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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53,001 | Skewed but bell-shaped still considered as normal distribution for ANOVA? | If the distributions are similar (in particular have the same variance) and the group sizes are identical (balanced design), you probably have no reason to worry. Formally, the normality assumption is violated and it can matter but it is less important than the equality of variance assumption and simulation studies hav... | Skewed but bell-shaped still considered as normal distribution for ANOVA? | If the distributions are similar (in particular have the same variance) and the group sizes are identical (balanced design), you probably have no reason to worry. Formally, the normality assumption is | Skewed but bell-shaped still considered as normal distribution for ANOVA?
If the distributions are similar (in particular have the same variance) and the group sizes are identical (balanced design), you probably have no reason to worry. Formally, the normality assumption is violated and it can matter but it is less imp... | Skewed but bell-shaped still considered as normal distribution for ANOVA?
If the distributions are similar (in particular have the same variance) and the group sizes are identical (balanced design), you probably have no reason to worry. Formally, the normality assumption is |
53,002 | Skewed but bell-shaped still considered as normal distribution for ANOVA? | There is a degree of sensitivity to heavy skewness in ANOVA
Times, in particular, tend to be much more skewed than speeds (inverse-times) and log-time. If your question of interest could be stated in terms of one of those (and they are less skew) then you may not have to rely on an assumption that doesn't hold.
Furth... | Skewed but bell-shaped still considered as normal distribution for ANOVA? | There is a degree of sensitivity to heavy skewness in ANOVA
Times, in particular, tend to be much more skewed than speeds (inverse-times) and log-time. If your question of interest could be stated i | Skewed but bell-shaped still considered as normal distribution for ANOVA?
There is a degree of sensitivity to heavy skewness in ANOVA
Times, in particular, tend to be much more skewed than speeds (inverse-times) and log-time. If your question of interest could be stated in terms of one of those (and they are less ske... | Skewed but bell-shaped still considered as normal distribution for ANOVA?
There is a degree of sensitivity to heavy skewness in ANOVA
Times, in particular, tend to be much more skewed than speeds (inverse-times) and log-time. If your question of interest could be stated i |
53,003 | R: How to interpret the QQplot's outlier numbers? | The number in the plot corresponds to the indices of the standardized residuals and the original data. By default, R labels the three most extreme residuals, even if they don't deviate much from the QQ-line. So the fact that the points are labelled doesn't mean that the fit is bad or anything. This behaviour can be cha... | R: How to interpret the QQplot's outlier numbers? | The number in the plot corresponds to the indices of the standardized residuals and the original data. By default, R labels the three most extreme residuals, even if they don't deviate much from the Q | R: How to interpret the QQplot's outlier numbers?
The number in the plot corresponds to the indices of the standardized residuals and the original data. By default, R labels the three most extreme residuals, even if they don't deviate much from the QQ-line. So the fact that the points are labelled doesn't mean that the... | R: How to interpret the QQplot's outlier numbers?
The number in the plot corresponds to the indices of the standardized residuals and the original data. By default, R labels the three most extreme residuals, even if they don't deviate much from the Q |
53,004 | Standard Deviation of Random effect is 0? | Sometimes the maximum likelihood estimate for a variance component is zero. Or more generally, sometimes a given algorithm for getting approximate MLEs will return zero. This happens when, for example, your fixed effects happen to be able to fit all the members of a group perfectly, and no variance is left over. This i... | Standard Deviation of Random effect is 0? | Sometimes the maximum likelihood estimate for a variance component is zero. Or more generally, sometimes a given algorithm for getting approximate MLEs will return zero. This happens when, for example | Standard Deviation of Random effect is 0?
Sometimes the maximum likelihood estimate for a variance component is zero. Or more generally, sometimes a given algorithm for getting approximate MLEs will return zero. This happens when, for example, your fixed effects happen to be able to fit all the members of a group perfe... | Standard Deviation of Random effect is 0?
Sometimes the maximum likelihood estimate for a variance component is zero. Or more generally, sometimes a given algorithm for getting approximate MLEs will return zero. This happens when, for example |
53,005 | Adding noise to a column of data | It depends on the kind of noise you want to add.
Here's an example:
x <- runif(100,100,150) # this is our original vector, which I'm just making up
corrupt <- rbinom(length(x),1,0.1) # choose an average of 10% to corrupt at random
corrupt <- as.logical(corrupt)
noise <- rnorm(sum(corrupt),1000,200) # generate the ... | Adding noise to a column of data | It depends on the kind of noise you want to add.
Here's an example:
x <- runif(100,100,150) # this is our original vector, which I'm just making up
corrupt <- rbinom(length(x),1,0.1) # choose an | Adding noise to a column of data
It depends on the kind of noise you want to add.
Here's an example:
x <- runif(100,100,150) # this is our original vector, which I'm just making up
corrupt <- rbinom(length(x),1,0.1) # choose an average of 10% to corrupt at random
corrupt <- as.logical(corrupt)
noise <- rnorm(sum(c... | Adding noise to a column of data
It depends on the kind of noise you want to add.
Here's an example:
x <- runif(100,100,150) # this is our original vector, which I'm just making up
corrupt <- rbinom(length(x),1,0.1) # choose an |
53,006 | Algorithm to produce autocorrelated uniformly distributed number | The first abstract might as well be the entire paper, because it perfectly describes an algorithm. :-) The following is my interpretation of that abstract.
The idea emulates that of generating a Gaussian process with specified autocorrelation $\rho = \cos(\theta)$ (re-expressing $\rho$ as the cosine of an angle betwee... | Algorithm to produce autocorrelated uniformly distributed number | The first abstract might as well be the entire paper, because it perfectly describes an algorithm. :-) The following is my interpretation of that abstract.
The idea emulates that of generating a Gaus | Algorithm to produce autocorrelated uniformly distributed number
The first abstract might as well be the entire paper, because it perfectly describes an algorithm. :-) The following is my interpretation of that abstract.
The idea emulates that of generating a Gaussian process with specified autocorrelation $\rho = \co... | Algorithm to produce autocorrelated uniformly distributed number
The first abstract might as well be the entire paper, because it perfectly describes an algorithm. :-) The following is my interpretation of that abstract.
The idea emulates that of generating a Gaus |
53,007 | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | For many purposes, you can use a normal approximation with continuity correction.
You can also use recursion for the probability that the total equals $y$, and add these from $y=x+1$ through $y=mn$.
There is also an exact formula for the probability that the sum equals $y$ involving a single summation, which gives yo... | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | For many purposes, you can use a normal approximation with continuity correction.
You can also use recursion for the probability that the total equals $y$, and add these from $y=x+1$ through $y=mn$. | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
For many purposes, you can use a normal approximation with continuity correction.
You can also use recursion for the probability that the total equals $y$, and add these from $y=x+1$ through $y=mn$.
There is also an exact formula for the pr... | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
For many purposes, you can use a normal approximation with continuity correction.
You can also use recursion for the probability that the total equals $y$, and add these from $y=x+1$ through $y=mn$. |
53,008 | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | Why don't you compute $P(sum > x)$ using a recursive formula with respect to the number of dices?
Something like $P(sum_n > x) = P(sum_{n - 1} + outcome_n > x) = \sum_{1}^{m}p_i1_{1 \le i \le m}P(sum_{n-1}>x-i)$. | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | Why don't you compute $P(sum > x)$ using a recursive formula with respect to the number of dices?
Something like $P(sum_n > x) = P(sum_{n - 1} + outcome_n > x) = \sum_{1}^{m}p_i1_{1 \le i \le m}P(sum_ | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
Why don't you compute $P(sum > x)$ using a recursive formula with respect to the number of dices?
Something like $P(sum_n > x) = P(sum_{n - 1} + outcome_n > x) = \sum_{1}^{m}p_i1_{1 \le i \le m}P(sum_{n-1}>x-i)$. | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
Why don't you compute $P(sum > x)$ using a recursive formula with respect to the number of dices?
Something like $P(sum_n > x) = P(sum_{n - 1} + outcome_n > x) = \sum_{1}^{m}p_i1_{1 \le i \le m}P(sum_ |
53,009 | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | Here's an implementation of @ThePawn's answer in Julia.
This computes the probability that they sum up to exactly n.
using Memoize # using Pkg; Pkg.add("Memoize")
@memoize function p_dice(dice, sides, n)
# Returns the probability dice dice with side sides
# sum up to n,
# where side ∈ 1:sides
if dice ==... | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | Here's an implementation of @ThePawn's answer in Julia.
This computes the probability that they sum up to exactly n.
using Memoize # using Pkg; Pkg.add("Memoize")
@memoize function p_dice(dice, sides, | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
Here's an implementation of @ThePawn's answer in Julia.
This computes the probability that they sum up to exactly n.
using Memoize # using Pkg; Pkg.add("Memoize")
@memoize function p_dice(dice, sides, n)
# Returns the probability dice dic... | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
Here's an implementation of @ThePawn's answer in Julia.
This computes the probability that they sum up to exactly n.
using Memoize # using Pkg; Pkg.add("Memoize")
@memoize function p_dice(dice, sides, |
53,010 | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | If the faces are uniform then the distribution will resemble a discrete form of the Irwin Hall distribution.
You could figure out the equations for the distribution, which will be some piecewise polynomial.
Possibly easier is to compute it by convolution (as given in another answer using a recursive formula) or by usi... | How to compute the distribution of sums when rolling 'N' dice with 'M' faces? | If the faces are uniform then the distribution will resemble a discrete form of the Irwin Hall distribution.
You could figure out the equations for the distribution, which will be some piecewise polyn | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
If the faces are uniform then the distribution will resemble a discrete form of the Irwin Hall distribution.
You could figure out the equations for the distribution, which will be some piecewise polynomial.
Possibly easier is to compute it b... | How to compute the distribution of sums when rolling 'N' dice with 'M' faces?
If the faces are uniform then the distribution will resemble a discrete form of the Irwin Hall distribution.
You could figure out the equations for the distribution, which will be some piecewise polyn |
53,011 | Can confidence interval be equal to zero? | In a remarkable paper, Gleser and Hwang showed that, for some models, confidence intervals must have infinite expected length for any positive confidence level $\alpha$ to be attained. More precisely, there is a subset of observations with positive measure for which the length of the confidence interval is infinite. Ex... | Can confidence interval be equal to zero? | In a remarkable paper, Gleser and Hwang showed that, for some models, confidence intervals must have infinite expected length for any positive confidence level $\alpha$ to be attained. More precisely, | Can confidence interval be equal to zero?
In a remarkable paper, Gleser and Hwang showed that, for some models, confidence intervals must have infinite expected length for any positive confidence level $\alpha$ to be attained. More precisely, there is a subset of observations with positive measure for which the length ... | Can confidence interval be equal to zero?
In a remarkable paper, Gleser and Hwang showed that, for some models, confidence intervals must have infinite expected length for any positive confidence level $\alpha$ to be attained. More precisely, |
53,012 | Can confidence interval be equal to zero? | An odd ratio of 2.97E006 (if you mean 2970000) seems odd to me, since it is way too high. Given your sample size it could be that some categories of the independed variables have a low frequency (e.g. a 1). Based on the information you provided it is indeed not safe to report the CI. I think no journal will expect a CI... | Can confidence interval be equal to zero? | An odd ratio of 2.97E006 (if you mean 2970000) seems odd to me, since it is way too high. Given your sample size it could be that some categories of the independed variables have a low frequency (e.g. | Can confidence interval be equal to zero?
An odd ratio of 2.97E006 (if you mean 2970000) seems odd to me, since it is way too high. Given your sample size it could be that some categories of the independed variables have a low frequency (e.g. a 1). Based on the information you provided it is indeed not safe to report t... | Can confidence interval be equal to zero?
An odd ratio of 2.97E006 (if you mean 2970000) seems odd to me, since it is way too high. Given your sample size it could be that some categories of the independed variables have a low frequency (e.g. |
53,013 | Experiment or simulation to undestand type I and type II errors | This would be the most basic procedure behind any such simulation:
Type I errors:
Have the computer generate a set (of size $n$) of pseudorandom numbers that conform to a particular distribution (the normal would be most typical).
Generate a second identical set (i.e., same distribution, parameters, and size).
... | Experiment or simulation to undestand type I and type II errors | This would be the most basic procedure behind any such simulation:
Type I errors:
Have the computer generate a set (of size $n$) of pseudorandom numbers that conform to a particular distribution ( | Experiment or simulation to undestand type I and type II errors
This would be the most basic procedure behind any such simulation:
Type I errors:
Have the computer generate a set (of size $n$) of pseudorandom numbers that conform to a particular distribution (the normal would be most typical).
