomial proportions, and see if they are too wide for your purposes.
In R, it can be done like this (data contains the numbers of the respondents from the 6 categories you mentioned):
if(!require(DescTools... | Help needed regarding sample size for a poll
You can calculate so called simultaneous confidence intervals for multinomial proportions, and see if they are too wide for your purposes.
In R, it can be done like this (data contains the numbers of |
52,464 | Help needed regarding sample size for a poll | The simplest quick and dirty answer is to quote everything as $\pm 1/\sqrt{N}$, which in this case is 4.5%. This is the same approach used in news media about public opinion polling, in which the standard "plus or minus three percent" means they asked about 1000 people (since $1/\sqrt{1000}\approx 0.0316$). The justi... | Help needed regarding sample size for a poll | The simplest quick and dirty answer is to quote everything as $\pm 1/\sqrt{N}$, which in this case is 4.5%. This is the same approach used in news media about public opinion polling, in which the sta | Help needed regarding sample size for a poll
The simplest quick and dirty answer is to quote everything as $\pm 1/\sqrt{N}$, which in this case is 4.5%. This is the same approach used in news media about public opinion polling, in which the standard "plus or minus three percent" means they asked about 1000 people (sin... | Help needed regarding sample size for a poll
The simplest quick and dirty answer is to quote everything as $\pm 1/\sqrt{N}$, which in this case is 4.5%. This is the same approach used in news media about public opinion polling, in which the sta |
52,465 | Help needed regarding sample size for a poll | As the population of interest is of size $\approx 1000$ and your sample half of that population, I do not think that a binomial approximation is warranted here. Instead I would argue for modelling your data using a Hypergeometric (e.g. reason A vs. all others, and cycle through the reasons) or Multivariate hypergeometr... | Help needed regarding sample size for a poll | As the population of interest is of size $\approx 1000$ and your sample half of that population, I do not think that a binomial approximation is warranted here. Instead I would argue for modelling you | Help needed regarding sample size for a poll
As the population of interest is of size $\approx 1000$ and your sample half of that population, I do not think that a binomial approximation is warranted here. Instead I would argue for modelling your data using a Hypergeometric (e.g. reason A vs. all others, and cycle thro... | Help needed regarding sample size for a poll
As the population of interest is of size $\approx 1000$ and your sample half of that population, I do not think that a binomial approximation is warranted here. Instead I would argue for modelling you |
52,466 | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution | A quick and--usually--easy way to verify an estimator is to apply it to simulated data. I will describe this approach in a way that generalizes to any estimator in any situation.
Begin by coding your estimator. Here is an R implementation. Its input is a sample in an array x. It outputs the estimated parameter $\ha... | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution | A quick and--usually--easy way to verify an estimator is to apply it to simulated data. I will describe this approach in a way that generalizes to any estimator in any situation.
Begin by coding your | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution
A quick and--usually--easy way to verify an estimator is to apply it to simulated data. I will describe this approach in a way that generalizes to any estimator in any situation.
Begin by coding your estimator. Here is an R implementation. ... | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution
A quick and--usually--easy way to verify an estimator is to apply it to simulated data. I will describe this approach in a way that generalizes to any estimator in any situation.
Begin by coding your |
52,467 | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution | As a sanity check, you can think of this as an iid sample from a shifted Bernoulli distribution with parameter $q=p^2/(1-(1-p)^2)$. This gives you the MLE of $q$. You can then in turn use functional equivalence of MLEs to obtain the MLE of $p$. | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution | As a sanity check, you can think of this as an iid sample from a shifted Bernoulli distribution with parameter $q=p^2/(1-(1-p)^2)$. This gives you the MLE of $q$. You can then in turn use functional | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution
As a sanity check, you can think of this as an iid sample from a shifted Bernoulli distribution with parameter $q=p^2/(1-(1-p)^2)$. This gives you the MLE of $q$. You can then in turn use functional equivalence of MLEs to obtain the MLE of ... | Maximum likelihood estimator of $p$ for the binomial (truncated) distribution
As a sanity check, you can think of this as an iid sample from a shifted Bernoulli distribution with parameter $q=p^2/(1-(1-p)^2)$. This gives you the MLE of $q$. You can then in turn use functional |
52,468 | Taylor expansion in Hoeffding's Lemma proof | This is the mean-value form of Taylor's theorem:
$$f(x)=f(0)+xf'(0)+\frac{x^2}{2}f''(c)$$
where $c$ is between $0$ and $x$
Take $x=h$ and $c=h\theta$ | Taylor expansion in Hoeffding's Lemma proof | This is the mean-value form of Taylor's theorem:
$$f(x)=f(0)+xf'(0)+\frac{x^2}{2}f''(c)$$
where $c$ is between $0$ and $x$
