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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1,801 | Generate a random variable with a defined correlation to an existing variable(s) | Let $X$ be your fixed variable and you want to generate $Y$ variable that correlates with $X$ by amount $r$. If $X$ is standardized then (because $r$ is beta coefficient in simple regression) $Y= rX+E$, where $E$ is random variable from normal distribution having mean $0$ and $\text{sd}=\sqrt{1-r^2}$. Observed correlat... | Generate a random variable with a defined correlation to an existing variable(s) | Let $X$ be your fixed variable and you want to generate $Y$ variable that correlates with $X$ by amount $r$. If $X$ is standardized then (because $r$ is beta coefficient in simple regression) $Y= rX+E | Generate a random variable with a defined correlation to an existing variable(s)
Let $X$ be your fixed variable and you want to generate $Y$ variable that correlates with $X$ by amount $r$. If $X$ is standardized then (because $r$ is beta coefficient in simple regression) $Y= rX+E$, where $E$ is random variable from no... | Generate a random variable with a defined correlation to an existing variable(s)
Let $X$ be your fixed variable and you want to generate $Y$ variable that correlates with $X$ by amount $r$. If $X$ is standardized then (because $r$ is beta coefficient in simple regression) $Y= rX+E |
1,802 | Generate a random variable with a defined correlation to an existing variable(s) | I felt like doing some programming, so I took @Adam's deleted answer and decided to write a nice implementation in R. I focus on using a functionally oriented style (i.e. lapply style looping). The general idea is to take two vectors, randomly permute one of the vectors until a certain correlation has been reached betw... | Generate a random variable with a defined correlation to an existing variable(s) | I felt like doing some programming, so I took @Adam's deleted answer and decided to write a nice implementation in R. I focus on using a functionally oriented style (i.e. lapply style looping). The ge | Generate a random variable with a defined correlation to an existing variable(s)
I felt like doing some programming, so I took @Adam's deleted answer and decided to write a nice implementation in R. I focus on using a functionally oriented style (i.e. lapply style looping). The general idea is to take two vectors, rand... | Generate a random variable with a defined correlation to an existing variable(s)
I felt like doing some programming, so I took @Adam's deleted answer and decided to write a nice implementation in R. I focus on using a functionally oriented style (i.e. lapply style looping). The ge |
1,803 | Generate a random variable with a defined correlation to an existing variable(s) | Let's solve a more general problem: given variable $Y_1$ how to generate the random variables $Y_2,\dots,Y_n$ with correlation matrix $R$?
Solution:
get the cholesky decomposition of the correlation matrix $CC^T=R$
create independent random vectors $X_2,\dots,X_n$ of the same length as $Y_1$
Use $Y_1$ as the first co... | Generate a random variable with a defined correlation to an existing variable(s) | Let's solve a more general problem: given variable $Y_1$ how to generate the random variables $Y_2,\dots,Y_n$ with correlation matrix $R$?
Solution:
get the cholesky decomposition of the correlation | Generate a random variable with a defined correlation to an existing variable(s)
Let's solve a more general problem: given variable $Y_1$ how to generate the random variables $Y_2,\dots,Y_n$ with correlation matrix $R$?
Solution:
get the cholesky decomposition of the correlation matrix $CC^T=R$
create independent ran... | Generate a random variable with a defined correlation to an existing variable(s)
Let's solve a more general problem: given variable $Y_1$ how to generate the random variables $Y_2,\dots,Y_n$ with correlation matrix $R$?
Solution:
get the cholesky decomposition of the correlation |
1,804 | Generate a random variable with a defined correlation to an existing variable(s) | Equivalent Python answer to @caracal 's :
import math
import numpy as np
import scipy.stats as ss
from scipy import linalg
n = 20 # length of vector
rho = 0.6 # desired correlation = cos(angle)
theta = math.acos(rho)# corresponding angle
mu1=3
sigma1 = 0.5
mu2= 2
sigma2=0.2
x1 = np.random.normal(mu1, sigma1, n)
x2... | Generate a random variable with a defined correlation to an existing variable(s) | Equivalent Python answer to @caracal 's :
import math
import numpy as np
import scipy.stats as ss
from scipy import linalg
n = 20 # length of vector
rho = 0.6 # desired correlation = cos(angle)
theta | Generate a random variable with a defined correlation to an existing variable(s)
Equivalent Python answer to @caracal 's :
import math
import numpy as np
import scipy.stats as ss
from scipy import linalg
n = 20 # length of vector
rho = 0.6 # desired correlation = cos(angle)
theta = math.acos(rho)# corresponding angle
... | Generate a random variable with a defined correlation to an existing variable(s)
Equivalent Python answer to @caracal 's :
import math
import numpy as np
import scipy.stats as ss
from scipy import linalg
n = 20 # length of vector
rho = 0.6 # desired correlation = cos(angle)
theta |
1,805 | Generate a random variable with a defined correlation to an existing variable(s) | Generate normal variables with SAMPLING covariance matrix as given
covsam <- function(nobs,covm, seed=1237) {;
library (expm);
# nons=number of observations, covm = given covariance matrix ;
nvar <- ncol(covm);
tot <- nvar*nobs;
dat <- matrix(rnorm(tot), ncol=nvar); ... | Generate a random variable with a defined correlation to an existing variable(s) | Generate normal variables with SAMPLING covariance matrix as given
covsam <- function(nobs,covm, seed=1237) {;
library (expm);
# nons=number of observations, covm = given covarian | Generate a random variable with a defined correlation to an existing variable(s)
Generate normal variables with SAMPLING covariance matrix as given
covsam <- function(nobs,covm, seed=1237) {;
library (expm);
# nons=number of observations, covm = given covariance matrix ;
nvar <- ncol(cov... | Generate a random variable with a defined correlation to an existing variable(s)
Generate normal variables with SAMPLING covariance matrix as given
covsam <- function(nobs,covm, seed=1237) {;
library (expm);
# nons=number of observations, covm = given covarian |
1,806 | Generate a random variable with a defined correlation to an existing variable(s) | Given:
$\rho$ = desired correlation between Y and Z
$Z$ = sample
Requested:
'Random' sample $Y$ such that $cor(Y, Z) = \rho$
Solution:
Let $x_1 =$ scale($Z$), which implies $E(x_1) = 0, Var(x_1) = 1$
Generate a random sample $x_2$ with $E(x_2) = 0$ and $Var(x_2) = 1$ (distribution not important)
We then determine scal... | Generate a random variable with a defined correlation to an existing variable(s) | Given:
$\rho$ = desired correlation between Y and Z
$Z$ = sample
Requested:
'Random' sample $Y$ such that $cor(Y, Z) = \rho$
Solution:
Let $x_1 =$ scale($Z$), which implies $E(x_1) = 0, Var(x_1) = 1$ | Generate a random variable with a defined correlation to an existing variable(s)
Given:
$\rho$ = desired correlation between Y and Z
$Z$ = sample
Requested:
'Random' sample $Y$ such that $cor(Y, Z) = \rho$
Solution:
Let $x_1 =$ scale($Z$), which implies $E(x_1) = 0, Var(x_1) = 1$
Generate a random sample $x_2$ with $E... | Generate a random variable with a defined correlation to an existing variable(s)
Given:
$\rho$ = desired correlation between Y and Z
$Z$ = sample
Requested:
'Random' sample $Y$ such that $cor(Y, Z) = \rho$
Solution:
Let $x_1 =$ scale($Z$), which implies $E(x_1) = 0, Var(x_1) = 1$ |
1,807 | Subscript notation in expectations | In an expression where more than one random variables are involved, the symbol $E$ alone does not clarify with respect to which random variable is the expected value "taken". For example
$$E[h(X,Y)] =\text{?} \int_{-\infty}^{\infty} h(x,y) f_X(x)\,dx$$
or
$$E[h(X,Y)] = \text{?} \int_{-\infty}^\infty h(x,y) f_Y(y)\,dy$$... | Subscript notation in expectations | In an expression where more than one random variables are involved, the symbol $E$ alone does not clarify with respect to which random variable is the expected value "taken". For example
$$E[h(X,Y)] = | Subscript notation in expectations
In an expression where more than one random variables are involved, the symbol $E$ alone does not clarify with respect to which random variable is the expected value "taken". For example
$$E[h(X,Y)] =\text{?} \int_{-\infty}^{\infty} h(x,y) f_X(x)\,dx$$
or
$$E[h(X,Y)] = \text{?} \int_{... | Subscript notation in expectations
In an expression where more than one random variables are involved, the symbol $E$ alone does not clarify with respect to which random variable is the expected value "taken". For example
$$E[h(X,Y)] = |
1,808 | Subscript notation in expectations | I just want to add a follow-up to Alecos' great answer. Sometimes it doesn't matter the exact R.V. (or set of RV) the expectation is over. For instance,
$$
E_{X\sim P(X)} [X] = E_{X\sim P(X,Y)}[X]
$$
In your particular question, I suspect that because you are given $h(X,Y)$ is linear in X and Y, then you will break i... | Subscript notation in expectations | I just want to add a follow-up to Alecos' great answer. Sometimes it doesn't matter the exact R.V. (or set of RV) the expectation is over. For instance,
$$
E_{X\sim P(X)} [X] = E_{X\sim P(X,Y)}[X]
$ | Subscript notation in expectations
I just want to add a follow-up to Alecos' great answer. Sometimes it doesn't matter the exact R.V. (or set of RV) the expectation is over. For instance,
$$
E_{X\sim P(X)} [X] = E_{X\sim P(X,Y)}[X]
$$
In your particular question, I suspect that because you are given $h(X,Y)$ is linea... | Subscript notation in expectations
I just want to add a follow-up to Alecos' great answer. Sometimes it doesn't matter the exact R.V. (or set of RV) the expectation is over. For instance,
$$
E_{X\sim P(X)} [X] = E_{X\sim P(X,Y)}[X]
$ |
1,809 | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | I'd like to start by seconding a statement in the question:
... my point is that the questions on unbalanced datasets at CV do not
mention such a tradeoff, but treat unbalanced classes as a
self-evident evil, completely apart from any costs of sample
collection.