Generate a second i... | Experiment or simulation to undestand type I and type II errors
This would be the most basic procedure behind any such simulation:
Type I errors:
Have the computer generate a set (of size $n$) of pseudorandom numbers that conform to a particular distribution ( |
53,014 | Experiment or simulation to undestand type I and type II errors | The most common example is of this kind: take a normal variate, $X_1$, which can be either $\mathcal{N}(0,1)$ or $\mathcal{N}(2,1)$. If you build a test accepting $\mathcal{N}(0,1)$ when $x_1<1.68$ and rejecting $\mathcal{N}(0,1)$ when $x_1>1.68$, it is rather simple to check by simulation that the type I error is $0.0... | Experiment or simulation to undestand type I and type II errors | The most common example is of this kind: take a normal variate, $X_1$, which can be either $\mathcal{N}(0,1)$ or $\mathcal{N}(2,1)$. If you build a test accepting $\mathcal{N}(0,1)$ when $x_1<1.68$ an | Experiment or simulation to undestand type I and type II errors
The most common example is of this kind: take a normal variate, $X_1$, which can be either $\mathcal{N}(0,1)$ or $\mathcal{N}(2,1)$. If you build a test accepting $\mathcal{N}(0,1)$ when $x_1<1.68$ and rejecting $\mathcal{N}(0,1)$ when $x_1>1.68$, it is ra... | Experiment or simulation to undestand type I and type II errors
The most common example is of this kind: take a normal variate, $X_1$, which can be either $\mathcal{N}(0,1)$ or $\mathcal{N}(2,1)$. If you build a test accepting $\mathcal{N}(0,1)$ when $x_1<1.68$ an |
53,015 | Experiment or simulation to undestand type I and type II errors | Check out Geoff Cumming's "dancing p-values"
http://www.youtube.com/watch?v=ez4DgdurRPg&feature=plcp
Cummings is the author of "Understanding the new statistics." | Experiment or simulation to undestand type I and type II errors | Check out Geoff Cumming's "dancing p-values"
http://www.youtube.com/watch?v=ez4DgdurRPg&feature=plcp
Cummings is the author of "Understanding the new statistics." | Experiment or simulation to undestand type I and type II errors
Check out Geoff Cumming's "dancing p-values"
http://www.youtube.com/watch?v=ez4DgdurRPg&feature=plcp
Cummings is the author of "Understanding the new statistics." | Experiment or simulation to undestand type I and type II errors
Check out Geoff Cumming's "dancing p-values"
http://www.youtube.com/watch?v=ez4DgdurRPg&feature=plcp
Cummings is the author of "Understanding the new statistics." |
53,016 | Relations between distributions | How about this:
http://www.johndcook.com/distribution_chart.html | Relations between distributions | How about this:
http://www.johndcook.com/distribution_chart.html | Relations between distributions
How about this:
http://www.johndcook.com/distribution_chart.html | Relations between distributions
How about this:
http://www.johndcook.com/distribution_chart.html |
53,017 | Relations between distributions | A fairly complete graph is given in
"Univariate Distribution Relationships" Lawrence M. Leemis and Jacquelyn T. McQueston The American Statistician 2008, vol. 62 n. 1 pp. 45-53. | Relations between distributions | A fairly complete graph is given in
"Univariate Distribution Relationships" Lawrence M. Leemis and Jacquelyn T. McQueston The American Statistician 2008, vol. 62 n. 1 pp. 45-53. | Relations between distributions
A fairly complete graph is given in
"Univariate Distribution Relationships" Lawrence M. Leemis and Jacquelyn T. McQueston The American Statistician 2008, vol. 62 n. 1 pp. 45-53. | Relations between distributions
A fairly complete graph is given in
"Univariate Distribution Relationships" Lawrence M. Leemis and Jacquelyn T. McQueston The American Statistician 2008, vol. 62 n. 1 pp. 45-53. |
53,018 | Singular covariance matrix in Mahalanobis distance in Matlab | To add on BGreene 's answer, you can use the Moore-Penrose inverse. When you use the Mahalanobis distance modified in this way, on the same data used to estimate the covariance matrix, you lose nothing. The covariance matrix is singular because your data happen to live in a linear subspace, and your modified Mahalanob... | Singular covariance matrix in Mahalanobis distance in Matlab | To add on BGreene 's answer, you can use the Moore-Penrose inverse. When you use the Mahalanobis distance modified in this way, on the same data used to estimate the covariance matrix, you lose nothin | Singular covariance matrix in Mahalanobis distance in Matlab
To add on BGreene 's answer, you can use the Moore-Penrose inverse. When you use the Mahalanobis distance modified in this way, on the same data used to estimate the covariance matrix, you lose nothing. The covariance matrix is singular because your data hap... | Singular covariance matrix in Mahalanobis distance in Matlab
To add on BGreene 's answer, you can use the Moore-Penrose inverse. When you use the Mahalanobis distance modified in this way, on the same data used to estimate the covariance matrix, you lose nothin |
53,019 | Singular covariance matrix in Mahalanobis distance in Matlab | You could try using the Moore-Penrose pseudoinverse (pinv function in Matlab), to invert your covariance matrix | Singular covariance matrix in Mahalanobis distance in Matlab | You could try using the Moore-Penrose pseudoinverse (pinv function in Matlab), to invert your covariance matrix | Singular covariance matrix in Mahalanobis distance in Matlab
You could try using the Moore-Penrose pseudoinverse (pinv function in Matlab), to invert your covariance matrix | Singular covariance matrix in Mahalanobis distance in Matlab
You could try using the Moore-Penrose pseudoinverse (pinv function in Matlab), to invert your covariance matrix |
53,020 | Singular covariance matrix in Mahalanobis distance in Matlab | The typical handwriting dataset everybody seems to use is quite ill formed for PCA and many mathematical methods. It is pixels, and obviously some of these (bottom right corner, whatever) are never really painted in any of the samples you have.
Even worse, the values are discrete. This can cause all kind of artifacts.
... | Singular covariance matrix in Mahalanobis distance in Matlab | The typical handwriting dataset everybody seems to use is quite ill formed for PCA and many mathematical methods. It is pixels, and obviously some of these (bottom right corner, whatever) are never re | Singular covariance matrix in Mahalanobis distance in Matlab
The typical handwriting dataset everybody seems to use is quite ill formed for PCA and many mathematical methods. It is pixels, and obviously some of these (bottom right corner, whatever) are never really painted in any of the samples you have.
Even worse, th... | Singular covariance matrix in Mahalanobis distance in Matlab
The typical handwriting dataset everybody seems to use is quite ill formed for PCA and many mathematical methods. It is pixels, and obviously some of these (bottom right corner, whatever) are never re |
53,021 | Singular covariance matrix in Mahalanobis distance in Matlab | This is really a comment but to long: Thanks Michael! The way to think about the Moore-Penrose inverse is as follows: Any Matrix represents a linear operator. First some notation: Let $A$ be an $n \times m$-matrix, where we assume for simplicity that $n \ge m$. This matrix really represents a linear transformation:... | Singular covariance matrix in Mahalanobis distance in Matlab | This is really a comment but to long: Thanks Michael! The way to think about the Moore-Penrose inverse is as follows: Any Matrix represents a linear operator. First some notation: Let $A$ be an $n | Singular covariance matrix in Mahalanobis distance in Matlab
This is really a comment but to long: Thanks Michael! The way to think about the Moore-Penrose inverse is as follows: Any Matrix represents a linear operator. First some notation: Let $A$ be an $n \times m$-matrix, where we assume for simplicity that $n \... | Singular covariance matrix in Mahalanobis distance in Matlab
This is really a comment but to long: Thanks Michael! The way to think about the Moore-Penrose inverse is as follows: Any Matrix represents a linear operator. First some notation: Let $A$ be an $n |
53,022 | Algorithim to determine if point is "too far from the average" | As Richard pointed out, the three-sigma "rule" only applies to the normal distribution (bell curve), which definitely doesn't apply since your runtimes can't be negative:
The log-normal distribution might possibly be more accurate, since it at least only allows for positive runtimes and might sort of make sense, anywa... | Algorithim to determine if point is "too far from the average" | As Richard pointed out, the three-sigma "rule" only applies to the normal distribution (bell curve), which definitely doesn't apply since your runtimes can't be negative:
The log-normal distribution | Algorithim to determine if point is "too far from the average"
As Richard pointed out, the three-sigma "rule" only applies to the normal distribution (bell curve), which definitely doesn't apply since your runtimes can't be negative:
The log-normal distribution might possibly be more accurate, since it at least only a... | Algorithim to determine if point is "too far from the average"
As Richard pointed out, the three-sigma "rule" only applies to the normal distribution (bell curve), which definitely doesn't apply since your runtimes can't be negative:
The log-normal distribution |
53,023 | Algorithim to determine if point is "too far from the average" | The "rule" that only 1% of a sample is outside 3 standard deviations works when the distribution of values is a Gaussian (also known as "Normal") Distribution. I don't know what distribution you will be getting for your run times. But they are likely not to be Normal (they can not be less than zero). Also the differen... | Algorithim to determine if point is "too far from the average" | The "rule" that only 1% of a sample is outside 3 standard deviations works when the distribution of values is a Gaussian (also known as "Normal") Distribution. I don't know what distribution you will | Algorithim to determine if point is "too far from the average"
The "rule" that only 1% of a sample is outside 3 standard deviations works when the distribution of values is a Gaussian (also known as "Normal") Distribution. I don't know what distribution you will be getting for your run times. But they are likely not t... | Algorithim to determine if point is "too far from the average"
The "rule" that only 1% of a sample is outside 3 standard deviations works when the distribution of values is a Gaussian (also known as "Normal") Distribution. I don't know what distribution you will |
53,024 | Generation of random numbers from the multivariate normal distribution in spherical coordinates | This book has this reference to this book here. Not exactly cheap, but I think it's the one you are looking for. ;) | Generation of random numbers from the multivariate normal distribution in spherical coordinates | This book has this reference to this book here. Not exactly cheap, but I think it's the one you are looking for. ;) | Generation of random numbers from the multivariate normal distribution in spherical coordinates
This book has this reference to this book here. Not exactly cheap, but I think it's the one you are looking for. ;) | Generation of random numbers from the multivariate normal distribution in spherical coordinates
This book has this reference to this book here. Not exactly cheap, but I think it's the one you are looking for. ;) |
53,025 | Generation of random numbers from the multivariate normal distribution in spherical coordinates | Given how easy it is to generate the normal variates, I would do just that, and then convert to the spherical coordinates directly.
If you need $N_p(0,I_p)$, where $p$ is the dimension, then in spherical coordinates, $r\sim \chi^2_p = \Gamma(p/2,1/2)$, and the angles are all independent of each other and the length, wi... | Generation of random numbers from the multivariate normal distribution in spherical coordinates | Given how easy it is to generate the normal variates, I would do just that, and then convert to the spherical coordinates directly.
If you need $N_p(0,I_p)$, where $p$ is the dimension, then in spheri | Generation of random numbers from the multivariate normal distribution in spherical coordinates
Given how easy it is to generate the normal variates, I would do just that, and then convert to the spherical coordinates directly.
If you need $N_p(0,I_p)$, where $p$ is the dimension, then in spherical coordinates, $r\sim ... | Generation of random numbers from the multivariate normal distribution in spherical coordinates
Given how easy it is to generate the normal variates, I would do just that, and then convert to the spherical coordinates directly.
If you need $N_p(0,I_p)$, where $p$ is the dimension, then in spheri |
53,026 | How does R's auto.arima() function determine the order of differencing when estimating a regression with seasonal ARIMA errors? | OCSB test: Osborn DR, Chui APL, Smith J, and Birchenhall CR (1988) "Seasonality and the order of integration for consumption", Oxford Bulletin of Economics and Statistics 50(4):361-377.
The change in the algorithm is explained at http://robjhyndman.com/researchtips/forecast3/
When regressors are used, auto.arima() fit... | How does R's auto.arima() function determine the order of differencing when estimating a regression | OCSB test: Osborn DR, Chui APL, Smith J, and Birchenhall CR (1988) "Seasonality and the order of integration for consumption", Oxford Bulletin of Economics and Statistics 50(4):361-377.
The change in | How does R's auto.arima() function determine the order of differencing when estimating a regression with seasonal ARIMA errors?
OCSB test: Osborn DR, Chui APL, Smith J, and Birchenhall CR (1988) "Seasonality and the order of integration for consumption", Oxford Bulletin of Economics and Statistics 50(4):361-377.
The ch... | How does R's auto.arima() function determine the order of differencing when estimating a regression
OCSB test: Osborn DR, Chui APL, Smith J, and Birchenhall CR (1988) "Seasonality and the order of integration for consumption", Oxford Bulletin of Economics and Statistics 50(4):361-377.
The change in |
53,027 | From confidence interval to standard deviation - what am I missing? | Analysis
The calculations in the question support the assumption that a binomial model is being used. This treats the incidents as if 211,101 slips of paper were drawn randomly from a hat having millions of slips (far more than the number observed). On each slip is drawn either a $1$ (an "incident") or a $0$. Eviden... | From confidence interval to standard deviation - what am I missing? | Analysis
The calculations in the question support the assumption that a binomial model is being used. This treats the incidents as if 211,101 slips of paper were drawn randomly from a hat having mill | From confidence interval to standard deviation - what am I missing?