Take $x=h$ and $c=h\theta$ | Taylor expansion in Hoeffding's Lemma proof
This is the mean-value form of Taylor's theorem:
$$f(x)=f(0)+xf'(0)+\frac{x^2}{2}f''(c)$$
where $c$ is between $0$ and $x$
Take $x=h$ and $c=h\theta$ | Taylor expansion in Hoeffding's Lemma proof
This is the mean-value form of Taylor's theorem:
$$f(x)=f(0)+xf'(0)+\frac{x^2}{2}f''(c)$$
where $c$ is between $0$ and $x$
Take $x=h$ and $c=h\theta$ |
52,469 | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed | Writing
$$ab - cd = \left(\left[\left(\frac{a+b}{\sqrt 2}\right)^2 + \left(\frac{c+d}{\sqrt 2}\right)^2 \right] - \left[\left(\frac{a-b}{\sqrt 2}\right)^2 + \left(\frac{c-d}{\sqrt 2}\right)^2 \right]\right)/2$$
and noting that $(a+b, c+d, a-b, c-d)/\sqrt{2}$ has a standard Normal distribution, it is immediate (from th... | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed | Writing
$$ab - cd = \left(\left[\left(\frac{a+b}{\sqrt 2}\right)^2 + \left(\frac{c+d}{\sqrt 2}\right)^2 \right] - \left[\left(\frac{a-b}{\sqrt 2}\right)^2 + \left(\frac{c-d}{\sqrt 2}\right)^2 \right] | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed
Writing
$$ab - cd = \left(\left[\left(\frac{a+b}{\sqrt 2}\right)^2 + \left(\frac{c+d}{\sqrt 2}\right)^2 \right] - \left[\left(\frac{a-b}{\sqrt 2}\right)^2 + \left(\frac{c-d}{\sqrt 2}\right)^2 \right]\right)/2$$
and noting that $(a+b,... | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed
Writing
$$ab - cd = \left(\left[\left(\frac{a+b}{\sqrt 2}\right)^2 + \left(\frac{c+d}{\sqrt 2}\right)^2 \right] - \left[\left(\frac{a-b}{\sqrt 2}\right)^2 + \left(\frac{c-d}{\sqrt 2}\right)^2 \right] |
52,470 | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed | There is an extensive theory on the properties of random matrices, including the distribution of their determinants.
From the answer here for example you can see that if you form the matrix $W=AA^T$, where the elements of $A$ are your $\mathcal N (0,1)$ random variables, then
$$ \det W \sim \chi^2_2 \chi^2_1 $$
namely ... | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed | There is an extensive theory on the properties of random matrices, including the distribution of their determinants.
From the answer here for example you can see that if you form the matrix $W=AA^T$, | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed
There is an extensive theory on the properties of random matrices, including the distribution of their determinants.
From the answer here for example you can see that if you form the matrix $W=AA^T$, where the elements of $A$ are your... | Unexpected distribution of ab-cd where a,b,c,d are independent and N(0,1) distributed
There is an extensive theory on the properties of random matrices, including the distribution of their determinants.
From the answer here for example you can see that if you form the matrix $W=AA^T$, |
52,471 | Motivating use of Bayesian splines in excess mortality estimation | The death rate can't be negative (the pandemic was bad but it wasn't zombie apocalypse bad), so a natural way to enforce that is to fit an additive/linear model on the log scale (hence why the model has offset $\log p$ and not simply $p$), and then map back to the interval $[0, \infty]$ via the inverse of the log, the ... | Motivating use of Bayesian splines in excess mortality estimation | The death rate can't be negative (the pandemic was bad but it wasn't zombie apocalypse bad), so a natural way to enforce that is to fit an additive/linear model on the log scale (hence why the model h | Motivating use of Bayesian splines in excess mortality estimation
The death rate can't be negative (the pandemic was bad but it wasn't zombie apocalypse bad), so a natural way to enforce that is to fit an additive/linear model on the log scale (hence why the model has offset $\log p$ and not simply $p$), and then map b... | Motivating use of Bayesian splines in excess mortality estimation
The death rate can't be negative (the pandemic was bad but it wasn't zombie apocalypse bad), so a natural way to enforce that is to fit an additive/linear model on the log scale (hence why the model h |
52,472 | Are there any way of removing impact of a certain data from a trained model (about "right to forget") | The keyword you're looking for is machine unlearning; if you search for that on Google scholar you'll find a large number of relevant studies. This is an active active area of research for exactly the reason you described. For CNNs, it seems to me that there is not really great solution yet (but I might be wrong).
For ... | Are there any way of removing impact of a certain data from a trained model (about "right to forget" | The keyword you're looking for is machine unlearning; if you search for that on Google scholar you'll find a large number of relevant studies. This is an active active area of research for exactly the | Are there any way of removing impact of a certain data from a trained model (about "right to forget")
The keyword you're looking for is machine unlearning; if you search for that on Google scholar you'll find a large number of relevant studies. This is an active active area of research for exactly the reason you descri... | Are there any way of removing impact of a certain data from a trained model (about "right to forget"
The keyword you're looking for is machine unlearning; if you search for that on Google scholar you'll find a large number of relevant studies. This is an active active area of research for exactly the |
52,473 | Are there any way of removing impact of a certain data from a trained model (about "right to forget") | It is possible, but amounts to the same effort as retraining the model.