I also have the same concern, my questions here and her... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | I'd like to start by seconding a statement in the question:
... my point is that the questions on unbalanced datasets at CV do not
mention such a tradeoff, but treat unbalanced classes as a
self-evid | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
I'd like to start by seconding a statement in the question:
... my point is that the questions on unbalanced datasets at CV do not
mention such a tradeoff, but treat unbalanced classes as a
self-evident evil, completely apart from any ... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
I'd like to start by seconding a statement in the question:
... my point is that the questions on unbalanced datasets at CV do not
mention such a tradeoff, but treat unbalanced classes as a
self-evid |
1,810 | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | I generally agree with your premise that there is an over-fixation on balancing classes, and that it is usually not necessary to do so. Your examples of when it is appropriate to do so are goods ones.
However, I disagree with your statement:
I conclude that unbalanced classes are not a problem, and that oversampling d... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | I generally agree with your premise that there is an over-fixation on balancing classes, and that it is usually not necessary to do so. Your examples of when it is appropriate to do so are goods ones. | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
I generally agree with your premise that there is an over-fixation on balancing classes, and that it is usually not necessary to do so. Your examples of when it is appropriate to do so are goods ones.
However, I disagree with your state... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
I generally agree with your premise that there is an over-fixation on balancing classes, and that it is usually not necessary to do so. Your examples of when it is appropriate to do so are goods ones. |
1,811 | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | I fully agree with a marked answer "No problem of imbalance per se" - the problem is Lack of data - when minority class do not form Gaussian distribution & thus minority class just remains to be the outlier in the overall distribution == this is problem for Unsupervised methods.
But if are making Supervised learning, k... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | I fully agree with a marked answer "No problem of imbalance per se" - the problem is Lack of data - when minority class do not form Gaussian distribution & thus minority class just remains to be the o | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
I fully agree with a marked answer "No problem of imbalance per se" - the problem is Lack of data - when minority class do not form Gaussian distribution & thus minority class just remains to be the outlier in the overall distribution =... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
I fully agree with a marked answer "No problem of imbalance per se" - the problem is Lack of data - when minority class do not form Gaussian distribution & thus minority class just remains to be the o |
1,812 | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | Edit to summarize the following arguments and simulations:
I propose that balancing by either over-/undersampling or class weights is an advantage during training of gradient descent models that use sampling procedures during training (i.e. subsampling, bootstraping, minibatches etc., as used in e.g. neural networks an... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help? | Edit to summarize the following arguments and simulations:
I propose that balancing by either over-/undersampling or class weights is an advantage during training of gradient descent models that use s | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
Edit to summarize the following arguments and simulations:
I propose that balancing by either over-/undersampling or class weights is an advantage during training of gradient descent models that use sampling procedures during training (... | Are unbalanced datasets problematic, and (how) does oversampling (purport to) help?
Edit to summarize the following arguments and simulations:
I propose that balancing by either over-/undersampling or class weights is an advantage during training of gradient descent models that use s |
1,813 | Under what conditions does correlation imply causation? | Correlation is not sufficient for causation. One can get around the Wikipedia example by imagining that those twins always cheated in their tests by having a device that gives them the answers. The twin that goes to the amusement park loses the device, hence the low grade.
A good way to get this stuff straight is to th... | Under what conditions does correlation imply causation? | Correlation is not sufficient for causation. One can get around the Wikipedia example by imagining that those twins always cheated in their tests by having a device that gives them the answers. The tw | Under what conditions does correlation imply causation?
Correlation is not sufficient for causation. One can get around the Wikipedia example by imagining that those twins always cheated in their tests by having a device that gives them the answers. The twin that goes to the amusement park loses the device, hence the l... | Under what conditions does correlation imply causation?
Correlation is not sufficient for causation. One can get around the Wikipedia example by imagining that those twins always cheated in their tests by having a device that gives them the answers. The tw |
1,814 | Under what conditions does correlation imply causation? | I'll just add some additional comments about causality as viewed from an epidemiological perspective. Most of these arguments are taken from Practical Psychiatric Epidemiology, by Prince et al. (2003).
Causation, or causality interpretation, are by far the most difficult aspects of epidemiological research. Cohort and ... | Under what conditions does correlation imply causation? | I'll just add some additional comments about causality as viewed from an epidemiological perspective. Most of these arguments are taken from Practical Psychiatric Epidemiology, by Prince et al. (2003) | Under what conditions does correlation imply causation?
I'll just add some additional comments about causality as viewed from an epidemiological perspective. Most of these arguments are taken from Practical Psychiatric Epidemiology, by Prince et al. (2003).
Causation, or causality interpretation, are by far the most di... | Under what conditions does correlation imply causation?
I'll just add some additional comments about causality as viewed from an epidemiological perspective. Most of these arguments are taken from Practical Psychiatric Epidemiology, by Prince et al. (2003) |
1,815 | Under what conditions does correlation imply causation? | At the heart of your question is the question "when is a relationship causal?" It doesn't just need to be correlation implying (or not) causation.
A good book on this topic is called Mostly Harmless Econometrics by Johua Angrist and Jorn-Steffen Pischke. They start from the experimental ideal where we are able to rando... | Under what conditions does correlation imply causation? | At the heart of your question is the question "when is a relationship causal?" It doesn't just need to be correlation implying (or not) causation.
A good book on this topic is called Mostly Harmless E | Under what conditions does correlation imply causation?
At the heart of your question is the question "when is a relationship causal?" It doesn't just need to be correlation implying (or not) causation.
A good book on this topic is called Mostly Harmless Econometrics by Johua Angrist and Jorn-Steffen Pischke. They star... | Under what conditions does correlation imply causation?
At the heart of your question is the question "when is a relationship causal?" It doesn't just need to be correlation implying (or not) causation.
A good book on this topic is called Mostly Harmless E |
1,816 | Under what conditions does correlation imply causation? | There is also a problem with the opposite case, when lack of correlation is used as a proof for the lack of causation. This problem is nonlinearity; when looking at correlation people usually check Pearson, which is only a tip of an iceberg. | Under what conditions does correlation imply causation? | There is also a problem with the opposite case, when lack of correlation is used as a proof for the lack of causation. This problem is nonlinearity; when looking at correlation people usually check Pe | Under what conditions does correlation imply causation?