Analysis
The calculations in the question support the assumption that a binomial model is being used. This treats the incidents as if 211,101 slips of paper were drawn randomly from a hat having millions of slips (far more than the number observed). ... | From confidence interval to standard deviation - what am I missing?
Analysis
The calculations in the question support the assumption that a binomial model is being used. This treats the incidents as if 211,101 slips of paper were drawn randomly from a hat having mill |
53,028 | From confidence interval to standard deviation - what am I missing? | I'd answer differently.
If you are talking about measured (ratio or interval) data, then the standard deviation of the data measures scatter, and the standard error of the mean quantifies how precisely that mean is known (from its sample size and SD). The two are very different. Converting from one to the other is str... | From confidence interval to standard deviation - what am I missing? | I'd answer differently.
If you are talking about measured (ratio or interval) data, then the standard deviation of the data measures scatter, and the standard error of the mean quantifies how precise | From confidence interval to standard deviation - what am I missing?
I'd answer differently.
If you are talking about measured (ratio or interval) data, then the standard deviation of the data measures scatter, and the standard error of the mean quantifies how precisely that mean is known (from its sample size and SD).... | From confidence interval to standard deviation - what am I missing?
I'd answer differently.
If you are talking about measured (ratio or interval) data, then the standard deviation of the data measures scatter, and the standard error of the mean quantifies how precise |
53,029 | Binary classification vs. continuous output with neural networks | It is a bad idea. It increases both type I and type II error. It also invokes "magical thinking" - that is, that something magical happens at the cutoff value. For example, with newborns, it is common to say babies under 2.5 kg are "low birth weight" and those above 2.5 kg are not. This treats a baby of 2.49 kg as bein... | Binary classification vs. continuous output with neural networks | It is a bad idea. It increases both type I and type II error. It also invokes "magical thinking" - that is, that something magical happens at the cutoff value. For example, with newborns, it is common | Binary classification vs. continuous output with neural networks
It is a bad idea. It increases both type I and type II error. It also invokes "magical thinking" - that is, that something magical happens at the cutoff value. For example, with newborns, it is common to say babies under 2.5 kg are "low birth weight" and ... | Binary classification vs. continuous output with neural networks
It is a bad idea. It increases both type I and type II error. It also invokes "magical thinking" - that is, that something magical happens at the cutoff value. For example, with newborns, it is common |
53,030 | Binary classification vs. continuous output with neural networks | If you convert a continous variable to binary you throw out a lot of detailed information. So in my opinion it is advisable not to do it. For tree classifiers binary splits are used but the information in the continuous variable if used to get the first split and the variable can be split again if it is very importan... | Binary classification vs. continuous output with neural networks | If you convert a continous variable to binary you throw out a lot of detailed information. So in my opinion it is advisable not to do it. For tree classifiers binary splits are used but the informat | Binary classification vs. continuous output with neural networks
If you convert a continous variable to binary you throw out a lot of detailed information. So in my opinion it is advisable not to do it. For tree classifiers binary splits are used but the information in the continuous variable if used to get the first... | Binary classification vs. continuous output with neural networks
If you convert a continous variable to binary you throw out a lot of detailed information. So in my opinion it is advisable not to do it. For tree classifiers binary splits are used but the informat |
53,031 | Binary classification vs. continuous output with neural networks | Peter Flom's answer here suggests that discretizing your output variable is going to hurt. If so, you obviously shouldn't do it! This is definitely the conventional wisdom for predictor variables. However, having thought about it for a little while, I'm not even sure how one could fairly compare the two situations for ... | Binary classification vs. continuous output with neural networks | Peter Flom's answer here suggests that discretizing your output variable is going to hurt. If so, you obviously shouldn't do it! This is definitely the conventional wisdom for predictor variables. How | Binary classification vs. continuous output with neural networks
Peter Flom's answer here suggests that discretizing your output variable is going to hurt. If so, you obviously shouldn't do it! This is definitely the conventional wisdom for predictor variables. However, having thought about it for a little while, I'm n... | Binary classification vs. continuous output with neural networks
Peter Flom's answer here suggests that discretizing your output variable is going to hurt. If so, you obviously shouldn't do it! This is definitely the conventional wisdom for predictor variables. How |
53,032 | Poisson likelihood and zero counts in expected value | I think that the sentence is poorly worded, one should not use the word "expect" in that context, it can induce confusion. Because to "expect either 0 or 1 count per bin" does NOT mean that "the expected value per bin is either 0 or 1 ($m_i=0$ or $m_i=1$)". It rather means that the expected value per bin is quite smal... | Poisson likelihood and zero counts in expected value | I think that the sentence is poorly worded, one should not use the word "expect" in that context, it can induce confusion. Because to "expect either 0 or 1 count per bin" does NOT mean that "the expe | Poisson likelihood and zero counts in expected value
I think that the sentence is poorly worded, one should not use the word "expect" in that context, it can induce confusion. Because to "expect either 0 or 1 count per bin" does NOT mean that "the expected value per bin is either 0 or 1 ($m_i=0$ or $m_i=1$)". It rathe... | Poisson likelihood and zero counts in expected value
I think that the sentence is poorly worded, one should not use the word "expect" in that context, it can induce confusion. Because to "expect either 0 or 1 count per bin" does NOT mean that "the expe |
53,033 | Poisson likelihood and zero counts in expected value | If $m_i=0$ then the likelihood $L_i$ of observing $0$ is $1$ and of observing anything else is $0$.
This is an example of the wider convention where $0^0$ is taken to be $1$ so $\frac{0^0}{0!}\exp(-0)=1$ | Poisson likelihood and zero counts in expected value | If $m_i=0$ then the likelihood $L_i$ of observing $0$ is $1$ and of observing anything else is $0$.
This is an example of the wider convention where $0^0$ is taken to be $1$ so $\frac{0^0}{0!}\exp(- | Poisson likelihood and zero counts in expected value
If $m_i=0$ then the likelihood $L_i$ of observing $0$ is $1$ and of observing anything else is $0$.
This is an example of the wider convention where $0^0$ is taken to be $1$ so $\frac{0^0}{0!}\exp(-0)=1$ | Poisson likelihood and zero counts in expected value
If $m_i=0$ then the likelihood $L_i$ of observing $0$ is $1$ and of observing anything else is $0$.
This is an example of the wider convention where $0^0$ is taken to be $1$ so $\frac{0^0}{0!}\exp(- |
53,034 | Poisson likelihood and zero counts in expected value | The statement "Suppose that in a particular model $m$, you expect there to be $m_i$ counts in bin $i$. Then if the model is correct the likelihood of actually observing $d_i$ counts in bin $i$ of the data is, from the Poisson distribution,*
$L_i = m_i^{d_i}/d_i! \; exp(-m_i)$"
is incorrect in a couple of ways. First, ... | Poisson likelihood and zero counts in expected value | The statement "Suppose that in a particular model $m$, you expect there to be $m_i$ counts in bin $i$. Then if the model is correct the likelihood of actually observing $d_i$ counts in bin $i$ of the | Poisson likelihood and zero counts in expected value
The statement "Suppose that in a particular model $m$, you expect there to be $m_i$ counts in bin $i$. Then if the model is correct the likelihood of actually observing $d_i$ counts in bin $i$ of the data is, from the Poisson distribution,*
$L_i = m_i^{d_i}/d_i! \; e... | Poisson likelihood and zero counts in expected value
The statement "Suppose that in a particular model $m$, you expect there to be $m_i$ counts in bin $i$. Then if the model is correct the likelihood of actually observing $d_i$ counts in bin $i$ of the |
53,035 | Poisson likelihood and zero counts in expected value | I think that, you are using Bayesian statistics here. The posterior probability is proportional to likelihood function, then you have
P(model(parameters)|data) \propto L(data|model(parameters)).
Therefore, you can have such problem. Actually, I have a similar problem. Nonetheless, I use greater bins. It is a possible s... | Poisson likelihood and zero counts in expected value | I think that, you are using Bayesian statistics here. The posterior probability is proportional to likelihood function, then you have
P(model(parameters)|data) \propto L(data|model(parameters)).
There | Poisson likelihood and zero counts in expected value
I think that, you are using Bayesian statistics here. The posterior probability is proportional to likelihood function, then you have
P(model(parameters)|data) \propto L(data|model(parameters)).
Therefore, you can have such problem. Actually, I have a similar problem... | Poisson likelihood and zero counts in expected value
I think that, you are using Bayesian statistics here. The posterior probability is proportional to likelihood function, then you have
P(model(parameters)|data) \propto L(data|model(parameters)).
There |
53,036 | Significance tests | This reply describes two good solutions, a permutation test and a Student t-test, and compares and contrasts them.
Michael Lew recommends a permutation test. This is good advice: such a test is conceptually simple and makes few assumptions. It interprets the null hypothesis as meaning it makes no difference which sa... | Significance tests | This reply describes two good solutions, a permutation test and a Student t-test, and compares and contrasts them.
Michael Lew recommends a permutation test. This is good advice: such a test is conc | Significance tests
This reply describes two good solutions, a permutation test and a Student t-test, and compares and contrasts them.
Michael Lew recommends a permutation test. This is good advice: such a test is conceptually simple and makes few assumptions. It interprets the null hypothesis as meaning it makes no ... | Significance tests
This reply describes two good solutions, a permutation test and a Student t-test, and compares and contrasts them.
Michael Lew recommends a permutation test. This is good advice: such a test is conc |
53,037 | Significance tests | You might consider a permutations test.
A permutations test assumes that the observations are drawn from one population and then treatments are randomly allocated. Thus in the context of a permutations test for a difference in the means the null hypothesis (no treatment effect) becomes equivalent to a statement that an... | Significance tests | You might consider a permutations test.
A permutations test assumes that the observations are drawn from one population and then treatments are randomly allocated. Thus in the context of a permutation | Significance tests
You might consider a permutations test.
A permutations test assumes that the observations are drawn from one population and then treatments are randomly allocated. Thus in the context of a permutations test for a difference in the means the null hypothesis (no treatment effect) becomes equivalent to ... | Significance tests
You might consider a permutations test.
A permutations test assumes that the observations are drawn from one population and then treatments are randomly allocated. Thus in the context of a permutation |
53,038 | Calculating the $p$-value of an $F$- statistic | More details than you probably want on the mathematics of the F distribution can be found here (and other places). The formula for the pdf is there and the p-value is just the integral from your F-statistic to infinity of that function. It also has the Cumulative distribution function for the F distribution and the p... | Calculating the $p$-value of an $F$- statistic | More details than you probably want on the mathematics of the F distribution can be found here (and other places). The formula for the pdf is there and the p-value is just the integral from your F-st | Calculating the $p$-value of an $F$- statistic
More details than you probably want on the mathematics of the F distribution can be found here (and other places). The formula for the pdf is there and the p-value is just the integral from your F-statistic to infinity of that function. It also has the Cumulative distrib... | Calculating the $p$-value of an $F$- statistic
More details than you probably want on the mathematics of the F distribution can be found here (and other places). The formula for the pdf is there and the p-value is just the integral from your F-st |
53,039 | Calculating the $p$-value of an $F$- statistic | About Scheme libraries specifically, here are two GSL bindings that you might be interested in:
Noel Welsh's fork of mzgsl.
The Science collection, by Doug Williams, provides a collection of modules for numerical computing; it includes random number distributions, among others.
The second project is readily available... | Calculating the $p$-value of an $F$- statistic | About Scheme libraries specifically, here are two GSL bindings that you might be interested in:
Noel Welsh's fork of mzgsl.
The Science collection, by Doug Williams, provides a collection of modules | Calculating the $p$-value of an $F$- statistic
About Scheme libraries specifically, here are two GSL bindings that you might be interested in:
Noel Welsh's fork of mzgsl.
The Science collection, by Doug Williams, provides a collection of modules for numerical computing; it includes random number distributions, among o... | Calculating the $p$-value of an $F$- statistic
About Scheme libraries specifically, here are two GSL bindings that you might be interested in:
Noel Welsh's fork of mzgsl.
The Science collection, by Doug Williams, provides a collection of modules |
53,040 | Calculating the $p$-value of an $F$- statistic | Calculating the p-value for an F-Test is a quite straightforward job in every statistical programme. Consider for example r (r-project). Here's an example in R:
pf(F, df1=dfa, df2=dfb)
where F is the value from the statistic and dfa and dfb are the degrees of freedom.
Hope this helps you! | Calculating the $p$-value of an $F$- statistic | Calculating the p-value for an F-Test is a quite straightforward job in every statistical programme. Consider for example r (r-project). Here's an example in R:
pf(F, df1=dfa, df2=dfb)
where F is the | Calculating the $p$-value of an $F$- statistic
Calculating the p-value for an F-Test is a quite straightforward job in every statistical programme. Consider for example r (r-project). Here's an example in R:
pf(F, df1=dfa, df2=dfb)
where F is the value from the statistic and dfa and dfb are the degrees of freedom.