The weights $\theta$ at iteration $t$ (a mini-batch within an epoch) are defined as:
$$\theta_t=\theta_{t-1}-\nabla_{\theta_{t-1}}\mathcal L_{t-1}$$
By recursion, it becomes obvious that:
$$\theta_t=\theta_0-\sum_{i=0}^{t-1}\nabla_{\theta_i}\mathc... | Are there any way of removing impact of a certain data from a trained model (about "right to forget" | It is possible, but amounts to the same effort as retraining the model.
The weights $\theta$ at iteration $t$ (a mini-batch within an epoch) are defined as:
$$\theta_t=\theta_{t-1}-\nabla_{\theta_{t- | Are there any way of removing impact of a certain data from a trained model (about "right to forget")
It is possible, but amounts to the same effort as retraining the model.
The weights $\theta$ at iteration $t$ (a mini-batch within an epoch) are defined as:
$$\theta_t=\theta_{t-1}-\nabla_{\theta_{t-1}}\mathcal L_{t-1... | Are there any way of removing impact of a certain data from a trained model (about "right to forget"
It is possible, but amounts to the same effort as retraining the model.
The weights $\theta$ at iteration $t$ (a mini-batch within an epoch) are defined as:
$$\theta_t=\theta_{t-1}-\nabla_{\theta_{t- |
52,474 | Can dropping an insignificant factor from a model make the model worse? | In this case you are relying on the wrong test to decide that Zone is not significant. Note that the coefficients of the Zone effect are large (>30) with huge standard errors. This happens when the likelihood keeps monotonically increasing as the estimate goes to infinity. In such cases the Wald test that gives you the... | Can dropping an insignificant factor from a model make the model worse? | In this case you are relying on the wrong test to decide that Zone is not significant. Note that the coefficients of the Zone effect are large (>30) with huge standard errors. This happens when the li | Can dropping an insignificant factor from a model make the model worse?
In this case you are relying on the wrong test to decide that Zone is not significant. Note that the coefficients of the Zone effect are large (>30) with huge standard errors. This happens when the likelihood keeps monotonically increasing as the e... | Can dropping an insignificant factor from a model make the model worse?
In this case you are relying on the wrong test to decide that Zone is not significant. Note that the coefficients of the Zone effect are large (>30) with huge standard errors. This happens when the li |
52,475 | Can dropping an insignificant factor from a model make the model worse? | AIC is a function of the number of parameters within your model k and its likelihood L. Formally, AIC = 2k - 2 ln(L). Since a smaller AIC is better, the term 2k serves as a penalty based on the number of parameters. Thus, AIC represents a trade-off between complexity (k) and fit (L). Imagine two models with similar lik... | Can dropping an insignificant factor from a model make the model worse? | AIC is a function of the number of parameters within your model k and its likelihood L. Formally, AIC = 2k - 2 ln(L). Since a smaller AIC is better, the term 2k serves as a penalty based on the number | Can dropping an insignificant factor from a model make the model worse?
AIC is a function of the number of parameters within your model k and its likelihood L. Formally, AIC = 2k - 2 ln(L). Since a smaller AIC is better, the term 2k serves as a penalty based on the number of parameters. Thus, AIC represents a trade-off... | Can dropping an insignificant factor from a model make the model worse?
AIC is a function of the number of parameters within your model k and its likelihood L. Formally, AIC = 2k - 2 ln(L). Since a smaller AIC is better, the term 2k serves as a penalty based on the number |
52,476 | Bootstrap optimism corrected - results interpretation | OK, so I've identified a few problems with your approach in the comments. The key thing to remember here is that "the model" is really a process and not a single thing. Anything you do in the process of creating the model is technically part of "the model" and so it needs to be validated. For example, you mention us... | Bootstrap optimism corrected - results interpretation | OK, so I've identified a few problems with your approach in the comments. The key thing to remember here is that "the model" is really a process and not a single thing. Anything you do in the proces | Bootstrap optimism corrected - results interpretation
OK, so I've identified a few problems with your approach in the comments. The key thing to remember here is that "the model" is really a process and not a single thing. Anything you do in the process of creating the model is technically part of "the model" and so ... | Bootstrap optimism corrected - results interpretation
OK, so I've identified a few problems with your approach in the comments. The key thing to remember here is that "the model" is really a process and not a single thing. Anything you do in the proces |
52,477 | How can I know If LASSO logistic regression model is good enough to be feature selection tool? | Many analysts automatically assume that feature selection is a good idea. This never followed. Parsimony is the enemy of predictive discrimination. Perhaps more important, feature selection, whether using lasso or other methods, is unreliable. The way to tell if lasso is good enough is to test its resilience/stabil... | How can I know If LASSO logistic regression model is good enough to be feature selection tool? | Many analysts automatically assume that feature selection is a good idea. This never followed. Parsimony is the enemy of predictive discrimination. Perhaps more important, feature selection, whethe | How can I know If LASSO logistic regression model is good enough to be feature selection tool?