There is also a problem with the opposite case, when lack of correlation is used as a proof for the lack of causation. This problem is nonlinearity; when looking at correlation people usually check Pearson, which is only a tip of an iceberg. | Under what conditions does correlation imply causation?
There is also a problem with the opposite case, when lack of correlation is used as a proof for the lack of causation. This problem is nonlinearity; when looking at correlation people usually check Pe |
1,817 | Under what conditions does correlation imply causation? | Your example is that of a controlled experiment. The only other context that I know of where a correlation can imply causation is that of a natural experiment.
Basically, a natural experiment takes advantage of an assignment of some respondents to a treatment that happens naturally in the real world. Since assignment ... | Under what conditions does correlation imply causation? | Your example is that of a controlled experiment. The only other context that I know of where a correlation can imply causation is that of a natural experiment.
Basically, a natural experiment takes a | Under what conditions does correlation imply causation?
Your example is that of a controlled experiment. The only other context that I know of where a correlation can imply causation is that of a natural experiment.
Basically, a natural experiment takes advantage of an assignment of some respondents to a treatment tha... | Under what conditions does correlation imply causation?
Your example is that of a controlled experiment. The only other context that I know of where a correlation can imply causation is that of a natural experiment.
Basically, a natural experiment takes a |
1,818 | Under what conditions does correlation imply causation? | In my opinion the APA Statistical Task force summarised it quite well
''Inferring causality from nonrandomized
designs is a risky enterprise.
Researchers using nonrandomized
designs have an extra obligation to
explain the logic behind covariates
included in their designs and to alert
the reader to plausibl... | Under what conditions does correlation imply causation? | In my opinion the APA Statistical Task force summarised it quite well
''Inferring causality from nonrandomized
designs is a risky enterprise.
Researchers using nonrandomized
designs have an ext | Under what conditions does correlation imply causation?
In my opinion the APA Statistical Task force summarised it quite well
''Inferring causality from nonrandomized
designs is a risky enterprise.
Researchers using nonrandomized
designs have an extra obligation to
explain the logic behind covariates
include... | Under what conditions does correlation imply causation?
In my opinion the APA Statistical Task force summarised it quite well
''Inferring causality from nonrandomized
designs is a risky enterprise.
Researchers using nonrandomized
designs have an ext |
1,819 | Under what conditions does correlation imply causation? | Sir Austin Bradford Hill's President's Address to the Royal Society of Medicine (The Environment and Disease: Association or Causation?) explains nine criteria which help to judge whether there is a causal relationship between two correlated or associated variables.
They are:
Strength of the association
Consistency: "... | Under what conditions does correlation imply causation? | Sir Austin Bradford Hill's President's Address to the Royal Society of Medicine (The Environment and Disease: Association or Causation?) explains nine criteria which help to judge whether there is a c | Under what conditions does correlation imply causation?
Sir Austin Bradford Hill's President's Address to the Royal Society of Medicine (The Environment and Disease: Association or Causation?) explains nine criteria which help to judge whether there is a causal relationship between two correlated or associated variable... | Under what conditions does correlation imply causation?
Sir Austin Bradford Hill's President's Address to the Royal Society of Medicine (The Environment and Disease: Association or Causation?) explains nine criteria which help to judge whether there is a c |
1,820 | Under what conditions does correlation imply causation? | In the twins example it is not just the correlation that suggests causality, but also the associated information or prior knowledge.
Suppose I add one further piece of information. Assume that the diligent twin spent 6 hours studying for a stats exam, but due to an unfortunate error the exam was in history. Would we s... | Under what conditions does correlation imply causation? | In the twins example it is not just the correlation that suggests causality, but also the associated information or prior knowledge.
Suppose I add one further piece of information. Assume that the di | Under what conditions does correlation imply causation?
In the twins example it is not just the correlation that suggests causality, but also the associated information or prior knowledge.
Suppose I add one further piece of information. Assume that the diligent twin spent 6 hours studying for a stats exam, but due to ... | Under what conditions does correlation imply causation?
In the twins example it is not just the correlation that suggests causality, but also the associated information or prior knowledge.
Suppose I add one further piece of information. Assume that the di |
1,821 | Under what conditions does correlation imply causation? | Correlation alone never implies causation. It's that simple.
But it's very rare to have only a correlation between two variables. Often you also know something about what those variables are and a theory, or theories, suggesting why there might be a causal relationship between the variables. If not, then we bother c... | Under what conditions does correlation imply causation? | Correlation alone never implies causation. It's that simple.
But it's very rare to have only a correlation between two variables. Often you also know something about what those variables are and a t | Under what conditions does correlation imply causation?
Correlation alone never implies causation. It's that simple.
But it's very rare to have only a correlation between two variables. Often you also know something about what those variables are and a theory, or theories, suggesting why there might be a causal relat... | Under what conditions does correlation imply causation?
Correlation alone never implies causation. It's that simple.
But it's very rare to have only a correlation between two variables. Often you also know something about what those variables are and a t |
1,822 | Under what conditions does correlation imply causation? | Almost always in randomized trials
Almost always in observational study when someone measure all confouders (almost never)
Sometimes when someone measure some counfounders (IC* algorithim of DAG discovery in Pearl's book Causality)
In non gaussian linear models with two or more variables but not using correlation as me... | Under what conditions does correlation imply causation? | Almost always in randomized trials
Almost always in observational study when someone measure all confouders (almost never)
Sometimes when someone measure some counfounders (IC* algorithim of DAG disco | Under what conditions does correlation imply causation?
Almost always in randomized trials
Almost always in observational study when someone measure all confouders (almost never)
Sometimes when someone measure some counfounders (IC* algorithim of DAG discovery in Pearl's book Causality)
In non gaussian linear models wi... | Under what conditions does correlation imply causation?
Almost always in randomized trials
Almost always in observational study when someone measure all confouders (almost never)
Sometimes when someone measure some counfounders (IC* algorithim of DAG disco |
1,823 | Under what conditions does correlation imply causation? | One useful sufficient condition for some definitions of causation:
Causation can be claimed when one of the correlated variables can be controlled (we can directly set its value) and correlation is still present. | Under what conditions does correlation imply causation? | One useful sufficient condition for some definitions of causation:
Causation can be claimed when one of the correlated variables can be controlled (we can directly set its value) and correlation is st | Under what conditions does correlation imply causation?
One useful sufficient condition for some definitions of causation:
Causation can be claimed when one of the correlated variables can be controlled (we can directly set its value) and correlation is still present. | Under what conditions does correlation imply causation?
One useful sufficient condition for some definitions of causation:
Causation can be claimed when one of the correlated variables can be controlled (we can directly set its value) and correlation is st |
1,824 | Under what conditions does correlation imply causation? | A related question might be -- under what conditions can you reliably extract causal relations from data?
A 2008 NIPS workshop try to address that question empirically. One of the tasks was to infer the direction of causality from observations of pairs of variables where one variable was known to cause another, and the... | Under what conditions does correlation imply causation? | A related question might be -- under what conditions can you reliably extract causal relations from data?
A 2008 NIPS workshop try to address that question empirically. One of the tasks was to infer t | Under what conditions does correlation imply causation?
A related question might be -- under what conditions can you reliably extract causal relations from data?
A 2008 NIPS workshop try to address that question empirically. One of the tasks was to infer the direction of causality from observations of pairs of variable... | Under what conditions does correlation imply causation?
A related question might be -- under what conditions can you reliably extract causal relations from data?
A 2008 NIPS workshop try to address that question empirically. One of the tasks was to infer t |
1,825 | Under what conditions does correlation imply causation? | Almost surely in a well designed experiment. (Designed, of course, to elicit such a connexion.) | Under what conditions does correlation imply causation? | Almost surely in a well designed experiment. (Designed, of course, to elicit such a connexion.) | Under what conditions does correlation imply causation?
Almost surely in a well designed experiment. (Designed, of course, to elicit such a connexion.) | Under what conditions does correlation imply causation?
Almost surely in a well designed experiment. (Designed, of course, to elicit such a connexion.) |
1,826 | Under what conditions does correlation imply causation? | Suppose we think the factor A is the cause of the phenomenon B. Then we try to vary it to see whether B changes.
If B doesn't change and if we can assume that everything else unchanged, strong evidence that A is not the cause of B.