Ho... | Calculating the $p$-value of an $F$- statistic
Calculating the p-value for an F-Test is a quite straightforward job in every statistical programme. Consider for example r (r-project). Here's an example in R:
pf(F, df1=dfa, df2=dfb)
where F is the |
53,041 | Adjusting kappa inter-rater agreement for prevalence | Kappa is regarded as a measure of chance-adjusted agreement, calculated as $\frac{{{p_{obs}} - {p_{exp}}}}{{1 - {p_{exp}}}}$ where ${p_{obs}} = \sum\limits_{i = 1}^k {{p_{ii}}} $ and ${p_{exp}} = \sum\limits_{i = 1}^k {{p_{i + }}{p_{ + i}}} $ ($p_{i+}$ and $p_{+i}$ are the marginal totals). Essentially, it is a measure... | Adjusting kappa inter-rater agreement for prevalence | Kappa is regarded as a measure of chance-adjusted agreement, calculated as $\frac{{{p_{obs}} - {p_{exp}}}}{{1 - {p_{exp}}}}$ where ${p_{obs}} = \sum\limits_{i = 1}^k {{p_{ii}}} $ and ${p_{exp}} = \sum | Adjusting kappa inter-rater agreement for prevalence
Kappa is regarded as a measure of chance-adjusted agreement, calculated as $\frac{{{p_{obs}} - {p_{exp}}}}{{1 - {p_{exp}}}}$ where ${p_{obs}} = \sum\limits_{i = 1}^k {{p_{ii}}} $ and ${p_{exp}} = \sum\limits_{i = 1}^k {{p_{i + }}{p_{ + i}}} $ ($p_{i+}$ and $p_{+i}$ a... | Adjusting kappa inter-rater agreement for prevalence
Kappa is regarded as a measure of chance-adjusted agreement, calculated as $\frac{{{p_{obs}} - {p_{exp}}}}{{1 - {p_{exp}}}}$ where ${p_{obs}} = \sum\limits_{i = 1}^k {{p_{ii}}} $ and ${p_{exp}} = \sum |
53,042 | Learning probability and statistics together | I have the 8th edition of Modern Elementary Statistics which I see has a companion answers book to odd numbered questions. I also have an older version of Ott's Introduction to Statistical Methods and Data Analysis which I find incredibly useful to pointing out to colleagues about how I would love to see GLM models spe... | Learning probability and statistics together | I have the 8th edition of Modern Elementary Statistics which I see has a companion answers book to odd numbered questions. I also have an older version of Ott's Introduction to Statistical Methods and | Learning probability and statistics together
I have the 8th edition of Modern Elementary Statistics which I see has a companion answers book to odd numbered questions. I also have an older version of Ott's Introduction to Statistical Methods and Data Analysis which I find incredibly useful to pointing out to colleagues... | Learning probability and statistics together
I have the 8th edition of Modern Elementary Statistics which I see has a companion answers book to odd numbered questions. I also have an older version of Ott's Introduction to Statistical Methods and |
53,043 | Learning probability and statistics together | The first book "All of Statistics" is nice book to read. I dont know about second book. However, I would recommend the following book. It is really nice book to get an idea whats going on in statistics and probability.
A Modern Introduction to Probability and Statistics: Understanding Why and How (Springer Texts in Sta... | Learning probability and statistics together | The first book "All of Statistics" is nice book to read. I dont know about second book. However, I would recommend the following book. It is really nice book to get an idea whats going on in statistic | Learning probability and statistics together
The first book "All of Statistics" is nice book to read. I dont know about second book. However, I would recommend the following book. It is really nice book to get an idea whats going on in statistics and probability.
A Modern Introduction to Probability and Statistics: Und... | Learning probability and statistics together
The first book "All of Statistics" is nice book to read. I dont know about second book. However, I would recommend the following book. It is really nice book to get an idea whats going on in statistic |
53,044 | Learning probability and statistics together | I still like DeGroot / Schervish. Please, take a look:
http://www.amazon.com/Probability-Statistics-Edition-Morris-DeGroot/dp/0321500466
It is highly self-contained, starting with basic set theory, covering all the standard material on probability (without measure theory). After that, the inference part shines, with ex... | Learning probability and statistics together | I still like DeGroot / Schervish. Please, take a look:
http://www.amazon.com/Probability-Statistics-Edition-Morris-DeGroot/dp/0321500466
It is highly self-contained, starting with basic set theory, co | Learning probability and statistics together
I still like DeGroot / Schervish. Please, take a look:
http://www.amazon.com/Probability-Statistics-Edition-Morris-DeGroot/dp/0321500466
It is highly self-contained, starting with basic set theory, covering all the standard material on probability (without measure theory). A... | Learning probability and statistics together
I still like DeGroot / Schervish. Please, take a look:
http://www.amazon.com/Probability-Statistics-Edition-Morris-DeGroot/dp/0321500466
It is highly self-contained, starting with basic set theory, co |
53,045 | Learning probability and statistics together | I worked through the entire book about a year ago (2019) and put most of my solutions to Chapters 8–16 on github.
Please comment and correct me if I’m wrong, but I believe the free pdf released is a preprint, and the printed book is the official version. I used the free pdf (and included a copy of it in my git repo) bu... | Learning probability and statistics together | I worked through the entire book about a year ago (2019) and put most of my solutions to Chapters 8–16 on github.
Please comment and correct me if I’m wrong, but I believe the free pdf released is a p | Learning probability and statistics together
I worked through the entire book about a year ago (2019) and put most of my solutions to Chapters 8–16 on github.
Please comment and correct me if I’m wrong, but I believe the free pdf released is a preprint, and the printed book is the official version. I used the free pdf ... | Learning probability and statistics together
I worked through the entire book about a year ago (2019) and put most of my solutions to Chapters 8–16 on github.
Please comment and correct me if I’m wrong, but I believe the free pdf released is a p |
53,046 | PCA to decorrelate variables | With just two variables $X$ and $Y$, there are two sample variances $s^2$ and $t^2$, respectively, and the sample correlation coefficient, $r$. If you standardize the variables in the usual way to have unit variances, so that $\xi = X/s$ and $\eta = Y/t$, then the two principal components are
$$PC_1 = \xi+\eta = X/s +... | PCA to decorrelate variables | With just two variables $X$ and $Y$, there are two sample variances $s^2$ and $t^2$, respectively, and the sample correlation coefficient, $r$. If you standardize the variables in the usual way to ha | PCA to decorrelate variables
With just two variables $X$ and $Y$, there are two sample variances $s^2$ and $t^2$, respectively, and the sample correlation coefficient, $r$. If you standardize the variables in the usual way to have unit variances, so that $\xi = X/s$ and $\eta = Y/t$, then the two principal components ... | PCA to decorrelate variables
With just two variables $X$ and $Y$, there are two sample variances $s^2$ and $t^2$, respectively, and the sample correlation coefficient, $r$. If you standardize the variables in the usual way to ha |
53,047 | PCA to decorrelate variables | It varies with your software, but you should have something like a component score matrix. Multiply that with your original variables to get the new set of transformed data. | PCA to decorrelate variables | It varies with your software, but you should have something like a component score matrix. Multiply that with your original variables to get the new set of transformed data. | PCA to decorrelate variables
It varies with your software, but you should have something like a component score matrix. Multiply that with your original variables to get the new set of transformed data. | PCA to decorrelate variables
It varies with your software, but you should have something like a component score matrix. Multiply that with your original variables to get the new set of transformed data. |
53,048 | PCA to decorrelate variables | You have loading for each component (P1, P2,....Pi).
$$P_1=l_1x_1+l_2x_2+...+l_jx_j$$
$$P_2=l_1x_1+l_2x_2+...+l_jx_j$$
$$.$$
$$.$$
$$P_i=l_1x_1+l_2x_2+...+l_jx_j$$
where $x$ is orginal data and $P_i$ is rotated component. The important is loadings ($l_1,l_2,...,l_j$). If you mulitple them with orginal data then you wil... | PCA to decorrelate variables | You have loading for each component (P1, P2,....Pi).
$$P_1=l_1x_1+l_2x_2+...+l_jx_j$$
$$P_2=l_1x_1+l_2x_2+...+l_jx_j$$
$$.$$
$$.$$
$$P_i=l_1x_1+l_2x_2+...+l_jx_j$$
where $x$ is orginal data and $P_i$ | PCA to decorrelate variables
You have loading for each component (P1, P2,....Pi).
$$P_1=l_1x_1+l_2x_2+...+l_jx_j$$
$$P_2=l_1x_1+l_2x_2+...+l_jx_j$$
$$.$$
$$.$$
$$P_i=l_1x_1+l_2x_2+...+l_jx_j$$
where $x$ is orginal data and $P_i$ is rotated component. The important is loadings ($l_1,l_2,...,l_j$). If you mulitple them w... | PCA to decorrelate variables
You have loading for each component (P1, P2,....Pi).
$$P_1=l_1x_1+l_2x_2+...+l_jx_j$$
$$P_2=l_1x_1+l_2x_2+...+l_jx_j$$
$$.$$
$$.$$
$$P_i=l_1x_1+l_2x_2+...+l_jx_j$$
where $x$ is orginal data and $P_i$ |
53,049 | How to calculate an overall job satisfaction score and test group differences? | You have two questions:
How to form an overall measure of job satisfaction?
How to examine group differences on the score that you create?
Forming the overall measure of job satisfaction
If you are using an established measure of job satisfaction, then the test manual should tell you how you should calculate the over... | How to calculate an overall job satisfaction score and test group differences? | You have two questions:
How to form an overall measure of job satisfaction?
How to examine group differences on the score that you create?
Forming the overall measure of job satisfaction
If you are | How to calculate an overall job satisfaction score and test group differences?
You have two questions:
How to form an overall measure of job satisfaction?
How to examine group differences on the score that you create?
Forming the overall measure of job satisfaction
If you are using an established measure of job satis... | How to calculate an overall job satisfaction score and test group differences?
You have two questions:
How to form an overall measure of job satisfaction?
How to examine group differences on the score that you create?
Forming the overall measure of job satisfaction
If you are |
53,050 | How to calculate an overall job satisfaction score and test group differences? | Your ultimate job satisfaction construct sounds suspect to me. When you summed up the different facets of job satisfaction to create your ultimate score, you implicitly assumed that each facet has the same weight - they really don't, as you'll see in the literature.
You'd have a much easier time with an explicit meas... | How to calculate an overall job satisfaction score and test group differences? | Your ultimate job satisfaction construct sounds suspect to me. When you summed up the different facets of job satisfaction to create your ultimate score, you implicitly assumed that each facet has th | How to calculate an overall job satisfaction score and test group differences?
Your ultimate job satisfaction construct sounds suspect to me. When you summed up the different facets of job satisfaction to create your ultimate score, you implicitly assumed that each facet has the same weight - they really don't, as you... | How to calculate an overall job satisfaction score and test group differences?
Your ultimate job satisfaction construct sounds suspect to me. When you summed up the different facets of job satisfaction to create your ultimate score, you implicitly assumed that each facet has th |
53,051 | How to calculate an overall job satisfaction score and test group differences? | I am just learning statistical analysis and I am unsure if my response would be helpful but I just want you to stop for a while and think about what you are trying to achieve through your analysis. (Often in a state of panic, one usually ends up doing all sorts of analysis)
One of the most valuable advice I have receiv... | How to calculate an overall job satisfaction score and test group differences? | I am just learning statistical analysis and I am unsure if my response would be helpful but I just want you to stop for a while and think about what you are trying to achieve through your analysis. (O | How to calculate an overall job satisfaction score and test group differences?
I am just learning statistical analysis and I am unsure if my response would be helpful but I just want you to stop for a while and think about what you are trying to achieve through your analysis. (Often in a state of panic, one usually end... | How to calculate an overall job satisfaction score and test group differences?
I am just learning statistical analysis and I am unsure if my response would be helpful but I just want you to stop for a while and think about what you are trying to achieve through your analysis. (O |
53,052 | How to calculate an overall job satisfaction score and test group differences? | The Job Satisfaction Survey or JSS, has some of its items written in each direction--positive and negative. Scores on each of nine facet subscales, based on 4 items each, can range from 4 to 24; while scores for total job satisfaction, based on the sum of all 36 items, can range from 36 to 216. Each item is scored from... | How to calculate an overall job satisfaction score and test group differences? | The Job Satisfaction Survey or JSS, has some of its items written in each direction--positive and negative. Scores on each of nine facet subscales, based on 4 items each, can range from 4 to 24; while | How to calculate an overall job satisfaction score and test group differences?
The Job Satisfaction Survey or JSS, has some of its items written in each direction--positive and negative. Scores on each of nine facet subscales, based on 4 items each, can range from 4 to 24; while scores for total job satisfaction, based... | How to calculate an overall job satisfaction score and test group differences?