Many analysts automatically assume that feature selection is a good idea. This never followed. Parsimony is the enemy of predictive discrimination. Perhaps more important, feature selection, whether using lasso or other me... | How can I know If LASSO logistic regression model is good enough to be feature selection tool?
Many analysts automatically assume that feature selection is a good idea. This never followed. Parsimony is the enemy of predictive discrimination. Perhaps more important, feature selection, whethe |
52,478 | How can I know If LASSO logistic regression model is good enough to be feature selection tool? | Lasso is a common regression technique for variable selection and regularization. By defining many cross validation folds and playing with different values of $\alpha$, you can find the best set of beta coefficients which confidently predicts your outcome without overfitting or underfitting. If the Lasso technique has ... | How can I know If LASSO logistic regression model is good enough to be feature selection tool? | Lasso is a common regression technique for variable selection and regularization. By defining many cross validation folds and playing with different values of $\alpha$, you can find the best set of be | How can I know If LASSO logistic regression model is good enough to be feature selection tool?
Lasso is a common regression technique for variable selection and regularization. By defining many cross validation folds and playing with different values of $\alpha$, you can find the best set of beta coefficients which con... | How can I know If LASSO logistic regression model is good enough to be feature selection tool?
Lasso is a common regression technique for variable selection and regularization. By defining many cross validation folds and playing with different values of $\alpha$, you can find the best set of be |
52,479 | Variance of a function of a random variable as function of the original variable | Let $X\sim \mathcal N(0,\sigma^2)$ denote a normal random variable and let $f$ be the function $$f(x) = \begin{cases}+1, & x > 0,\\-1, &x \leq 0.\end{cases}$$
Then, $f(X)$ is a random variable taking on values $\pm 1$ with equal probability and so $f(X)$ has variance $1$. On the other hand, if $X\sim \mathcal N(1,\sig... | Variance of a function of a random variable as function of the original variable | Let $X\sim \mathcal N(0,\sigma^2)$ denote a normal random variable and let $f$ be the function $$f(x) = \begin{cases}+1, & x > 0,\\-1, &x \leq 0.\end{cases}$$
Then, $f(X)$ is a random variable taking | Variance of a function of a random variable as function of the original variable
Let $X\sim \mathcal N(0,\sigma^2)$ denote a normal random variable and let $f$ be the function $$f(x) = \begin{cases}+1, & x > 0,\\-1, &x \leq 0.\end{cases}$$
Then, $f(X)$ is a random variable taking on values $\pm 1$ with equal probabilit... | Variance of a function of a random variable as function of the original variable
Let $X\sim \mathcal N(0,\sigma^2)$ denote a normal random variable and let $f$ be the function $$f(x) = \begin{cases}+1, & x > 0,\\-1, &x \leq 0.\end{cases}$$
Then, $f(X)$ is a random variable taking |
52,480 | Variance of a function of a random variable as function of the original variable | The exact formula for the variance of $Y$ requires use of the function $f$ and the full distribution of $X$ (not just its variance). Nevertheless, while there is no exact formula of the kind you want, you can get approximate formulae using Taylor approximation (also called the "delta method").
To facilitate analysis ... | Variance of a function of a random variable as function of the original variable | The exact formula for the variance of $Y$ requires use of the function $f$ and the full distribution of $X$ (not just its variance). Nevertheless, while there is no exact formula of the kind you want | Variance of a function of a random variable as function of the original variable
The exact formula for the variance of $Y$ requires use of the function $f$ and the full distribution of $X$ (not just its variance). Nevertheless, while there is no exact formula of the kind you want, you can get approximate formulae usin... | Variance of a function of a random variable as function of the original variable
The exact formula for the variance of $Y$ requires use of the function $f$ and the full distribution of $X$ (not just its variance). Nevertheless, while there is no exact formula of the kind you want |
52,481 | Variance of a function of a random variable as function of the original variable | Let's see how far we can towards characterizing functions $f$ where such a formula will work. We know it works for linear functions, but are there any others? How about when the random variables $X$ have restricted values?
The setting of the question is one in which $f$ is given but the distribution of the random va... | Variance of a function of a random variable as function of the original variable | Let's see how far we can towards characterizing functions $f$ where such a formula will work. We know it works for linear functions, but are there any others? How about when the random variables $X$ | Variance of a function of a random variable as function of the original variable
Let's see how far we can towards characterizing functions $f$ where such a formula will work. We know it works for linear functions, but are there any others? How about when the random variables $X$ have restricted values?