If B does change, we can't conclude that A is the cause because the change of A might ... | Under what conditions does correlation imply causation? | Suppose we think the factor A is the cause of the phenomenon B. Then we try to vary it to see whether B changes.
If B doesn't change and if we can assume that everything else unchanged, strong eviden | Under what conditions does correlation imply causation?
Suppose we think the factor A is the cause of the phenomenon B. Then we try to vary it to see whether B changes.
If B doesn't change and if we can assume that everything else unchanged, strong evidence that A is not the cause of B.
If B does change, we can't con... | Under what conditions does correlation imply causation?
Suppose we think the factor A is the cause of the phenomenon B. Then we try to vary it to see whether B changes.
If B doesn't change and if we can assume that everything else unchanged, strong eviden |
1,827 | Under what conditions does correlation imply causation? | I noticed that 'proof' was used here when discussing the empirical paradigm. There is no such thing. First comes the hypothesis, where the idea is advanced; then comes testing, under "controlled conditions"[note a] and if "sufficient" lack of disproof is encountered, it advances to the stage of hypothesis...period. ... | Under what conditions does correlation imply causation? | I noticed that 'proof' was used here when discussing the empirical paradigm. There is no such thing. First comes the hypothesis, where the idea is advanced; then comes testing, under "controlled con | Under what conditions does correlation imply causation?
I noticed that 'proof' was used here when discussing the empirical paradigm. There is no such thing. First comes the hypothesis, where the idea is advanced; then comes testing, under "controlled conditions"[note a] and if "sufficient" lack of disproof is encount... | Under what conditions does correlation imply causation?
I noticed that 'proof' was used here when discussing the empirical paradigm. There is no such thing. First comes the hypothesis, where the idea is advanced; then comes testing, under "controlled con |
1,828 | Under what conditions does correlation imply causation? | I read all the answers. Some useful insight are given but no one answer seems me decisive, neither the accepted one (it can be correct but too vague).
I offered here (Under which assumptions a regression can be interpreted causally?) an answer about:
Under which assumptions a [linear] regression can be interpreted cau... | Under what conditions does correlation imply causation? | I read all the answers. Some useful insight are given but no one answer seems me decisive, neither the accepted one (it can be correct but too vague).
I offered here (Under which assumptions a regress | Under what conditions does correlation imply causation?
I read all the answers. Some useful insight are given but no one answer seems me decisive, neither the accepted one (it can be correct but too vague).
I offered here (Under which assumptions a regression can be interpreted causally?) an answer about:
Under which ... | Under what conditions does correlation imply causation?
I read all the answers. Some useful insight are given but no one answer seems me decisive, neither the accepted one (it can be correct but too vague).
I offered here (Under which assumptions a regress |
1,829 | Under what conditions does correlation imply causation? | If you want to determine whether $X$ causes $Y$, and you run the regression
$Y = bX + u$
Then $b$ is an unbiased estimator of the causal effect of $X$ on $Y$ (that is $\mathrm{E}(b)=B$) if and only if there is no correlation between $X$ and $u$, that is $\mathrm{E}(u|X)=0$. This is because $u$ can be thought of as anyt... | Under what conditions does correlation imply causation? | If you want to determine whether $X$ causes $Y$, and you run the regression
$Y = bX + u$
Then $b$ is an unbiased estimator of the causal effect of $X$ on $Y$ (that is $\mathrm{E}(b)=B$) if and only if | Under what conditions does correlation imply causation?
If you want to determine whether $X$ causes $Y$, and you run the regression
$Y = bX + u$
Then $b$ is an unbiased estimator of the causal effect of $X$ on $Y$ (that is $\mathrm{E}(b)=B$) if and only if there is no correlation between $X$ and $u$, that is $\mathrm{E... | Under what conditions does correlation imply causation?
If you want to determine whether $X$ causes $Y$, and you run the regression
$Y = bX + u$
Then $b$ is an unbiased estimator of the causal effect of $X$ on $Y$ (that is $\mathrm{E}(b)=B$) if and only if |
1,830 | Understanding "variance" intuitively | I would probably use a similar analogy to the one I've learned to give 'laypeople' when introducing the concept of bias and variance: the dartboard analogy. See below:
The particular image above is from Encyclopedia of Machine Learning, and the reference within the image is Moore and McCabe's "Introduction to the Pra... | Understanding "variance" intuitively | I would probably use a similar analogy to the one I've learned to give 'laypeople' when introducing the concept of bias and variance: the dartboard analogy. See below:
The particular image above is | Understanding "variance" intuitively
I would probably use a similar analogy to the one I've learned to give 'laypeople' when introducing the concept of bias and variance: the dartboard analogy. See below:
The particular image above is from Encyclopedia of Machine Learning, and the reference within the image is Moore ... | Understanding "variance" intuitively
I would probably use a similar analogy to the one I've learned to give 'laypeople' when introducing the concept of bias and variance: the dartboard analogy. See below:
The particular image above is |
1,831 | Understanding "variance" intuitively | I used to teach statistics to a layman by jokes, and I found they learn a lot.
Suppose for variance or standard deviation the following joke is quite useful:
Joke
Once two statistician of height 4 feet and 5 feet have to cross a river of AVERAGE depth 3 feet. Meanwhile, a third statistician comes and said, "what are yo... | Understanding "variance" intuitively | I used to teach statistics to a layman by jokes, and I found they learn a lot.
Suppose for variance or standard deviation the following joke is quite useful:
Joke
Once two statistician of height 4 fee | Understanding "variance" intuitively
I used to teach statistics to a layman by jokes, and I found they learn a lot.
Suppose for variance or standard deviation the following joke is quite useful:
Joke
Once two statistician of height 4 feet and 5 feet have to cross a river of AVERAGE depth 3 feet. Meanwhile, a third stat... | Understanding "variance" intuitively
I used to teach statistics to a layman by jokes, and I found they learn a lot.
Suppose for variance or standard deviation the following joke is quite useful:
Joke
Once two statistician of height 4 fee |
1,832 | Understanding "variance" intuitively | I disagree with a lot of the answers advocating people to purely think of variance as spread. As smart people (Nassim Taleb) have pointed out, when people think of variance as spread they just assume it is MAD.
Variance is a description of how far members are from the mean, AND it judges each observation's importance b... | Understanding "variance" intuitively | I disagree with a lot of the answers advocating people to purely think of variance as spread. As smart people (Nassim Taleb) have pointed out, when people think of variance as spread they just assume | Understanding "variance" intuitively
I disagree with a lot of the answers advocating people to purely think of variance as spread. As smart people (Nassim Taleb) have pointed out, when people think of variance as spread they just assume it is MAD.
Variance is a description of how far members are from the mean, AND it j... | Understanding "variance" intuitively
I disagree with a lot of the answers advocating people to purely think of variance as spread. As smart people (Nassim Taleb) have pointed out, when people think of variance as spread they just assume |
1,833 | Understanding "variance" intuitively | I would focus on the standard deviation rather than the variance; the variance is on the wrong scale.
Just as the average is a typical value, the SD is a typical (absolute) difference from the average. It's not unlike folding the distribution over at the average and taking the average of that. | Understanding "variance" intuitively | I would focus on the standard deviation rather than the variance; the variance is on the wrong scale.
Just as the average is a typical value, the SD is a typical (absolute) difference from the avera | Understanding "variance" intuitively
I would focus on the standard deviation rather than the variance; the variance is on the wrong scale.
Just as the average is a typical value, the SD is a typical (absolute) difference from the average. It's not unlike folding the distribution over at the average and taking the av... | Understanding "variance" intuitively
I would focus on the standard deviation rather than the variance; the variance is on the wrong scale.
Just as the average is a typical value, the SD is a typical (absolute) difference from the avera |
1,834 | Understanding "variance" intuitively | Have a lot of practice giving lectures about standard deviation and variance to a novice audience.
Lets assume, one knows about average already. By average (or e.g. median) - one gets a single value from many measurements (that is how one usually uses them). But it is very import to say, that knowing some average is ... | Understanding "variance" intuitively | Have a lot of practice giving lectures about standard deviation and variance to a novice audience.
Lets assume, one knows about average already. By average (or e.g. median) - one gets a single value | Understanding "variance" intuitively
Have a lot of practice giving lectures about standard deviation and variance to a novice audience.