The Job Satisfaction Survey or JSS, has some of its items written in each direction--positive and negative. Scores on each of nine facet subscales, based on 4 items each, can range from 4 to 24; while |
53,053 | Grouping data in ranges in R by summing them | One option is to create a new variable for your bins with cut or cut2 in package Hmisc.
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, 10))
I would then probably use plyr to do the group by summary:
library(plyr)
ddply(dat, "bin", summarize, totVal = sum(value))
The help... | Grouping data in ranges in R by summing them | One option is to create a new variable for your bins with cut or cut2 in package Hmisc.
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, 10))
I would then | Grouping data in ranges in R by summing them
One option is to create a new variable for your bins with cut or cut2 in package Hmisc.
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, 10))
I would then probably use plyr to do the group by summary:
library(plyr)
ddply(dat, "bi... | Grouping data in ranges in R by summing them
One option is to create a new variable for your bins with cut or cut2 in package Hmisc.
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, 10))
I would then |
53,054 | Grouping data in ranges in R by summing them | Interesting Chase. I hasn't seen transform and would have likely done it this (second) way:
set.seed(1234)
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, 10))
set.seed(1234)
dat2 <- data.frame(year = 1901:2000, value = runif(100))
dat2$bin <- cut(dat$year, 10)
identical(... | Grouping data in ranges in R by summing them | Interesting Chase. I hasn't seen transform and would have likely done it this (second) way:
set.seed(1234)
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, | Grouping data in ranges in R by summing them
Interesting Chase. I hasn't seen transform and would have likely done it this (second) way:
set.seed(1234)
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, 10))
set.seed(1234)
dat2 <- data.frame(year = 1901:2000, value = runif(10... | Grouping data in ranges in R by summing them
Interesting Chase. I hasn't seen transform and would have likely done it this (second) way:
set.seed(1234)
dat <- data.frame(year = 1901:2000, value = runif(100))
dat <- transform(dat, bin = cut(year, |
53,055 | Logistic regression and Wilcoxon test | Did you just fit one big glm model then look at the individual p-values?
Remember that those p-values are measuring the effect of that variable above and beyond all other variables in the model. It is possible that more of your covariates are really contributing, but there is redundant information, so they don't show ... | Logistic regression and Wilcoxon test | Did you just fit one big glm model then look at the individual p-values?
Remember that those p-values are measuring the effect of that variable above and beyond all other variables in the model. It i | Logistic regression and Wilcoxon test
Did you just fit one big glm model then look at the individual p-values?
Remember that those p-values are measuring the effect of that variable above and beyond all other variables in the model. It is possible that more of your covariates are really contributing, but there is redu... | Logistic regression and Wilcoxon test
Did you just fit one big glm model then look at the individual p-values?
Remember that those p-values are measuring the effect of that variable above and beyond all other variables in the model. It i |
53,056 | Logistic regression and Wilcoxon test | The tests make different assumptions, and so do not give exactly the same result. The bigger problem is the (incorrect) assumption that failure to reject the null "indicates that there is no difference". It does not. It just means that you don't have enough evidence to reject the null of no difference. | Logistic regression and Wilcoxon test | The tests make different assumptions, and so do not give exactly the same result. The bigger problem is the (incorrect) assumption that failure to reject the null "indicates that there is no differenc | Logistic regression and Wilcoxon test
The tests make different assumptions, and so do not give exactly the same result. The bigger problem is the (incorrect) assumption that failure to reject the null "indicates that there is no difference". It does not. It just means that you don't have enough evidence to reject the n... | Logistic regression and Wilcoxon test
The tests make different assumptions, and so do not give exactly the same result. The bigger problem is the (incorrect) assumption that failure to reject the null "indicates that there is no differenc |
53,057 | Logistic regression and Wilcoxon test | The more appropriate comparator is the proportional odds model, which contains the Wilcoxon test as a special case. And note that 'multivariate' refers to the simultaneous analysis of more than one dependent variable. I think you meant to say 'multivariable'. | Logistic regression and Wilcoxon test | The more appropriate comparator is the proportional odds model, which contains the Wilcoxon test as a special case. And note that 'multivariate' refers to the simultaneous analysis of more than one d | Logistic regression and Wilcoxon test
The more appropriate comparator is the proportional odds model, which contains the Wilcoxon test as a special case. And note that 'multivariate' refers to the simultaneous analysis of more than one dependent variable. I think you meant to say 'multivariable'. | Logistic regression and Wilcoxon test
The more appropriate comparator is the proportional odds model, which contains the Wilcoxon test as a special case. And note that 'multivariate' refers to the simultaneous analysis of more than one d |
53,058 | Logistic regression and Wilcoxon test | If I understand things correctly, you're testing if the mean value of predictor $A$ associated with outcome $1$ differ from the mean value of predictor A associated with outcome $2$. Even if they don't differ, this result says nothing to your research question. What it says is only that in your sample, the average valu... | Logistic regression and Wilcoxon test | If I understand things correctly, you're testing if the mean value of predictor $A$ associated with outcome $1$ differ from the mean value of predictor A associated with outcome $2$. Even if they don' | Logistic regression and Wilcoxon test
If I understand things correctly, you're testing if the mean value of predictor $A$ associated with outcome $1$ differ from the mean value of predictor A associated with outcome $2$. Even if they don't differ, this result says nothing to your research question. What it says is only... | Logistic regression and Wilcoxon test
If I understand things correctly, you're testing if the mean value of predictor $A$ associated with outcome $1$ differ from the mean value of predictor A associated with outcome $2$. Even if they don' |
53,059 | Logistic regression and Wilcoxon test | The p-value that you got for the parametric test (from glm) depends on the effect size, i.e., by how much can the predicted values change depending on the value of A. Now if a small proportion (that proportion may be dependent on other predictors) of predicted values change by a large quantity due to the variable A, yo... | Logistic regression and Wilcoxon test | The p-value that you got for the parametric test (from glm) depends on the effect size, i.e., by how much can the predicted values change depending on the value of A. Now if a small proportion (that p | Logistic regression and Wilcoxon test
The p-value that you got for the parametric test (from glm) depends on the effect size, i.e., by how much can the predicted values change depending on the value of A. Now if a small proportion (that proportion may be dependent on other predictors) of predicted values change by a la... | Logistic regression and Wilcoxon test
The p-value that you got for the parametric test (from glm) depends on the effect size, i.e., by how much can the predicted values change depending on the value of A. Now if a small proportion (that p |
53,060 | Interpreting Gaussian probabilities greater than 1 [duplicate] | The code in the question returns the values of probability density function. The values of probability density function can be greater than one. The actual probability $P(X<x)$ for random variable $X$ with probability density function $p(x)$ is integral $\int_{-\infty}^xp(t)dt$. The values of this integral are of cours... | Interpreting Gaussian probabilities greater than 1 [duplicate] | The code in the question returns the values of probability density function. The values of probability density function can be greater than one. The actual probability $P(X<x)$ for random variable $X$ | Interpreting Gaussian probabilities greater than 1 [duplicate]
The code in the question returns the values of probability density function. The values of probability density function can be greater than one. The actual probability $P(X<x)$ for random variable $X$ with probability density function $p(x)$ is integral $\i... | Interpreting Gaussian probabilities greater than 1 [duplicate]
The code in the question returns the values of probability density function. The values of probability density function can be greater than one. The actual probability $P(X<x)$ for random variable $X$ |
53,061 | Excel xy chart with unequal x values in series | Use a Scatter Plot where the horizontal axis is time. Below is a screenshot of an Excel sheet where two temperatures are shown. Temp 1 starts at 9:00:00 AM and increments by 1 minute and 26 seconds. Temp 2 starts at 9:30:00 AM and increments by 2 minutes and 53 seconds. They are both plotted in the graph.
As sh... | Excel xy chart with unequal x values in series | Use a Scatter Plot where the horizontal axis is time. Below is a screenshot of an Excel sheet where two temperatures are shown. Temp 1 starts at 9:00:00 AM and increments by 1 minute and 26 seconds | Excel xy chart with unequal x values in series
Use a Scatter Plot where the horizontal axis is time. Below is a screenshot of an Excel sheet where two temperatures are shown. Temp 1 starts at 9:00:00 AM and increments by 1 minute and 26 seconds. Temp 2 starts at 9:30:00 AM and increments by 2 minutes and 53 secon... | Excel xy chart with unequal x values in series
Use a Scatter Plot where the horizontal axis is time. Below is a screenshot of an Excel sheet where two temperatures are shown. Temp 1 starts at 9:00:00 AM and increments by 1 minute and 26 seconds |
53,062 | Excel xy chart with unequal x values in series | Simple answer:
Select one set of X and Y values, and create your XY chart.
Copy the second set of X and Y values, select the chart, and use paste special to add the data as a new series. | Excel xy chart with unequal x values in series | Simple answer:
Select one set of X and Y values, and create your XY chart.
Copy the second set of X and Y values, select the chart, and use paste special to add the data as a new series. | Excel xy chart with unequal x values in series
Simple answer:
Select one set of X and Y values, and create your XY chart.
Copy the second set of X and Y values, select the chart, and use paste special to add the data as a new series. | Excel xy chart with unequal x values in series
Simple answer:
Select one set of X and Y values, and create your XY chart.
Copy the second set of X and Y values, select the chart, and use paste special to add the data as a new series. |
53,063 | Determinant perturbation approximation | I'll assume that you already know the eigenvalues of $B$. Since $B$ is symmetric positive semidefinite, it can be decomposed as
$$
B = U D U^T
$$
where $U$ is an orthogonal matrix and $D$ is the diagonal of nonnegative eigenvalues (some of which may be exactly zero).
Now
$$
B+xI = U D U^T + x U U^T = U (D + x I) U^T... | Determinant perturbation approximation | I'll assume that you already know the eigenvalues of $B$. Since $B$ is symmetric positive semidefinite, it can be decomposed as
$$
B = U D U^T
$$
where $U$ is an orthogonal matrix and $D$ is the dia | Determinant perturbation approximation
I'll assume that you already know the eigenvalues of $B$. Since $B$ is symmetric positive semidefinite, it can be decomposed as
$$
B = U D U^T
$$
where $U$ is an orthogonal matrix and $D$ is the diagonal of nonnegative eigenvalues (some of which may be exactly zero).
Now
$$
B+x... | Determinant perturbation approximation
I'll assume that you already know the eigenvalues of $B$. Since $B$ is symmetric positive semidefinite, it can be decomposed as
$$
B = U D U^T
$$
where $U$ is an orthogonal matrix and $D$ is the dia |
53,064 | Determinant perturbation approximation | I second @cardinal's answer, but provide a simple trick: If $p(z)$ is a polynomial (with integer powers), and $\mathbf{v}, \lambda$ are eigenvector and corresponding eigenvalue of matrix $M$, then $\mathbf{v}, p(\lambda)$ are eigenvector and corresponding eigenvalue of $p(M)$. The proof is a simple exercise. The polyno... | Determinant perturbation approximation | I second @cardinal's answer, but provide a simple trick: If $p(z)$ is a polynomial (with integer powers), and $\mathbf{v}, \lambda$ are eigenvector and corresponding eigenvalue of matrix $M$, then $\m | Determinant perturbation approximation
I second @cardinal's answer, but provide a simple trick: If $p(z)$ is a polynomial (with integer powers), and $\mathbf{v}, \lambda$ are eigenvector and corresponding eigenvalue of matrix $M$, then $\mathbf{v}, p(\lambda)$ are eigenvector and corresponding eigenvalue of $p(M)$. The... | Determinant perturbation approximation
I second @cardinal's answer, but provide a simple trick: If $p(z)$ is a polynomial (with integer powers), and $\mathbf{v}, \lambda$ are eigenvector and corresponding eigenvalue of matrix $M$, then $\m |
53,065 | Derivative of a linear model | @onestop points in the right direction. Belsley, Kuh, and Welsch describe this approach on pp. 24-26 of their book. To differentiate with respect to an observation (and not just one of its attributes), they introduce a weight, perform weighted least squares, and differentiate with respect to the weight.
Specifically,... | Derivative of a linear model | @onestop points in the right direction. Belsley, Kuh, and Welsch describe this approach on pp. 24-26 of their book. To differentiate with respect to an observation (and not just one of its attribute | Derivative of a linear model
@onestop points in the right direction. Belsley, Kuh, and Welsch describe this approach on pp. 24-26 of their book. To differentiate with respect to an observation (and not just one of its attributes), they introduce a weight, perform weighted least squares, and differentiate with respect... | Derivative of a linear model
@onestop points in the right direction. Belsley, Kuh, and Welsch describe this approach on pp. 24-26 of their book. To differentiate with respect to an observation (and not just one of its attribute |
53,066 | Derivative of a linear model | I guess this would come under the heading of regression diagnostics. I haven't seen this precise statistic before, but something that comes fairly close is DFBETAij, which is the the change in regression coefficient i when the jth observation is omitted divided by the estimated standard error of coefficient i.