The setting o... | Variance of a function of a random variable as function of the original variable
Let's see how far we can towards characterizing functions $f$ where such a formula will work. We know it works for linear functions, but are there any others? How about when the random variables $X$ |
52,482 | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large? | Think buying hundreds of fair dice. You do not know they are, though, and hence test if each has an expected value of 3.5 points, via throwing each many times (1000+). One of them must come up as "best", and if you do not account for multiple testing, almost certainly statistically significantly so.
Recall that the pro... | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large? | Think buying hundreds of fair dice. You do not know they are, though, and hence test if each has an expected value of 3.5 points, via throwing each many times (1000+). One of them must come up as "bes | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large?
Think buying hundreds of fair dice. You do not know they are, though, and hence test if each has an expected value of 3.5 points, via throwing each many times (1000+). One of them must come up as "best", and if you do not a... | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large?
Think buying hundreds of fair dice. You do not know they are, though, and hence test if each has an expected value of 3.5 points, via throwing each many times (1000+). One of them must come up as "bes |
52,483 | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large? | A easy way to make sense of this is in terms of effect sizes, Type 1 errors, Type 2 errors, and Power.
Let's say that you're looking at correlations, and you have $N$ data points.
Your effect size is the correlation coefficient, $r$.
Your Type 1 error rate, $\alpha$, is the probability of concluding that there is an e... | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large? | A easy way to make sense of this is in terms of effect sizes, Type 1 errors, Type 2 errors, and Power.
Let's say that you're looking at correlations, and you have $N$ data points.
Your effect size is | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large?
A easy way to make sense of this is in terms of effect sizes, Type 1 errors, Type 2 errors, and Power.
Let's say that you're looking at correlations, and you have $N$ data points.
Your effect size is the correlation coeffi... | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large?
A easy way to make sense of this is in terms of effect sizes, Type 1 errors, Type 2 errors, and Power.
Let's say that you're looking at correlations, and you have $N$ data points.
Your effect size is |
52,484 | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large? | Their suggestion was that we don't have to worry about [multiple testing], because the sample size of each test is going to be big enough (we're looking at minimum of n=100 but frequently n=1000+).
Here's a scenario where your colleagues would be right in practice even if wrong in theory.
Your many tests fall neatly i... | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large? | Their suggestion was that we don't have to worry about [multiple testing], because the sample size of each test is going to be big enough (we're looking at minimum of n=100 but frequently n=1000+).
H | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large?
Their suggestion was that we don't have to worry about [multiple testing], because the sample size of each test is going to be big enough (we're looking at minimum of n=100 but frequently n=1000+).
Here's a scenario where ... | Is it still necessary to correct for multiple comparisons/testing if the sample sizes are large?
Their suggestion was that we don't have to worry about [multiple testing], because the sample size of each test is going to be big enough (we're looking at minimum of n=100 but frequently n=1000+).
H |
52,485 | Likelihood vs quasi-likelihood vs pseudo-likelihood and restricted likelihood | I think you may be conflating likelihood with maximum likelihood methods. I'll try to separate them as best I can below.
Likelihood
The likelihood function is one which relates the probability of an observation with a particular parameterization of a specific distributional family. It is not necessarily the same thing ... | Likelihood vs quasi-likelihood vs pseudo-likelihood and restricted likelihood | I think you may be conflating likelihood with maximum likelihood methods. I'll try to separate them as best I can below.
Likelihood
The likelihood function is one which relates the probability of an o | Likelihood vs quasi-likelihood vs pseudo-likelihood and restricted likelihood
I think you may be conflating likelihood with maximum likelihood methods. I'll try to separate them as best I can below.
Likelihood
The likelihood function is one which relates the probability of an observation with a particular parameterizat... | Likelihood vs quasi-likelihood vs pseudo-likelihood and restricted likelihood
I think you may be conflating likelihood with maximum likelihood methods. I'll try to separate them as best I can below.