Lets assume, one knows about average already. By average (or e.g. median) - one gets a single value from many measurements (that is how one usually uses them). But it is very import ... | Understanding "variance" intuitively
Have a lot of practice giving lectures about standard deviation and variance to a novice audience.
Lets assume, one knows about average already. By average (or e.g. median) - one gets a single value |
1,835 | Understanding "variance" intuitively | I was sitting down trying to puzzle out variance and the thing that finally made it click into place for me was to look at it graphically.
Say you draw out a number line with four points, -7, -1, 1 and 7. Now draw an imaginary Y axis with the same four points along the Y dimension, and use the XY pairs to draw out the ... | Understanding "variance" intuitively | I was sitting down trying to puzzle out variance and the thing that finally made it click into place for me was to look at it graphically.
Say you draw out a number line with four points, -7, -1, 1 an | Understanding "variance" intuitively
I was sitting down trying to puzzle out variance and the thing that finally made it click into place for me was to look at it graphically.
Say you draw out a number line with four points, -7, -1, 1 and 7. Now draw an imaginary Y axis with the same four points along the Y dimension, ... | Understanding "variance" intuitively
I was sitting down trying to puzzle out variance and the thing that finally made it click into place for me was to look at it graphically.
Say you draw out a number line with four points, -7, -1, 1 an |
1,836 | Understanding "variance" intuitively | Imagine you ask 1000 people to correctly guess how many beans are in a jar filled with jelly beans. Now imagine that you are not necessarily interested in knowing the correct answer (which may be of some use) but you wish to get a better understanding of how people estimate the answer.
Variance could be explained to a ... | Understanding "variance" intuitively | Imagine you ask 1000 people to correctly guess how many beans are in a jar filled with jelly beans. Now imagine that you are not necessarily interested in knowing the correct answer (which may be of s | Understanding "variance" intuitively
Imagine you ask 1000 people to correctly guess how many beans are in a jar filled with jelly beans. Now imagine that you are not necessarily interested in knowing the correct answer (which may be of some use) but you wish to get a better understanding of how people estimate the answ... | Understanding "variance" intuitively
Imagine you ask 1000 people to correctly guess how many beans are in a jar filled with jelly beans. Now imagine that you are not necessarily interested in knowing the correct answer (which may be of s |
1,837 | Understanding "variance" intuitively | I think the key phrase to use when explaining both variance and standard deviation is "measure of spread". In the most basic language, the variance and standard deviation tell us how well spread out the data is. To be a little more accurate, although still addressing the layman, they tell us how well the data is spread... | Understanding "variance" intuitively | I think the key phrase to use when explaining both variance and standard deviation is "measure of spread". In the most basic language, the variance and standard deviation tell us how well spread out t | Understanding "variance" intuitively
I think the key phrase to use when explaining both variance and standard deviation is "measure of spread". In the most basic language, the variance and standard deviation tell us how well spread out the data is. To be a little more accurate, although still addressing the layman, the... | Understanding "variance" intuitively
I think the key phrase to use when explaining both variance and standard deviation is "measure of spread". In the most basic language, the variance and standard deviation tell us how well spread out t |
1,838 | Understanding "variance" intuitively | I'd like to provide two perspectives:
I regard the variance of distribution as the moment of inertia with the axis that at the mean of the distribution and each mass as 1. This intuition would make the abstract concept concrete. The first moment is the mean of the distribution and the second moment is the variance.
P... | Understanding "variance" intuitively | I'd like to provide two perspectives:
I regard the variance of distribution as the moment of inertia with the axis that at the mean of the distribution and each mass as 1. This intuition would make t | Understanding "variance" intuitively
I'd like to provide two perspectives:
I regard the variance of distribution as the moment of inertia with the axis that at the mean of the distribution and each mass as 1. This intuition would make the abstract concept concrete. The first moment is the mean of the distribution and ... | Understanding "variance" intuitively
I'd like to provide two perspectives:
I regard the variance of distribution as the moment of inertia with the axis that at the mean of the distribution and each mass as 1. This intuition would make t |
1,839 | Convergence in probability vs. almost sure convergence | From my point of view the difference is important, but largely for philosophical reasons. Assume you have some device, that improves with time. So, every time you use the device the probability of it failing is less than before.
Convergence in probability says that the chance of failure goes to zero as the number o... | Convergence in probability vs. almost sure convergence | From my point of view the difference is important, but largely for philosophical reasons. Assume you have some device, that improves with time. So, every time you use the device the probability of i | Convergence in probability vs. almost sure convergence
From my point of view the difference is important, but largely for philosophical reasons. Assume you have some device, that improves with time. So, every time you use the device the probability of it failing is less than before.
Convergence in probability says ... | Convergence in probability vs. almost sure convergence
From my point of view the difference is important, but largely for philosophical reasons. Assume you have some device, that improves with time. So, every time you use the device the probability of i |
1,840 | Convergence in probability vs. almost sure convergence | I know this question has already been answered (and quite well, in my view), but there was a different question here which had a comment @NRH that mentioned the graphical explanation, and rather than put the pictures there it would seem more fitting to put them here.
So, here goes. It's not as cool as an R package. B... | Convergence in probability vs. almost sure convergence | I know this question has already been answered (and quite well, in my view), but there was a different question here which had a comment @NRH that mentioned the graphical explanation, and rather than | Convergence in probability vs. almost sure convergence
I know this question has already been answered (and quite well, in my view), but there was a different question here which had a comment @NRH that mentioned the graphical explanation, and rather than put the pictures there it would seem more fitting to put them her... | Convergence in probability vs. almost sure convergence
I know this question has already been answered (and quite well, in my view), but there was a different question here which had a comment @NRH that mentioned the graphical explanation, and rather than |
1,841 | Convergence in probability vs. almost sure convergence | I understand it as follows,
Convergence in probability
The probability that the sequence of random variables equals the target value is asymptotically decreasing and approaches 0 but never actually attains 0.
Almost Sure Convergence
The sequence of random variables will equal the target value asymptotically but you can... | Convergence in probability vs. almost sure convergence | I understand it as follows,
Convergence in probability
The probability that the sequence of random variables equals the target value is asymptotically decreasing and approaches 0 but never actually at | Convergence in probability vs. almost sure convergence
I understand it as follows,
Convergence in probability
The probability that the sequence of random variables equals the target value is asymptotically decreasing and approaches 0 but never actually attains 0.
Almost Sure Convergence
The sequence of random variables... | Convergence in probability vs. almost sure convergence
I understand it as follows,
Convergence in probability
The probability that the sequence of random variables equals the target value is asymptotically decreasing and approaches 0 but never actually at |
1,842 | Convergence in probability vs. almost sure convergence | If you enjoy visual explanations, there was a nice 'Teacher's Corner' article on this subject in the American Statistician (cite below). As a bonus, the authors included an R package to facilitate learning.
@article{lafaye09,
title={Understanding Convergence Concepts: A Visual-Minded and Graphical Simulation-Based A... | Convergence in probability vs. almost sure convergence | If you enjoy visual explanations, there was a nice 'Teacher's Corner' article on this subject in the American Statistician (cite below). As a bonus, the authors included an R package to facilitate le | Convergence in probability vs. almost sure convergence
If you enjoy visual explanations, there was a nice 'Teacher's Corner' article on this subject in the American Statistician (cite below). As a bonus, the authors included an R package to facilitate learning.