The book... | Derivative of a linear model | I guess this would come under the heading of regression diagnostics. I haven't seen this precise statistic before, but something that comes fairly close is DFBETAij, which is the the change in regress | Derivative of a linear model
I guess this would come under the heading of regression diagnostics. I haven't seen this precise statistic before, but something that comes fairly close is DFBETAij, which is the the change in regression coefficient i when the jth observation is omitted divided by the estimated standard err... | Derivative of a linear model
I guess this would come under the heading of regression diagnostics. I haven't seen this precise statistic before, but something that comes fairly close is DFBETAij, which is the the change in regress |
53,067 | Java implementations of the lasso [closed] | About clean implementation in Python, there is the scikit.learn toolkit. The L1/L2 regularization scheme (incl. elasticnet) works great with GLM (LARS and coordinate descent algorithms available). Don't know about Java implementation. | Java implementations of the lasso [closed] | About clean implementation in Python, there is the scikit.learn toolkit. The L1/L2 regularization scheme (incl. elasticnet) works great with GLM (LARS and coordinate descent algorithms available). Don | Java implementations of the lasso [closed]
About clean implementation in Python, there is the scikit.learn toolkit. The L1/L2 regularization scheme (incl. elasticnet) works great with GLM (LARS and coordinate descent algorithms available). Don't know about Java implementation. | Java implementations of the lasso [closed]
About clean implementation in Python, there is the scikit.learn toolkit. The L1/L2 regularization scheme (incl. elasticnet) works great with GLM (LARS and coordinate descent algorithms available). Don |
53,068 | Java implementations of the lasso [closed] | lasso4j is an open source Java implementation of Lasso for linear regression. | Java implementations of the lasso [closed] | lasso4j is an open source Java implementation of Lasso for linear regression. | Java implementations of the lasso [closed]
lasso4j is an open source Java implementation of Lasso for linear regression. | Java implementations of the lasso [closed]
lasso4j is an open source Java implementation of Lasso for linear regression. |
53,069 | Java implementations of the lasso [closed] | I've just come across mlpy, which also has an implementation of the lasso (in Python.) | Java implementations of the lasso [closed] | I've just come across mlpy, which also has an implementation of the lasso (in Python.) | Java implementations of the lasso [closed]
I've just come across mlpy, which also has an implementation of the lasso (in Python.) | Java implementations of the lasso [closed]
I've just come across mlpy, which also has an implementation of the lasso (in Python.) |
53,070 | How to deduce $ \mathbb{E}(\sqrt{X}) < \infty \implies\int_{\mathbb{R}^+} (1 - F(x))^2 dx < \infty,~X$ being a non-negative integrable rv? | Interesting problem. The proof goes as follows: let $X, X_1, X_2$ i.i.d. $\sim F$, then
\begin{align}
\int_0^\infty (1 - F(x))^2dx = E[\min(X_1, X_2)] \leq E[\sqrt{X_1}\sqrt{X_2}]
= (E[\sqrt{X}])^2 < \infty.
\end{align}
By the way, the proof to the first implication is a straightforward application of Cauchy-Schwar... | How to deduce $ \mathbb{E}(\sqrt{X}) < \infty \implies\int_{\mathbb{R}^+} (1 - F(x))^2 dx < \infty,~ | Interesting problem. The proof goes as follows: let $X, X_1, X_2$ i.i.d. $\sim F$, then
\begin{align}
\int_0^\infty (1 - F(x))^2dx = E[\min(X_1, X_2)] \leq E[\sqrt{X_1}\sqrt{X_2}]
= (E[\sqrt{X}])^2 | How to deduce $ \mathbb{E}(\sqrt{X}) < \infty \implies\int_{\mathbb{R}^+} (1 - F(x))^2 dx < \infty,~X$ being a non-negative integrable rv?
Interesting problem. The proof goes as follows: let $X, X_1, X_2$ i.i.d. $\sim F$, then
\begin{align}
\int_0^\infty (1 - F(x))^2dx = E[\min(X_1, X_2)] \leq E[\sqrt{X_1}\sqrt{X_2}]... | How to deduce $ \mathbb{E}(\sqrt{X}) < \infty \implies\int_{\mathbb{R}^+} (1 - F(x))^2 dx < \infty,~
Interesting problem. The proof goes as follows: let $X, X_1, X_2$ i.i.d. $\sim F$, then
\begin{align}
\int_0^\infty (1 - F(x))^2dx = E[\min(X_1, X_2)] \leq E[\sqrt{X_1}\sqrt{X_2}]
= (E[\sqrt{X}])^2 |
53,071 | Using the Chebyshev inequality to uncover saturating distribution | I don't think Chebyshev's inequality helps in proving this reversed problem (Chebyshev's inequality only tells you, with the given condition, that $P[|X - 1/2| > \epsilon] \leq \frac{1}{4\epsilon^2}$. When $\epsilon \leq 1/2$, this is weaker than the trivial statement that $P[|X - 1/2| > \epsilon] \leq 1$. When $\epsi... | Using the Chebyshev inequality to uncover saturating distribution | I don't think Chebyshev's inequality helps in proving this reversed problem (Chebyshev's inequality only tells you, with the given condition, that $P[|X - 1/2| > \epsilon] \leq \frac{1}{4\epsilon^2}$. | Using the Chebyshev inequality to uncover saturating distribution
I don't think Chebyshev's inequality helps in proving this reversed problem (Chebyshev's inequality only tells you, with the given condition, that $P[|X - 1/2| > \epsilon] \leq \frac{1}{4\epsilon^2}$. When $\epsilon \leq 1/2$, this is weaker than the tri... | Using the Chebyshev inequality to uncover saturating distribution
I don't think Chebyshev's inequality helps in proving this reversed problem (Chebyshev's inequality only tells you, with the given condition, that $P[|X - 1/2| > \epsilon] \leq \frac{1}{4\epsilon^2}$. |
53,072 | Using the Chebyshev inequality to uncover saturating distribution | Yes, the logic of the Chebyshev's inequality can be reversed. You could say that $$\mathrm{P}(|X - \mathrm{E}[X]| \leq \sqrt{\mathrm{Var}[X]}) = 1$$
if and only if $X$ is a Bernoulli variable with parameter $p = 0.5$ shifted and scaled to match the specific mean and variance.
"If $X$ is a random variable with $0 \leq... | Using the Chebyshev inequality to uncover saturating distribution | Yes, the logic of the Chebyshev's inequality can be reversed. You could say that $$\mathrm{P}(|X - \mathrm{E}[X]| \leq \sqrt{\mathrm{Var}[X]}) = 1$$
if and only if $X$ is a Bernoulli variable with pa | Using the Chebyshev inequality to uncover saturating distribution
Yes, the logic of the Chebyshev's inequality can be reversed. You could say that $$\mathrm{P}(|X - \mathrm{E}[X]| \leq \sqrt{\mathrm{Var}[X]}) = 1$$
if and only if $X$ is a Bernoulli variable with parameter $p = 0.5$ shifted and scaled to match the spec... | Using the Chebyshev inequality to uncover saturating distribution
Yes, the logic of the Chebyshev's inequality can be reversed. You could say that $$\mathrm{P}(|X - \mathrm{E}[X]| \leq \sqrt{\mathrm{Var}[X]}) = 1$$
if and only if $X$ is a Bernoulli variable with pa |
53,073 | Are the coefficients in `lme4` correct with nested effects? | coef() gives you the adjusted coefficients (fixed + random effects) for each random-effect term separately; the key thing to know here is that Cohort/Subject is counted as two separate random effect terms by the model. That is, (Days | Cohort/Subject) is internally expanded to (Days | Cohort) + (Days | Cohort:Subject),... | Are the coefficients in `lme4` correct with nested effects? | coef() gives you the adjusted coefficients (fixed + random effects) for each random-effect term separately; the key thing to know here is that Cohort/Subject is counted as two separate random effect t | Are the coefficients in `lme4` correct with nested effects?
coef() gives you the adjusted coefficients (fixed + random effects) for each random-effect term separately; the key thing to know here is that Cohort/Subject is counted as two separate random effect terms by the model. That is, (Days | Cohort/Subject) is inter... | Are the coefficients in `lme4` correct with nested effects?
coef() gives you the adjusted coefficients (fixed + random effects) for each random-effect term separately; the key thing to know here is that Cohort/Subject is counted as two separate random effect t |
53,074 | Interpretability for chi-squared test? | The chi-square test of a 2x2 contingency table such as this basically tests the following null hypothesis: gender should produce no difference in diabetes rates. Essentially, your chi-square test poses the following question: "Is the difference in diabetes rates by gender more than we would expect?".
In this case, you ... | Interpretability for chi-squared test? | The chi-square test of a 2x2 contingency table such as this basically tests the following null hypothesis: gender should produce no difference in diabetes rates. Essentially, your chi-square test pose | Interpretability for chi-squared test?
The chi-square test of a 2x2 contingency table such as this basically tests the following null hypothesis: gender should produce no difference in diabetes rates. Essentially, your chi-square test poses the following question: "Is the difference in diabetes rates by gender more tha... | Interpretability for chi-squared test?
The chi-square test of a 2x2 contingency table such as this basically tests the following null hypothesis: gender should produce no difference in diabetes rates. Essentially, your chi-square test pose |
53,075 | Plotting a cdf in r | Note that yours is not a valid probability density function.
Indeed, you have $f(x)< 0$, for all $x< -1$. But, by definition, a PDF is always non-negative, ie.
$$f(x)\geq 0, \text{ for all } x.$$
In addition,
$$
\int_{-\infty}^{-1} 1/x^3\,dx + \int_{1}^{\infty} 1/x^3\, dx= -\frac{1}{2}+\frac{1}{2}=0.
$$
Thus the CDF is... | Plotting a cdf in r | Note that yours is not a valid probability density function.
Indeed, you have $f(x)< 0$, for all $x< -1$. But, by definition, a PDF is always non-negative, ie.
$$f(x)\geq 0, \text{ for all } x.$$
In a | Plotting a cdf in r
Note that yours is not a valid probability density function.
Indeed, you have $f(x)< 0$, for all $x< -1$. But, by definition, a PDF is always non-negative, ie.
$$f(x)\geq 0, \text{ for all } x.$$
In addition,
$$
\int_{-\infty}^{-1} 1/x^3\,dx + \int_{1}^{\infty} 1/x^3\, dx= -\frac{1}{2}+\frac{1}{2}=0... | Plotting a cdf in r
Note that yours is not a valid probability density function.
Indeed, you have $f(x)< 0$, for all $x< -1$. But, by definition, a PDF is always non-negative, ie.
$$f(x)\geq 0, \text{ for all } x.$$
In a |
53,076 | How can I compute variance of X^2 + XY where (X,Y) are normal distributed random variables? | By definition
\begin{align}
\operatorname{Var}(X(X+Y))
&=E(X^2(X+Y)^2)-(E(X(X+Y)))^2
\\&=E(X^4)+2E(X^3Y)+E(X^2Y^2)-(E(X^2)+E(XY))^2. \tag{1}
\end{align}
Using Isserlis' theorem, in terms of the variances and covariance $\sigma_{11},\sigma_{22},\sigma_{12}$ of $X$ and $Y$,
\begin{align}
E(X^4)&=3\sigma_{11}^2
\\E(X^3Y... | How can I compute variance of X^2 + XY where (X,Y) are normal distributed random variables? | By definition
\begin{align}
\operatorname{Var}(X(X+Y))
&=E(X^2(X+Y)^2)-(E(X(X+Y)))^2
\\&=E(X^4)+2E(X^3Y)+E(X^2Y^2)-(E(X^2)+E(XY))^2. \tag{1}
\end{align}
Using Isserlis' theorem, in terms of the vari | How can I compute variance of X^2 + XY where (X,Y) are normal distributed random variables?
By definition
\begin{align}
\operatorname{Var}(X(X+Y))
&=E(X^2(X+Y)^2)-(E(X(X+Y)))^2
\\&=E(X^4)+2E(X^3Y)+E(X^2Y^2)-(E(X^2)+E(XY))^2. \tag{1}
\end{align}
Using Isserlis' theorem, in terms of the variances and covariance $\sigma... | How can I compute variance of X^2 + XY where (X,Y) are normal distributed random variables?
By definition
\begin{align}
\operatorname{Var}(X(X+Y))
&=E(X^2(X+Y)^2)-(E(X(X+Y)))^2
\\&=E(X^4)+2E(X^3Y)+E(X^2Y^2)-(E(X^2)+E(XY))^2. \tag{1}
\end{align}
Using Isserlis' theorem, in terms of the vari |
53,077 | Derivative of the Backshift Operator? | The backshift operator is a mapping (an "operator") between vector spaces, namely spaces of time series or sequences,
$$ B\colon \mathbb{R}^\mathbb{N} \to \mathbb{R}^\mathbb{N}, (y_i)\mapsto (y_{i-1}). $$
Here, $\mathbb{R}^\mathbb{N}$ is the space of mappings from $\mathbb{N}$ to $\mathbb{R}$, i.e., of real-valued sequ... | Derivative of the Backshift Operator? | The backshift operator is a mapping (an "operator") between vector spaces, namely spaces of time series or sequences,
$$ B\colon \mathbb{R}^\mathbb{N} \to \mathbb{R}^\mathbb{N}, (y_i)\mapsto (y_{i-1}) | Derivative of the Backshift Operator?