Likelihood
The likelihood function is one which relates the probability of an o |
52,486 | Inverse Predictive Posterior | Denoting all the conditioning explicitly (which you should make a habit of doing in Bayesian analysis), your nonlinear regression model is actually specifying:
$$p(y_i | x_i, \theta, \sigma) = \text{N}(y_i | f_\theta(x_i), \sigma^2).$$
Now, if you want to make a Bayesian inference about any of the values in the conditi... | Inverse Predictive Posterior | Denoting all the conditioning explicitly (which you should make a habit of doing in Bayesian analysis), your nonlinear regression model is actually specifying:
$$p(y_i | x_i, \theta, \sigma) = \text{N | Inverse Predictive Posterior
Denoting all the conditioning explicitly (which you should make a habit of doing in Bayesian analysis), your nonlinear regression model is actually specifying:
$$p(y_i | x_i, \theta, \sigma) = \text{N}(y_i | f_\theta(x_i), \sigma^2).$$
Now, if you want to make a Bayesian inference about any... | Inverse Predictive Posterior
Denoting all the conditioning explicitly (which you should make a habit of doing in Bayesian analysis), your nonlinear regression model is actually specifying:
$$p(y_i | x_i, \theta, \sigma) = \text{N |
52,487 | Inverse Predictive Posterior | Ok, I've edited my response taking into account feedback from the OP. Below is a DAG that captures the assumptions provided. So for example, $x^{(\mathrm{new})}$ need not be equal in distribution to $x$ as required, and $y^{(\mathrm{new})}$ is conditionally independent of the training data $\mathbf{Y}$ given $\theta$
... | Inverse Predictive Posterior | Ok, I've edited my response taking into account feedback from the OP. Below is a DAG that captures the assumptions provided. So for example, $x^{(\mathrm{new})}$ need not be equal in distribution to | Inverse Predictive Posterior
Ok, I've edited my response taking into account feedback from the OP. Below is a DAG that captures the assumptions provided. So for example, $x^{(\mathrm{new})}$ need not be equal in distribution to $x$ as required, and $y^{(\mathrm{new})}$ is conditionally independent of the training data... | Inverse Predictive Posterior
Ok, I've edited my response taking into account feedback from the OP. Below is a DAG that captures the assumptions provided. So for example, $x^{(\mathrm{new})}$ need not be equal in distribution to |
52,488 | Inverse Predictive Posterior | I'm going to take a Bayesian approach to this.
As far as I can tell, the existence of the training set is irrelevant for this problem -- it doesn't matter how we obtained the model, we can just take it as given and fixed.
So, the actual inference problem is to obtain posterior distribution for $\vec{x}' = [x_1', x_2' \... | Inverse Predictive Posterior | I'm going to take a Bayesian approach to this.
As far as I can tell, the existence of the training set is irrelevant for this problem -- it doesn't matter how we obtained the model, we can just take i | Inverse Predictive Posterior
I'm going to take a Bayesian approach to this.
As far as I can tell, the existence of the training set is irrelevant for this problem -- it doesn't matter how we obtained the model, we can just take it as given and fixed.
So, the actual inference problem is to obtain posterior distribution ... | Inverse Predictive Posterior
I'm going to take a Bayesian approach to this.
As far as I can tell, the existence of the training set is irrelevant for this problem -- it doesn't matter how we obtained the model, we can just take i |
52,489 | Inverse Predictive Posterior | This is an observation rather than an answer, and if $f_{\theta}$ has some heinous form and/or your sample size is small may not have any practical relevance for your particular problem.
You know the form of $f_{\theta}$, and that must help! In particular all plausible potential values of $X_{new}|y_{new}$ must be cons... | Inverse Predictive Posterior | This is an observation rather than an answer, and if $f_{\theta}$ has some heinous form and/or your sample size is small may not have any practical relevance for your particular problem.
You know the | Inverse Predictive Posterior
This is an observation rather than an answer, and if $f_{\theta}$ has some heinous form and/or your sample size is small may not have any practical relevance for your particular problem.
You know the form of $f_{\theta}$, and that must help! In particular all plausible potential values of $... | Inverse Predictive Posterior
This is an observation rather than an answer, and if $f_{\theta}$ has some heinous form and/or your sample size is small may not have any practical relevance for your particular problem.
You know the |
52,490 | Which approaches exist for optimization in machine learning? | Towards Data Science isn't a reliable website, and the text you've quoted is, unfortunately, nonsense.
For any Optimization problem with respect to Machine Learning, there can be either a numerical approach or an analytical approach. The numerical problems are Deterministic, meaning that they have a closed form soluti... | Which approaches exist for optimization in machine learning? | Towards Data Science isn't a reliable website, and the text you've quoted is, unfortunately, nonsense.
For any Optimization problem with respect to Machine Learning, there can be either a numerical a | Which approaches exist for optimization in machine learning?
Towards Data Science isn't a reliable website, and the text you've quoted is, unfortunately, nonsense.
For any Optimization problem with respect to Machine Learning, there can be either a numerical approach or an analytical approach. The numerical problems a... | Which approaches exist for optimization in machine learning?
Towards Data Science isn't a reliable website, and the text you've quoted is, unfortunately, nonsense.