@article{lafaye09,
title={Understanding Convergence Con... | Convergence in probability vs. almost sure convergence
If you enjoy visual explanations, there was a nice 'Teacher's Corner' article on this subject in the American Statistician (cite below). As a bonus, the authors included an R package to facilitate le |
1,843 | Convergence in probability vs. almost sure convergence | One thing that helped me to grasp the difference is the following equivalence
$$P\left({\lim_{n\to\infty}|X_n-X|=0}\right) = 1 \iff \lim_{n\to\infty} P\left({\sup_{m\geq n}|X_m-X|>\epsilon }\right) = 0 ~\forall \epsilon > 0.$$
In comparison stochastic convergence:
$$\lim_{n\to\infty}P(|X_n-X|>\epsilon) = 0 ~\forall ... | Convergence in probability vs. almost sure convergence | One thing that helped me to grasp the difference is the following equivalence
$$P\left({\lim_{n\to\infty}|X_n-X|=0}\right) = 1 \iff \lim_{n\to\infty} P\left({\sup_{m\geq n}|X_m-X|>\epsilon }\right) = | Convergence in probability vs. almost sure convergence
One thing that helped me to grasp the difference is the following equivalence
$$P\left({\lim_{n\to\infty}|X_n-X|=0}\right) = 1 \iff \lim_{n\to\infty} P\left({\sup_{m\geq n}|X_m-X|>\epsilon }\right) = 0 ~\forall \epsilon > 0.$$
In comparison stochastic convergence:... | Convergence in probability vs. almost sure convergence
One thing that helped me to grasp the difference is the following equivalence
$$P\left({\lim_{n\to\infty}|X_n-X|=0}\right) = 1 \iff \lim_{n\to\infty} P\left({\sup_{m\geq n}|X_m-X|>\epsilon }\right) = |
1,844 | Convergence in probability vs. almost sure convergence | This last guy explains it very well. If you take a sequence of random variables Xn= 1 with probability 1/n and zero otherwise. It is easy to see taking limits that this converges to zero in probability, but fails to converge almost surely. As he said, probability doesn't care that we might get a one down the road. ... | Convergence in probability vs. almost sure convergence | This last guy explains it very well. If you take a sequence of random variables Xn= 1 with probability 1/n and zero otherwise. It is easy to see taking limits that this converges to zero in probabi | Convergence in probability vs. almost sure convergence
This last guy explains it very well. If you take a sequence of random variables Xn= 1 with probability 1/n and zero otherwise. It is easy to see taking limits that this converges to zero in probability, but fails to converge almost surely. As he said, probabili... | Convergence in probability vs. almost sure convergence
This last guy explains it very well. If you take a sequence of random variables Xn= 1 with probability 1/n and zero otherwise. It is easy to see taking limits that this converges to zero in probabi |
1,845 | What, precisely, is a confidence interval? | I found this thought experiment helpful when thinking about confidence intervals. It also answers your question 3.
Let $X\sim U(0,1)$ and $Y=X+a-\frac{1}{2}$. Consider two observations of $Y$ taking the values $y_1$ and $y_2$ corresponding to observations $x_1$ and $x_2$ of $X$, and let $y_l=\min(y_1,y_2)$ and $y_u=\ma... | What, precisely, is a confidence interval? | I found this thought experiment helpful when thinking about confidence intervals. It also answers your question 3.
Let $X\sim U(0,1)$ and $Y=X+a-\frac{1}{2}$. Consider two observations of $Y$ taking t | What, precisely, is a confidence interval?
I found this thought experiment helpful when thinking about confidence intervals. It also answers your question 3.
Let $X\sim U(0,1)$ and $Y=X+a-\frac{1}{2}$. Consider two observations of $Y$ taking the values $y_1$ and $y_2$ corresponding to observations $x_1$ and $x_2$ of $X... | What, precisely, is a confidence interval?
I found this thought experiment helpful when thinking about confidence intervals. It also answers your question 3.
Let $X\sim U(0,1)$ and $Y=X+a-\frac{1}{2}$. Consider two observations of $Y$ taking t |
1,846 | What, precisely, is a confidence interval? | There are many issues concerning confidence intervals, but let's focus on the quotations. The problem lies in possible misinterpretations rather than being a matter of correctness. When people say a "parameter has a particular probability of" something, they are thinking of the parameter as being a random variable. ... | What, precisely, is a confidence interval? | There are many issues concerning confidence intervals, but let's focus on the quotations. The problem lies in possible misinterpretations rather than being a matter of correctness. When people say a | What, precisely, is a confidence interval?
There are many issues concerning confidence intervals, but let's focus on the quotations. The problem lies in possible misinterpretations rather than being a matter of correctness. When people say a "parameter has a particular probability of" something, they are thinking of ... | What, precisely, is a confidence interval?
There are many issues concerning confidence intervals, but let's focus on the quotations. The problem lies in possible misinterpretations rather than being a matter of correctness. When people say a |
1,847 | What, precisely, is a confidence interval? | I wouldn't call the definition of CIs as wrong, but they are easy to mis-interpret, due to there being more than one definition of probability. CIs are based on the following definition of Probability (Frequentist or ontological)
(1)probability of a proposition=long run proportion of times that proposition is observed... | What, precisely, is a confidence interval? | I wouldn't call the definition of CIs as wrong, but they are easy to mis-interpret, due to there being more than one definition of probability. CIs are based on the following definition of Probabilit | What, precisely, is a confidence interval?
I wouldn't call the definition of CIs as wrong, but they are easy to mis-interpret, due to there being more than one definition of probability. CIs are based on the following definition of Probability (Frequentist or ontological)
(1)probability of a proposition=long run propo... | What, precisely, is a confidence interval?
I wouldn't call the definition of CIs as wrong, but they are easy to mis-interpret, due to there being more than one definition of probability. CIs are based on the following definition of Probabilit |
1,848 | What, precisely, is a confidence interval? | R.A. Fisher had a criterion for the usefulness of confidence intervals: A CI should not admit of "identifiable subsets" that imply a different confidence level. In most (if not all) counterexamples, we have cases where there are identifiable subsets that have different coverage probabilities.
In theses cases, you can ... | What, precisely, is a confidence interval? | R.A. Fisher had a criterion for the usefulness of confidence intervals: A CI should not admit of "identifiable subsets" that imply a different confidence level. In most (if not all) counterexamples, w | What, precisely, is a confidence interval?
R.A. Fisher had a criterion for the usefulness of confidence intervals: A CI should not admit of "identifiable subsets" that imply a different confidence level. In most (if not all) counterexamples, we have cases where there are identifiable subsets that have different coverag... | What, precisely, is a confidence interval?
R.A. Fisher had a criterion for the usefulness of confidence intervals: A CI should not admit of "identifiable subsets" that imply a different confidence level. In most (if not all) counterexamples, w |
1,849 | What, precisely, is a confidence interval? | This is thing that may be hard to understand:
if on average 95% of all confidence intervals will contain the
parameter
and I have one specific confidence interval
why isn't the the probability that this interval contains the parameter also 95% ?
A confidence interval relates to the sampling procedure. If you would t... | What, precisely, is a confidence interval? | This is thing that may be hard to understand:
if on average 95% of all confidence intervals will contain the
parameter
and I have one specific confidence interval
why isn't the the probability that t | What, precisely, is a confidence interval?
This is thing that may be hard to understand:
if on average 95% of all confidence intervals will contain the
parameter
and I have one specific confidence interval
why isn't the the probability that this interval contains the parameter also 95% ?
A confidence interval relate... | What, precisely, is a confidence interval?
This is thing that may be hard to understand:
if on average 95% of all confidence intervals will contain the
parameter
and I have one specific confidence interval
why isn't the the probability that t |
1,850 | What, precisely, is a confidence interval? | From a theoretical perspective Questions 2 and 3 are based on the incorrect assumption that the definitions are wrong. So I am in agreement with @whuber's answer in that respect, and @whuber's answer to question 1 does not require any additional input from me.
However, from a more practical perspective a confidence in... | What, precisely, is a confidence interval? | From a theoretical perspective Questions 2 and 3 are based on the incorrect assumption that the definitions are wrong. So I am in agreement with @whuber's answer in that respect, and @whuber's answer | What, precisely, is a confidence interval?
From a theoretical perspective Questions 2 and 3 are based on the incorrect assumption that the definitions are wrong. So I am in agreement with @whuber's answer in that respect, and @whuber's answer to question 1 does not require any additional input from me.
However, from a... | What, precisely, is a confidence interval?
From a theoretical perspective Questions 2 and 3 are based on the incorrect assumption that the definitions are wrong. So I am in agreement with @whuber's answer in that respect, and @whuber's answer |
1,851 | What, precisely, is a confidence interval? | Suppose we are in a simple situation. You have an unknown parameter $\theta$ and $T$ an estimator of $\theta$ that has an imprecision around 1 (informally). You think (informally) $\theta$ should be in $[T-1;T+1]$ most often.
In a real experiment you observe $T=12$.
It is natural to ask the question "Given what I see ... | What, precisely, is a confidence interval? | Suppose we are in a simple situation. You have an unknown parameter $\theta$ and $T$ an estimator of $\theta$ that has an imprecision around 1 (informally). You think (informally) $\theta$ should be i | What, precisely, is a confidence interval?