The backshift operator is a mapping (an "operator") between vector spaces, namely spaces of time series or sequences,
$$ B\colon \mathbb{R}^\mathbb{N} \to \mathbb{R}^\mathbb{N}, (y_i)\mapsto (y_{i-1}). $$
Here, $\mathbb{R}^\mathbb{N}$ is the space of mappings from $\mathbb{N}$ to $... | Derivative of the Backshift Operator?
The backshift operator is a mapping (an "operator") between vector spaces, namely spaces of time series or sequences,
$$ B\colon \mathbb{R}^\mathbb{N} \to \mathbb{R}^\mathbb{N}, (y_i)\mapsto (y_{i-1}) |
53,078 | Log of a log-transformed variable | One thing that comes to mind for exploratory data analysis (EDA), applicable for 1D distributions, is to plot the quantiles (related to the empirical cumulative distribution function) in various transformed axes: linear-vs-linear, log-vs-linear, linear-vs-log, log-vs-log, etc.
Having done so, some hypotheses may be for... | Log of a log-transformed variable | One thing that comes to mind for exploratory data analysis (EDA), applicable for 1D distributions, is to plot the quantiles (related to the empirical cumulative distribution function) in various trans | Log of a log-transformed variable
One thing that comes to mind for exploratory data analysis (EDA), applicable for 1D distributions, is to plot the quantiles (related to the empirical cumulative distribution function) in various transformed axes: linear-vs-linear, log-vs-linear, linear-vs-log, log-vs-log, etc.
Having d... | Log of a log-transformed variable
One thing that comes to mind for exploratory data analysis (EDA), applicable for 1D distributions, is to plot the quantiles (related to the empirical cumulative distribution function) in various trans |
53,079 | Is the sample proportion ($\hat p$) a random variable? | In the frequentist tradition (which is what you are using here) the random variable is the data. The population parameters are mathematically treated as constant. This is what leads to the somewhat counterintuitive "null hypothesis" setup we use in intro statistics, because the probability we return (usually in the for... | Is the sample proportion ($\hat p$) a random variable? | In the frequentist tradition (which is what you are using here) the random variable is the data. The population parameters are mathematically treated as constant. This is what leads to the somewhat co | Is the sample proportion ($\hat p$) a random variable?
In the frequentist tradition (which is what you are using here) the random variable is the data. The population parameters are mathematically treated as constant. This is what leads to the somewhat counterintuitive "null hypothesis" setup we use in intro statistics... | Is the sample proportion ($\hat p$) a random variable?
In the frequentist tradition (which is what you are using here) the random variable is the data. The population parameters are mathematically treated as constant. This is what leads to the somewhat co |
53,080 | Is the sample proportion ($\hat p$) a random variable? | I don't see a $\hat{p}$ in the figure you posted, but from the formula in the figure, $p_1$ and $p_2$ are statistics. Once you calculate a statistic, it becomes a realization of the random variable (Be aware that I am not saying that your statistic is the true population parameter).
Above all, remember that in most cas... | Is the sample proportion ($\hat p$) a random variable? | I don't see a $\hat{p}$ in the figure you posted, but from the formula in the figure, $p_1$ and $p_2$ are statistics. Once you calculate a statistic, it becomes a realization of the random variable (B | Is the sample proportion ($\hat p$) a random variable?
I don't see a $\hat{p}$ in the figure you posted, but from the formula in the figure, $p_1$ and $p_2$ are statistics. Once you calculate a statistic, it becomes a realization of the random variable (Be aware that I am not saying that your statistic is the true popu... | Is the sample proportion ($\hat p$) a random variable?
I don't see a $\hat{p}$ in the figure you posted, but from the formula in the figure, $p_1$ and $p_2$ are statistics. Once you calculate a statistic, it becomes a realization of the random variable (B |
53,081 | Is the sample proportion ($\hat p$) a random variable? | A statistic is a function of a random sample, therefore it is also random variable.
Like Tanner Phillips says in his answer, the frequentist school of statistics establishes a difference between a population and a sample taken from the population. Population parameters are [always] constants and to estimate those param... | Is the sample proportion ($\hat p$) a random variable? | A statistic is a function of a random sample, therefore it is also random variable.
Like Tanner Phillips says in his answer, the frequentist school of statistics establishes a difference between a pop | Is the sample proportion ($\hat p$) a random variable?
A statistic is a function of a random sample, therefore it is also random variable.
Like Tanner Phillips says in his answer, the frequentist school of statistics establishes a difference between a population and a sample taken from the population. Population parame... | Is the sample proportion ($\hat p$) a random variable?
A statistic is a function of a random sample, therefore it is also random variable.
Like Tanner Phillips says in his answer, the frequentist school of statistics establishes a difference between a pop |
53,082 | What is the correct interpretation of the $\beta_1$ coefficient in a linear regression model? | Here is what $E[Y|X]$ changes when $X$ changes by one unit (using that the expectation operator is linear and that $\epsilon$ is independent of $X$ with $E[\epsilon] = 0$):
$$
\begin{align}
E[Y|X = x_0+1] - E[Y|X=x_0] &= E[\beta_0 + \beta_1X + \epsilon|X=x_0+1] - E[\beta_0 + \beta_1X + \epsilon|X=x_0]\\
&= \beta_0 ... | What is the correct interpretation of the $\beta_1$ coefficient in a linear regression model? | Here is what $E[Y|X]$ changes when $X$ changes by one unit (using that the expectation operator is linear and that $\epsilon$ is independent of $X$ with $E[\epsilon] = 0$):
$$
\begin{align}
E[Y|X = x_ | What is the correct interpretation of the $\beta_1$ coefficient in a linear regression model?
Here is what $E[Y|X]$ changes when $X$ changes by one unit (using that the expectation operator is linear and that $\epsilon$ is independent of $X$ with $E[\epsilon] = 0$):
$$
\begin{align}
E[Y|X = x_0+1] - E[Y|X=x_0] &= E[\be... | What is the correct interpretation of the $\beta_1$ coefficient in a linear regression model?
Here is what $E[Y|X]$ changes when $X$ changes by one unit (using that the expectation operator is linear and that $\epsilon$ is independent of $X$ with $E[\epsilon] = 0$):
$$
\begin{align}
E[Y|X = x_ |
53,083 | How are sums and differences of independent Exponential random variables distributed? | Because the characteristic function of an exponential distribution is
$$\phi(t) = \frac{1}{1 - it},$$
when $X_1,\ldots, X_4$ are independent exponentially distributed variables (all with the same rate, which with no loss of generality may be taken as unity), the characteristic function of $X = X_1+X_2+X_3-X_4$ is
$$\ph... | How are sums and differences of independent Exponential random variables distributed? | Because the characteristic function of an exponential distribution is
$$\phi(t) = \frac{1}{1 - it},$$
when $X_1,\ldots, X_4$ are independent exponentially distributed variables (all with the same rate | How are sums and differences of independent Exponential random variables distributed?
Because the characteristic function of an exponential distribution is
$$\phi(t) = \frac{1}{1 - it},$$
when $X_1,\ldots, X_4$ are independent exponentially distributed variables (all with the same rate, which with no loss of generality... | How are sums and differences of independent Exponential random variables distributed?
Because the characteristic function of an exponential distribution is
$$\phi(t) = \frac{1}{1 - it},$$
when $X_1,\ldots, X_4$ are independent exponentially distributed variables (all with the same rate |
53,084 | When does the sum of two $t$-distributed random variables follow a $t$ distribution? | Characteristic functions are handy for studying sums of independent variables, because the c.f. of the sum is the product of the c.f.s of the addends and c.f.s determine the distribution.
The c.f. of a Student t variable with parameter ("degrees of freedom") $\nu \ge 1$ is, up to a constant of proportionality $C(\nu)$ ... | When does the sum of two $t$-distributed random variables follow a $t$ distribution? | Characteristic functions are handy for studying sums of independent variables, because the c.f. of the sum is the product of the c.f.s of the addends and c.f.s determine the distribution.
The c.f. of | When does the sum of two $t$-distributed random variables follow a $t$ distribution?
Characteristic functions are handy for studying sums of independent variables, because the c.f. of the sum is the product of the c.f.s of the addends and c.f.s determine the distribution.
The c.f. of a Student t variable with parameter... | When does the sum of two $t$-distributed random variables follow a $t$ distribution?
Characteristic functions are handy for studying sums of independent variables, because the c.f. of the sum is the product of the c.f.s of the addends and c.f.s determine the distribution.
The c.f. of |
53,085 | When does the sum of two $t$-distributed random variables follow a $t$ distribution? | Here is a much less formal approach that (mainly) relies on the fact that moments of order $\nu$ or larger do not exist for Student's t-distributions with $\nu$ degrees of freedom.
If $X_\nu$ and $Y_\nu$ have independent Student's t-distributions with $\nu$ degrees of freedom where the moments of order $\nu$ or higher ... | When does the sum of two $t$-distributed random variables follow a $t$ distribution? | Here is a much less formal approach that (mainly) relies on the fact that moments of order $\nu$ or larger do not exist for Student's t-distributions with $\nu$ degrees of freedom.
If $X_\nu$ and $Y_\ | When does the sum of two $t$-distributed random variables follow a $t$ distribution?
Here is a much less formal approach that (mainly) relies on the fact that moments of order $\nu$ or larger do not exist for Student's t-distributions with $\nu$ degrees of freedom.
If $X_\nu$ and $Y_\nu$ have independent Student's t-di... | When does the sum of two $t$-distributed random variables follow a $t$ distribution?
Here is a much less formal approach that (mainly) relies on the fact that moments of order $\nu$ or larger do not exist for Student's t-distributions with $\nu$ degrees of freedom.
If $X_\nu$ and $Y_\ |
53,086 | Setting null hypothesis for Binomial test | No, it is not correct. In this example you have two samples so you should be using a two-sample hypothesis test. There are a few different two-sample binomial tests available, so you will need to choose one. | Setting null hypothesis for Binomial test | No, it is not correct. In this example you have two samples so you should be using a two-sample hypothesis test. There are a few different two-sample binomial tests available, so you will need to ch | Setting null hypothesis for Binomial test
No, it is not correct. In this example you have two samples so you should be using a two-sample hypothesis test. There are a few different two-sample binomial tests available, so you will need to choose one. | Setting null hypothesis for Binomial test
No, it is not correct. In this example you have two samples so you should be using a two-sample hypothesis test. There are a few different two-sample binomial tests available, so you will need to ch |
53,087 | Setting null hypothesis for Binomial test | Is it correct to use one sample binomial test to check if 9 out of 10 (90%) is significantly different using 68% as expected probability?
I don't think this is correct because you would assume that 68% was measured without uncertainty. Intuitively, 68% obtained from 10000 flips is "better", more certain than 68% from ... | Setting null hypothesis for Binomial test | Is it correct to use one sample binomial test to check if 9 out of 10 (90%) is significantly different using 68% as expected probability?
I don't think this is correct because you would assume that 6 | Setting null hypothesis for Binomial test
Is it correct to use one sample binomial test to check if 9 out of 10 (90%) is significantly different using 68% as expected probability?
I don't think this is correct because you would assume that 68% was measured without uncertainty. Intuitively, 68% obtained from 10000 flip... | Setting null hypothesis for Binomial test
Is it correct to use one sample binomial test to check if 9 out of 10 (90%) is significantly different using 68% as expected probability?