For any Optimization problem with respect to Machine Learning, there can be either a numerical a |
52,491 | $H_0$ vs $H_1$ in diagnostic testing | The somewhat unsettling truth is that misspecification testing is not suitable for "persuading a skeptic that the model is valid". Generally, as you obviously understand, not rejecting the $H_0$ does not imply that the $H_0$ is true, and this is the case also in misspecification testing. What the test does is something... | $H_0$ vs $H_1$ in diagnostic testing | The somewhat unsettling truth is that misspecification testing is not suitable for "persuading a skeptic that the model is valid". Generally, as you obviously understand, not rejecting the $H_0$ does | $H_0$ vs $H_1$ in diagnostic testing
The somewhat unsettling truth is that misspecification testing is not suitable for "persuading a skeptic that the model is valid". Generally, as you obviously understand, not rejecting the $H_0$ does not imply that the $H_0$ is true, and this is the case also in misspecification tes... | $H_0$ vs $H_1$ in diagnostic testing
The somewhat unsettling truth is that misspecification testing is not suitable for "persuading a skeptic that the model is valid". Generally, as you obviously understand, not rejecting the $H_0$ does |
52,492 | $H_0$ vs $H_1$ in diagnostic testing | I think it is exactly what the two one-sided tests procedure (TOST) does. TOST concedes that there might be some small effect but shows, with some level of confidence, that the effect is below the threshold of causing us to care. Perhaps there is a bit of autocorrelation, but an autocorrelation of $0.01$ might be effec... | $H_0$ vs $H_1$ in diagnostic testing | I think it is exactly what the two one-sided tests procedure (TOST) does. TOST concedes that there might be some small effect but shows, with some level of confidence, that the effect is below the thr | $H_0$ vs $H_1$ in diagnostic testing
I think it is exactly what the two one-sided tests procedure (TOST) does. TOST concedes that there might be some small effect but shows, with some level of confidence, that the effect is below the threshold of causing us to care. Perhaps there is a bit of autocorrelation, but an aut... | $H_0$ vs $H_1$ in diagnostic testing
I think it is exactly what the two one-sided tests procedure (TOST) does. TOST concedes that there might be some small effect but shows, with some level of confidence, that the effect is below the thr |
52,493 | $H_0$ vs $H_1$ in diagnostic testing | This is a great question. If we were to set autocorrelation as the null hypothesis we would have to be very specific about the type and amount. If we reject this hypothesis we have not brought evidence against all types or amounts of autocorrelation, just the one we tested. For this reason we set no autocorrelation ... | $H_0$ vs $H_1$ in diagnostic testing | This is a great question. If we were to set autocorrelation as the null hypothesis we would have to be very specific about the type and amount. If we reject this hypothesis we have not brought evide | $H_0$ vs $H_1$ in diagnostic testing
This is a great question. If we were to set autocorrelation as the null hypothesis we would have to be very specific about the type and amount. If we reject this hypothesis we have not brought evidence against all types or amounts of autocorrelation, just the one we tested. For t... | $H_0$ vs $H_1$ in diagnostic testing
This is a great question. If we were to set autocorrelation as the null hypothesis we would have to be very specific about the type and amount. If we reject this hypothesis we have not brought evide |
52,494 | $H_0$ vs $H_1$ in diagnostic testing | I don't think your premise is accurate regarding model testing. All the diagnostic tests for models that I am familiar with stipulate the model assumption as the null hypothesis and test for a departure from this that would falsify the assumption. Even if we are talking to someone who is a skeptic of the model assump... | $H_0$ vs $H_1$ in diagnostic testing | I don't think your premise is accurate regarding model testing. All the diagnostic tests for models that I am familiar with stipulate the model assumption as the null hypothesis and test for a depart | $H_0$ vs $H_1$ in diagnostic testing
I don't think your premise is accurate regarding model testing. All the diagnostic tests for models that I am familiar with stipulate the model assumption as the null hypothesis and test for a departure from this that would falsify the assumption. Even if we are talking to someone... | $H_0$ vs $H_1$ in diagnostic testing
I don't think your premise is accurate regarding model testing. All the diagnostic tests for models that I am familiar with stipulate the model assumption as the null hypothesis and test for a depart |
52,495 | $H_0$ vs $H_1$ in diagnostic testing | Aa
Hello mr. Hardy
I did read page, but cant comment so i post
Having autocorrelation in residuals for me is good thing (from usage stand point)- it give me "assurance" that info about next error term can be "known" from previous
I mean, many tests were designed to help solving real issues - and it works widely.
I cant... | $H_0$ vs $H_1$ in diagnostic testing | Aa
Hello mr. Hardy
I did read page, but cant comment so i post
Having autocorrelation in residuals for me is good thing (from usage stand point)- it give me "assurance" that info about next error term | $H_0$ vs $H_1$ in diagnostic testing
Aa
Hello mr. Hardy
I did read page, but cant comment so i post
Having autocorrelation in residuals for me is good thing (from usage stand point)- it give me "assurance" that info about next error term can be "known" from previous
I mean, many tests were designed to help solving real... | $H_0$ vs $H_1$ in diagnostic testing
Aa
Hello mr. Hardy
I did read page, but cant comment so i post
Having autocorrelation in residuals for me is good thing (from usage stand point)- it give me "assurance" that info about next error term |
52,496 | Model misfit with DHARMa - What needs/can be done? | Interesting problem! In addition to what Florian has suggested, here are my thoughts:
The mixed effects models you fitted may not be the best for teasing out the effect of person-level predictors (just recently I came upon a reference discussing the challenge with interpreting such effects - I'll see if I can find it... | Model misfit with DHARMa - What needs/can be done? | Interesting problem! In addition to what Florian has suggested, here are my thoughts:
The mixed effects models you fitted may not be the best for teasing out the effect of person-level predictors (j | Model misfit with DHARMa - What needs/can be done?