Suppose we are in a simple situation. You have an unknown parameter $\theta$ and $T$ an estimator of $\theta$ that has an imprecision around 1 (informally). You think (informally) $\theta$ should be in $[T-1;T+1]$ most often.
In a real experiment you observe $T=12$.
It is nat... | What, precisely, is a confidence interval?
Suppose we are in a simple situation. You have an unknown parameter $\theta$ and $T$ an estimator of $\theta$ that has an imprecision around 1 (informally). You think (informally) $\theta$ should be i |
1,852 | What, precisely, is a confidence interval? | Here's the most degenerate example. If I want to build a 95% confidence interval $I$ for a real-valued parameter $\mu$, I can use the following distribution:
$$
\mathbb P(I = (-\infty, +\infty)) = 0.95 \\
\mathbb P(I = \emptyset) = 0.05
$$
(Some definitions of confidence interval may not technically include infinite or... | What, precisely, is a confidence interval? | Here's the most degenerate example. If I want to build a 95% confidence interval $I$ for a real-valued parameter $\mu$, I can use the following distribution:
$$
\mathbb P(I = (-\infty, +\infty)) = 0.9 | What, precisely, is a confidence interval?
Here's the most degenerate example. If I want to build a 95% confidence interval $I$ for a real-valued parameter $\mu$, I can use the following distribution:
$$
\mathbb P(I = (-\infty, +\infty)) = 0.95 \\
\mathbb P(I = \emptyset) = 0.05
$$
(Some definitions of confidence inter... | What, precisely, is a confidence interval?
Here's the most degenerate example. If I want to build a 95% confidence interval $I$ for a real-valued parameter $\mu$, I can use the following distribution:
$$
\mathbb P(I = (-\infty, +\infty)) = 0.9 |
1,853 | What, precisely, is a confidence interval? | Okay, I realize that when you calculate a 95% confidence interval for a parameter using classical frequentist methods, it doesn't mean that there is a 95% probability that the parameter lies within that interval. And yet ... when you approach the problem from a Bayesian perspective, and calculate a 95% credible interva... | What, precisely, is a confidence interval? | Okay, I realize that when you calculate a 95% confidence interval for a parameter using classical frequentist methods, it doesn't mean that there is a 95% probability that the parameter lies within th | What, precisely, is a confidence interval?
Okay, I realize that when you calculate a 95% confidence interval for a parameter using classical frequentist methods, it doesn't mean that there is a 95% probability that the parameter lies within that interval. And yet ... when you approach the problem from a Bayesian perspe... | What, precisely, is a confidence interval?
Okay, I realize that when you calculate a 95% confidence interval for a parameter using classical frequentist methods, it doesn't mean that there is a 95% probability that the parameter lies within th |
1,854 | What, precisely, is a confidence interval? | You are asking about the Frequentist confidence interval. The definition (note that none of your 2 citation is a definition! Just statements, which both are correct) is:
If I had repeated this experiment a big number of times, given this fitted model with this parameter values, in 95% of experiments the estimated valu... | What, precisely, is a confidence interval? | You are asking about the Frequentist confidence interval. The definition (note that none of your 2 citation is a definition! Just statements, which both are correct) is:
If I had repeated this experi | What, precisely, is a confidence interval?
You are asking about the Frequentist confidence interval. The definition (note that none of your 2 citation is a definition! Just statements, which both are correct) is:
If I had repeated this experiment a big number of times, given this fitted model with this parameter value... | What, precisely, is a confidence interval?
You are asking about the Frequentist confidence interval. The definition (note that none of your 2 citation is a definition! Just statements, which both are correct) is:
If I had repeated this experi |
1,855 | What, precisely, is a confidence interval? | Suppose that we want to study the height of men $X$ in Canada for the last 2 years. Assume also that $X \sim N(\mu,\sigma^2)$ with $\sigma^2$ known. Then, talking about the probability
\begin{equation*}
P(X>1.80)=P(\omega \in \Omega:X(\omega)>1.80)
\end{equation*}
that a random man from Canada has a height more than $1... | What, precisely, is a confidence interval? | Suppose that we want to study the height of men $X$ in Canada for the last 2 years. Assume also that $X \sim N(\mu,\sigma^2)$ with $\sigma^2$ known. Then, talking about the probability
\begin{equation | What, precisely, is a confidence interval?
Suppose that we want to study the height of men $X$ in Canada for the last 2 years. Assume also that $X \sim N(\mu,\sigma^2)$ with $\sigma^2$ known. Then, talking about the probability
\begin{equation*}
P(X>1.80)=P(\omega \in \Omega:X(\omega)>1.80)
\end{equation*}
that a rando... | What, precisely, is a confidence interval?
Suppose that we want to study the height of men $X$ in Canada for the last 2 years. Assume also that $X \sim N(\mu,\sigma^2)$ with $\sigma^2$ known. Then, talking about the probability
\begin{equation |
1,856 | What, precisely, is a confidence interval? | A "confidence interval" is a specific case of the broader concept of a "confidence set", which may or may not be a single connected interval. The broader concept can be conceived mathematically as follows. Suppose we have an observable data vector $\mathbf{X}_n \equiv (X_1,...,X_n)$ from a distribution with unknown p... | What, precisely, is a confidence interval? | A "confidence interval" is a specific case of the broader concept of a "confidence set", which may or may not be a single connected interval. The broader concept can be conceived mathematically as fo | What, precisely, is a confidence interval?
A "confidence interval" is a specific case of the broader concept of a "confidence set", which may or may not be a single connected interval. The broader concept can be conceived mathematically as follows. Suppose we have an observable data vector $\mathbf{X}_n \equiv (X_1,.... | What, precisely, is a confidence interval?
A "confidence interval" is a specific case of the broader concept of a "confidence set", which may or may not be a single connected interval. The broader concept can be conceived mathematically as fo |
1,857 | Principled way of collapsing categorical variables with many levels? | If I understood correctly, you imagine a linear model where one of the predictors is categorical (e.g. college major); and you expect that for some subgroups of its levels (subgroups of categories) the coefficients might be exactly the same. So perhaps the regression coefficients for Maths and Physics are the same, but... | Principled way of collapsing categorical variables with many levels? | If I understood correctly, you imagine a linear model where one of the predictors is categorical (e.g. college major); and you expect that for some subgroups of its levels (subgroups of categories) th | Principled way of collapsing categorical variables with many levels?
If I understood correctly, you imagine a linear model where one of the predictors is categorical (e.g. college major); and you expect that for some subgroups of its levels (subgroups of categories) the coefficients might be exactly the same. So perhap... | Principled way of collapsing categorical variables with many levels?
If I understood correctly, you imagine a linear model where one of the predictors is categorical (e.g. college major); and you expect that for some subgroups of its levels (subgroups of categories) th |
1,858 | Principled way of collapsing categorical variables with many levels? | I've wrestled with this on a project I've been working on, and at this point I've decided there really isn't a good way to fuse categories and so I'm trying a hierarchical/mixed-effects model where my equivalent of your major is a random effect.
Also, in situations like this there seem to actually be two fusing decisio... | Principled way of collapsing categorical variables with many levels? | I've wrestled with this on a project I've been working on, and at this point I've decided there really isn't a good way to fuse categories and so I'm trying a hierarchical/mixed-effects model where my | Principled way of collapsing categorical variables with many levels?
I've wrestled with this on a project I've been working on, and at this point I've decided there really isn't a good way to fuse categories and so I'm trying a hierarchical/mixed-effects model where my equivalent of your major is a random effect.
Also,... | Principled way of collapsing categorical variables with many levels?
I've wrestled with this on a project I've been working on, and at this point I've decided there really isn't a good way to fuse categories and so I'm trying a hierarchical/mixed-effects model where my |
1,859 | Principled way of collapsing categorical variables with many levels? | If you have an auxiliary independent variable that is logical to use as an anchor for the categorical predictor, consider the use of Fisher's optimum scoring algorithm, which is related to his linear discriminant analysis. Suppose that you wanted to map the college major into a single continuous metric, and suppose th... | Principled way of collapsing categorical variables with many levels? | If you have an auxiliary independent variable that is logical to use as an anchor for the categorical predictor, consider the use of Fisher's optimum scoring algorithm, which is related to his linear | Principled way of collapsing categorical variables with many levels?