I don't think this is correct because you would assume that 6 |
53,088 | Setting null hypothesis for Binomial test | No, you treat the result from your sample of 100 ($\hat{p}=68/100$) as a sample statistic not a population proportion. If you repeated that trial of $100$ before the second bending, you would be very likely not to get $68$ on the second attempt; you'd see $65$ or $74$ or $70$ or $63$, or some other number, and a third ... | Setting null hypothesis for Binomial test | No, you treat the result from your sample of 100 ($\hat{p}=68/100$) as a sample statistic not a population proportion. If you repeated that trial of $100$ before the second bending, you would be very | Setting null hypothesis for Binomial test
No, you treat the result from your sample of 100 ($\hat{p}=68/100$) as a sample statistic not a population proportion. If you repeated that trial of $100$ before the second bending, you would be very likely not to get $68$ on the second attempt; you'd see $65$ or $74$ or $70$ o... | Setting null hypothesis for Binomial test
No, you treat the result from your sample of 100 ($\hat{p}=68/100$) as a sample statistic not a population proportion. If you repeated that trial of $100$ before the second bending, you would be very |
53,089 | Linear regression: highly-correlated features but not redundant | The correlation affects the standard errors on coefficients, but, at least under nice conditions that are typical to assume, the OLS solution is unbiased. Regress away, knowing that there is uncertainty in your estimates. If that uncertainty is small enough (that's a decision for you to make with your knowledge of the ... | Linear regression: highly-correlated features but not redundant | The correlation affects the standard errors on coefficients, but, at least under nice conditions that are typical to assume, the OLS solution is unbiased. Regress away, knowing that there is uncertain | Linear regression: highly-correlated features but not redundant
The correlation affects the standard errors on coefficients, but, at least under nice conditions that are typical to assume, the OLS solution is unbiased. Regress away, knowing that there is uncertainty in your estimates. If that uncertainty is small enoug... | Linear regression: highly-correlated features but not redundant
The correlation affects the standard errors on coefficients, but, at least under nice conditions that are typical to assume, the OLS solution is unbiased. Regress away, knowing that there is uncertain |
53,090 | Why does the von Mises-Fisher distribution need two parameters? | The von Mises-Fisher distribution is a distribution on the surface of a sphere. To make it as easy to visualize, think of a circle. The vM-F distribution has two parameters: the mean direction in which points are distributed on the circle, and how concentrated they are around the point on the circle in that mean dire... | Why does the von Mises-Fisher distribution need two parameters? | The von Mises-Fisher distribution is a distribution on the surface of a sphere. To make it as easy to visualize, think of a circle. The vM-F distribution has two parameters: the mean direction in wh | Why does the von Mises-Fisher distribution need two parameters?
The von Mises-Fisher distribution is a distribution on the surface of a sphere. To make it as easy to visualize, think of a circle. The vM-F distribution has two parameters: the mean direction in which points are distributed on the circle, and how concen... | Why does the von Mises-Fisher distribution need two parameters?
The von Mises-Fisher distribution is a distribution on the surface of a sphere. To make it as easy to visualize, think of a circle. The vM-F distribution has two parameters: the mean direction in wh |
53,091 | Why does the von Mises-Fisher distribution need two parameters? | In geometry we represent directions with a unit norm vector, so $\mu$ represents the direction. That's why its norm is $||\mu||=1.$ The other parameter is similar to variance in that it represents how directions are concentrated around $\mu.$
You can pack $\kappa$ into $\vec\mu$ as its magnitude $\vec\mu'=\kappa\vec\mu... | Why does the von Mises-Fisher distribution need two parameters? | In geometry we represent directions with a unit norm vector, so $\mu$ represents the direction. That's why its norm is $||\mu||=1.$ The other parameter is similar to variance in that it represents how | Why does the von Mises-Fisher distribution need two parameters?
In geometry we represent directions with a unit norm vector, so $\mu$ represents the direction. That's why its norm is $||\mu||=1.$ The other parameter is similar to variance in that it represents how directions are concentrated around $\mu.$
You can pack ... | Why does the von Mises-Fisher distribution need two parameters?
In geometry we represent directions with a unit norm vector, so $\mu$ represents the direction. That's why its norm is $||\mu||=1.$ The other parameter is similar to variance in that it represents how |
53,092 | Why does the von Mises-Fisher distribution need two parameters? | Why does the von Mises-Fisher distribution need two parameters?
We do not necessarily need two sets of parameters: location and scale. You can combine them into one set or in another alternative parameterization. But, nobody has found it useful to describe the distribution that way (or at least not enough people such ... | Why does the von Mises-Fisher distribution need two parameters? | Why does the von Mises-Fisher distribution need two parameters?
We do not necessarily need two sets of parameters: location and scale. You can combine them into one set or in another alternative para | Why does the von Mises-Fisher distribution need two parameters?
Why does the von Mises-Fisher distribution need two parameters?
We do not necessarily need two sets of parameters: location and scale. You can combine them into one set or in another alternative parameterization. But, nobody has found it useful to describ... | Why does the von Mises-Fisher distribution need two parameters?
Why does the von Mises-Fisher distribution need two parameters?
We do not necessarily need two sets of parameters: location and scale. You can combine them into one set or in another alternative para |
53,093 | Does it make sense to have 2 branches resulting in same decision while using one single variable to divide the predictor multiple times? | Does it make sense to use one variable multiple times for dividing the
predictor?
Yes, if the variable is useful and has different regions that are not connnected, it can be used mutliple times, e.g. return 1 if 1<x<4 else 0 would require two splits.
Is it possible that two splits result in the same decision?
It is ... | Does it make sense to have 2 branches resulting in same decision while using one single variable to | Does it make sense to use one variable multiple times for dividing the
predictor?
Yes, if the variable is useful and has different regions that are not connnected, it can be used mutliple times, e.g. | Does it make sense to have 2 branches resulting in same decision while using one single variable to divide the predictor multiple times?
Does it make sense to use one variable multiple times for dividing the
predictor?
Yes, if the variable is useful and has different regions that are not connnected, it can be used mut... | Does it make sense to have 2 branches resulting in same decision while using one single variable to
Does it make sense to use one variable multiple times for dividing the
predictor?
Yes, if the variable is useful and has different regions that are not connnected, it can be used mutliple times, e.g. |
53,094 | Does it make sense to have 2 branches resulting in same decision while using one single variable to divide the predictor multiple times? | Absolutely. In one particular case, you may have a non-monotonic relationship between the continuous variable and the target, so that the "correct" tree will have several switches from No to Yes along the leaves from left to right.
Yes. While the final "answer" Yes/No can be the same in two leaves from the same pare... | Does it make sense to have 2 branches resulting in same decision while using one single variable to | Absolutely. In one particular case, you may have a non-monotonic relationship between the continuous variable and the target, so that the "correct" tree will have several switches from No to Yes alon | Does it make sense to have 2 branches resulting in same decision while using one single variable to divide the predictor multiple times?
Absolutely. In one particular case, you may have a non-monotonic relationship between the continuous variable and the target, so that the "correct" tree will have several switches fr... | Does it make sense to have 2 branches resulting in same decision while using one single variable to
Absolutely. In one particular case, you may have a non-monotonic relationship between the continuous variable and the target, so that the "correct" tree will have several switches from No to Yes alon |
53,095 | Does it make sense to have 2 branches resulting in same decision while using one single variable to divide the predictor multiple times? | YES & YES
set.seed(2021)
N <- 10
x0 <- c(runif(N, -4, -2), runif(N, 2, 4))
x1 <- runif(2*N, -2, 2)
plot(x0, rep(1, 2*N), col = 'red')
points(x1, rep(1, 2*N), col = 'blue')
(If someone could run this in R and post the picture, that would be fantastic.)
If you're above $0$, the color depends on if you're above $2$. If y... | Does it make sense to have 2 branches resulting in same decision while using one single variable to | YES & YES
set.seed(2021)
N <- 10
x0 <- c(runif(N, -4, -2), runif(N, 2, 4))
x1 <- runif(2*N, -2, 2)
plot(x0, rep(1, 2*N), col = 'red')
points(x1, rep(1, 2*N), col = 'blue')
(If someone could run this | Does it make sense to have 2 branches resulting in same decision while using one single variable to divide the predictor multiple times?
YES & YES
set.seed(2021)
N <- 10
x0 <- c(runif(N, -4, -2), runif(N, 2, 4))
x1 <- runif(2*N, -2, 2)
plot(x0, rep(1, 2*N), col = 'red')
points(x1, rep(1, 2*N), col = 'blue')
(If someon... | Does it make sense to have 2 branches resulting in same decision while using one single variable to
YES & YES
set.seed(2021)
N <- 10
x0 <- c(runif(N, -4, -2), runif(N, 2, 4))
x1 <- runif(2*N, -2, 2)
plot(x0, rep(1, 2*N), col = 'red')
points(x1, rep(1, 2*N), col = 'blue')
(If someone could run this |
53,096 | Why the pearson correlation p-value doesn't fully correspond to CI in R? | Nearly all such questions are answered in the help on the relevant functions.
From the help for cor.test:
If method is "pearson", the test statistic is based on Pearson's product moment correlation coefficient cor(x, y) and follows a t distribution with length(x)-2 degrees of freedom if the samples follow independent ... | Why the pearson correlation p-value doesn't fully correspond to CI in R? | Nearly all such questions are answered in the help on the relevant functions.
From the help for cor.test:
If method is "pearson", the test statistic is based on Pearson's product moment correlation c | Why the pearson correlation p-value doesn't fully correspond to CI in R?
Nearly all such questions are answered in the help on the relevant functions.
From the help for cor.test:
If method is "pearson", the test statistic is based on Pearson's product moment correlation coefficient cor(x, y) and follows a t distributi... | Why the pearson correlation p-value doesn't fully correspond to CI in R?
Nearly all such questions are answered in the help on the relevant functions.
From the help for cor.test:
If method is "pearson", the test statistic is based on Pearson's product moment correlation c |
53,097 | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference? | Note that the likelihood function as defined by Etz is still given by the same conditional probability. I.e.:
$$
L(H) = p(D|H)
$$
When we write it as $L(H)$ (or $\mathcal{L}(H)$, or similar), we emphasize that we're evaluating $p(D|H)$ as a function of $H$ (with $D$ fixed), rather than of $D$ (with $H$ fixed).
However,... | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference? | Note that the likelihood function as defined by Etz is still given by the same conditional probability. I.e.:
$$
L(H) = p(D|H)
$$
When we write it as $L(H)$ (or $\mathcal{L}(H)$, or similar), we empha | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference?
Note that the likelihood function as defined by Etz is still given by the same conditional probability. I.e.:
$$
L(H) = p(D|H)
$$
When we write it as $L(H)$ (or $\mathcal{L}(H)$, or similar), we emphasize that we're evaluating $p(D|H)$ as a function ... | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference?
Note that the likelihood function as defined by Etz is still given by the same conditional probability. I.e.:
$$
L(H) = p(D|H)
$$
When we write it as $L(H)$ (or $\mathcal{L}(H)$, or similar), we empha |
53,098 | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference? | This seems to be mostly matters of convention. Let me say mine, and clarify the actual important properties besides the nomenclature.
$$
\text{Likelihood} = L(\theta) = P\left(\text{Observed data} \, \middle| \, \theta\right)
$$
Note well, that here we consider the observed data. This is neither a distribution in terms... | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference? | This seems to be mostly matters of convention. Let me say mine, and clarify the actual important properties besides the nomenclature.
$$
\text{Likelihood} = L(\theta) = P\left(\text{Observed data} \, | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference?
This seems to be mostly matters of convention. Let me say mine, and clarify the actual important properties besides the nomenclature.
$$
\text{Likelihood} = L(\theta) = P\left(\text{Observed data} \, \middle| \, \theta\right)
$$
Note well, that here ... | Is it accurate to call P(D|H) the 'likelihood' in Bayesian inference?
This seems to be mostly matters of convention. Let me say mine, and clarify the actual important properties besides the nomenclature.
$$
\text{Likelihood} = L(\theta) = P\left(\text{Observed data} \, |
53,099 | Should I make equally sized samples for the Mann-Whitney U test if originally I have unequal sample sizes | Use your original data.
Claims about losing power when groups have unequal sizes make more sense in the context of designing the experiment. If you have enough resources to make $100$ observations, the greatest power will be when you allocate $50$ to the control group and the other $50$ to the treatment group. However,... | Should I make equally sized samples for the Mann-Whitney U test if originally I have unequal sample | Use your original data.
Claims about losing power when groups have unequal sizes make more sense in the context of designing the experiment. If you have enough resources to make $100$ observations, th | Should I make equally sized samples for the Mann-Whitney U test if originally I have unequal sample sizes
Use your original data.
Claims about losing power when groups have unequal sizes make more sense in the context of designing the experiment. If you have enough resources to make $100$ observations, the greatest pow... | Should I make equally sized samples for the Mann-Whitney U test if originally I have unequal sample
Use your original data.
Claims about losing power when groups have unequal sizes make more sense in the context of designing the experiment. If you have enough resources to make $100$ observations, th |
53,100 | Riddler puzzle - distance from origin after two random jumps of equal length | The original 'riddler' problem at FiveThirtyEight appears to be asking about the mode of the distribution rather than its expected value. In any case, if we can find the distribution then we can find both the mode and the expected value.
Your initial trigonometric expression for the length looks wrong to me, and I thi... | Riddler puzzle - distance from origin after two random jumps of equal length | The original 'riddler' problem at FiveThirtyEight appears to be asking about the mode of the distribution rather than its expected value. In any case, if we can find the distribution then we can find | Riddler puzzle - distance from origin after two random jumps of equal length
The original 'riddler' problem at FiveThirtyEight appears to be asking about the mode of the distribution rather than its expected value. In any case, if we can find the distribution then we can find both the mode and the expected value.
Your... | Riddler puzzle - distance from origin after two random jumps of equal length
The original 'riddler' problem at FiveThirtyEight appears to be asking about the mode of the distribution rather than its expected value. In any case, if we can find the distribution then we can find |
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