Interesting problem! In addition to what Florian has suggested, here are my thoughts:
The mixed effects models you fitted may not be the best for teasing out the effect of person-level predictors (just recently I came upon a reference discussing the challenge with in... | Model misfit with DHARMa - What needs/can be done?
Interesting problem! In addition to what Florian has suggested, here are my thoughts:
The mixed effects models you fitted may not be the best for teasing out the effect of person-level predictors (j |
52,497 | Model misfit with DHARMa - What needs/can be done? | I think what's pretty clear is that the chosen distributions don't fit the data very well. I don't find this particular surprising. For example active days gambling per month is not really a count variable, as the month has a strict max (30/31) days, so if you count how many of those days someone gambles, this is more ... | Model misfit with DHARMa - What needs/can be done? | I think what's pretty clear is that the chosen distributions don't fit the data very well. I don't find this particular surprising. For example active days gambling per month is not really a count var | Model misfit with DHARMa - What needs/can be done?
I think what's pretty clear is that the chosen distributions don't fit the data very well. I don't find this particular surprising. For example active days gambling per month is not really a count variable, as the month has a strict max (30/31) days, so if you count ho... | Model misfit with DHARMa - What needs/can be done?
I think what's pretty clear is that the chosen distributions don't fit the data very well. I don't find this particular surprising. For example active days gambling per month is not really a count var |
52,498 | Can we always pull a joint posterior apart? | No, it is not. In order for that to be true, $A$ and $B$ should be conditionally independent given $\theta$. | Can we always pull a joint posterior apart? | No, it is not. In order for that to be true, $A$ and $B$ should be conditionally independent given $\theta$. | Can we always pull a joint posterior apart?
No, it is not. In order for that to be true, $A$ and $B$ should be conditionally independent given $\theta$. | Can we always pull a joint posterior apart?
No, it is not. In order for that to be true, $A$ and $B$ should be conditionally independent given $\theta$. |
52,499 | Why is the variance of a binomial distribution not $n^2p(1-p)$? | The problem with your solution is at this step. $Var(X) = Var(nB)$
Because $X \neq nB$
I mean yes, $X = B_1 + B_2 + ... +B_n$ because all the $B_i$'s are $0$ or $1$, and X is the number of $1$'s in n trails. But you can't call it $nB$ because all $B$'s don't have the same value. Some of them are $0$ and some are $1$.
Y... | Why is the variance of a binomial distribution not $n^2p(1-p)$? | The problem with your solution is at this step. $Var(X) = Var(nB)$
Because $X \neq nB$
I mean yes, $X = B_1 + B_2 + ... +B_n$ because all the $B_i$'s are $0$ or $1$, and X is the number of $1$'s in n | Why is the variance of a binomial distribution not $n^2p(1-p)$?
The problem with your solution is at this step. $Var(X) = Var(nB)$
Because $X \neq nB$
I mean yes, $X = B_1 + B_2 + ... +B_n$ because all the $B_i$'s are $0$ or $1$, and X is the number of $1$'s in n trails. But you can't call it $nB$ because all $B$'s don... | Why is the variance of a binomial distribution not $n^2p(1-p)$?
The problem with your solution is at this step. $Var(X) = Var(nB)$
Because $X \neq nB$
I mean yes, $X = B_1 + B_2 + ... +B_n$ because all the $B_i$'s are $0$ or $1$, and X is the number of $1$'s in n |
52,500 | Why is the variance of a binomial distribution not $n^2p(1-p)$? | It might be worth examining the binomial as a sum of $n$ i.i.d. bernoulli trials. Let $X_i$ be i.i.d. bernoulli draws. $Y = \sum_i X_i$ is then a binomial random variable. The variance of this is
$$ \operatorname{Var}(Y) = \operatorname{Var}(\sum_i X_i) = \sum_i \operatorname{Var}(X_i) $$
Where I have used the prope... | Why is the variance of a binomial distribution not $n^2p(1-p)$? | It might be worth examining the binomial as a sum of $n$ i.i.d. bernoulli trials. Let $X_i$ be i.i.d. bernoulli draws. $Y = \sum_i X_i$ is then a binomial random variable. The variance of this is
$ | Why is the variance of a binomial distribution not $n^2p(1-p)$?
It might be worth examining the binomial as a sum of $n$ i.i.d. bernoulli trials. Let $X_i$ be i.i.d. bernoulli draws. $Y = \sum_i X_i$ is then a binomial random variable. The variance of this is
$$ \operatorname{Var}(Y) = \operatorname{Var}(\sum_i X_i)... | Why is the variance of a binomial distribution not $n^2p(1-p)$?
It might be worth examining the binomial as a sum of $n$ i.i.d. bernoulli trials. Let $X_i$ be i.i.d. bernoulli draws. $Y = \sum_i X_i$ is then a binomial random variable. The variance of this is
$ |
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