If you have an auxiliary independent variable that is logical to use as an anchor for the categorical predictor, consider the use of Fisher's optimum scoring algorithm, which is related to his linear discriminant analysis. Suppose that you wanted to ... | Principled way of collapsing categorical variables with many levels?
If you have an auxiliary independent variable that is logical to use as an anchor for the categorical predictor, consider the use of Fisher's optimum scoring algorithm, which is related to his linear |
1,860 | Principled way of collapsing categorical variables with many levels? | One way to handle this situation is to recode the categorical variable into a continuous one, using what is known as "target coding" (aka "impact coding") [1]. Let $Z$ be an input variable with categorical levels ${z^1, ..., z^K }$, and let $Y$ be the output/target/response variable. Replace $Z$ with $\operatorname{Imp... | Principled way of collapsing categorical variables with many levels? | One way to handle this situation is to recode the categorical variable into a continuous one, using what is known as "target coding" (aka "impact coding") [1]. Let $Z$ be an input variable with catego | Principled way of collapsing categorical variables with many levels?
One way to handle this situation is to recode the categorical variable into a continuous one, using what is known as "target coding" (aka "impact coding") [1]. Let $Z$ be an input variable with categorical levels ${z^1, ..., z^K }$, and let $Y$ be the... | Principled way of collapsing categorical variables with many levels?
One way to handle this situation is to recode the categorical variable into a continuous one, using what is known as "target coding" (aka "impact coding") [1]. Let $Z$ be an input variable with catego |
1,861 | Principled way of collapsing categorical variables with many levels? | There are multiple questions here, and some of them are asked & answered earlier. If the problem is computation taking a long time: There are multiple methods to deal with that, see large scale regression with sparse feature matrix and the paper by Maechler and Bates.
But it might well be that the problem is with ... | Principled way of collapsing categorical variables with many levels? | There are multiple questions here, and some of them are asked & answered earlier. If the problem is computation taking a long time: There are multiple methods to deal with that, see large scale regr | Principled way of collapsing categorical variables with many levels?
There are multiple questions here, and some of them are asked & answered earlier. If the problem is computation taking a long time: There are multiple methods to deal with that, see large scale regression with sparse feature matrix and the paper by... | Principled way of collapsing categorical variables with many levels?
There are multiple questions here, and some of them are asked & answered earlier. If the problem is computation taking a long time: There are multiple methods to deal with that, see large scale regr |
1,862 | Principled way of collapsing categorical variables with many levels? | The paper "A preprocessing scheme for high-cardinality categorical attributes in classification and prediction problems" leverages hierarchical structure in the category attributes in a nested 'empirical Bayes' scheme at every pool/level to map the categorical variable into a posterior class probability, which can be u... | Principled way of collapsing categorical variables with many levels? | The paper "A preprocessing scheme for high-cardinality categorical attributes in classification and prediction problems" leverages hierarchical structure in the category attributes in a nested 'empiri | Principled way of collapsing categorical variables with many levels?
The paper "A preprocessing scheme for high-cardinality categorical attributes in classification and prediction problems" leverages hierarchical structure in the category attributes in a nested 'empirical Bayes' scheme at every pool/level to map the ca... | Principled way of collapsing categorical variables with many levels?
The paper "A preprocessing scheme for high-cardinality categorical attributes in classification and prediction problems" leverages hierarchical structure in the category attributes in a nested 'empiri |
1,863 | What is meant by a "random variable"? | A random variable is a variable whose value depends on unknown events. We can summarize the unknown events as "state", and then the random variable is a function of the state.
Example:
Suppose we have three dice rolls ($D_{1}$,$D_{2}$,$D_{3}$). Then the state $S=(D_{1},D_{2},D_{3})$.
One random variable $X$ is th... | What is meant by a "random variable"? | A random variable is a variable whose value depends on unknown events. We can summarize the unknown events as "state", and then the random variable is a function of the state.
Example:
Suppose we h | What is meant by a "random variable"?
A random variable is a variable whose value depends on unknown events. We can summarize the unknown events as "state", and then the random variable is a function of the state.
Example:
Suppose we have three dice rolls ($D_{1}$,$D_{2}$,$D_{3}$). Then the state $S=(D_{1},D_{2},D_... | What is meant by a "random variable"?
A random variable is a variable whose value depends on unknown events. We can summarize the unknown events as "state", and then the random variable is a function of the state.
Example:
Suppose we h |
1,864 | What is meant by a "random variable"? | Introduction
In thinking over a recent comment, I notice that all replies so far suffer from the use of undefined terms like "variable" and vague terms like "unknown," or appeal to technical mathematical concepts like "function" and "probability space." What should we say to the non-mathematical person who would like ... | What is meant by a "random variable"? | Introduction
In thinking over a recent comment, I notice that all replies so far suffer from the use of undefined terms like "variable" and vague terms like "unknown," or appeal to technical mathemati | What is meant by a "random variable"?
Introduction
In thinking over a recent comment, I notice that all replies so far suffer from the use of undefined terms like "variable" and vague terms like "unknown," or appeal to technical mathematical concepts like "function" and "probability space." What should we say to the n... | What is meant by a "random variable"?
Introduction
In thinking over a recent comment, I notice that all replies so far suffer from the use of undefined terms like "variable" and vague terms like "unknown," or appeal to technical mathemati |
1,865 | What is meant by a "random variable"? | Informally, a random variable is a way to assign a numerical code to each possible outcome.*
Example 1
I flip a coin. The set of possible outcomes (also called the "sample space") may be written as $\{H,T\}$.
An example of a random variable $X$ might assign $X(H)=1$ and $X(T)=0$. That is, heads is "coded" as $1$ and t... | What is meant by a "random variable"? | Informally, a random variable is a way to assign a numerical code to each possible outcome.*
Example 1
I flip a coin. The set of possible outcomes (also called the "sample space") may be written as $\ | What is meant by a "random variable"?
Informally, a random variable is a way to assign a numerical code to each possible outcome.*
Example 1
I flip a coin. The set of possible outcomes (also called the "sample space") may be written as $\{H,T\}$.
An example of a random variable $X$ might assign $X(H)=1$ and $X(T)=0$. ... | What is meant by a "random variable"?
Informally, a random variable is a way to assign a numerical code to each possible outcome.*
Example 1
I flip a coin. The set of possible outcomes (also called the "sample space") may be written as $\ |
1,866 | What is meant by a "random variable"? | I was told this story:
A random variable can be compared with the holy roman empire: The
Holy Roman Empire was not holy, it was not roman, and it was not an
empire.
In the same way, a Random Variable is neither random, nor a variable. It is just a function. (the story was told here: source).
This is at least ... | What is meant by a "random variable"? | I was told this story:
A random variable can be compared with the holy roman empire: The
Holy Roman Empire was not holy, it was not roman, and it was not an
empire.
In the same way, a Random Va | What is meant by a "random variable"?
I was told this story:
A random variable can be compared with the holy roman empire: The
Holy Roman Empire was not holy, it was not roman, and it was not an
empire.
In the same way, a Random Variable is neither random, nor a variable. It is just a function. (the story was ... | What is meant by a "random variable"?
I was told this story:
A random variable can be compared with the holy roman empire: The
Holy Roman Empire was not holy, it was not roman, and it was not an
empire.
In the same way, a Random Va |
1,867 | What is meant by a "random variable"? | Unlike a regular variable, a random variable may not be substituted for a single, unchanging value. Rather statistical properties such as the distribution of the random variable may be stated. The distribution is a function that provides the probability the variable will take on a given value, or fall within a range ... | What is meant by a "random variable"? | Unlike a regular variable, a random variable may not be substituted for a single, unchanging value. Rather statistical properties such as the distribution of the random variable may be stated. The d | What is meant by a "random variable"?
Unlike a regular variable, a random variable may not be substituted for a single, unchanging value. Rather statistical properties such as the distribution of the random variable may be stated. The distribution is a function that provides the probability the variable will take on ... | What is meant by a "random variable"?
Unlike a regular variable, a random variable may not be substituted for a single, unchanging value. Rather statistical properties such as the distribution of the random variable may be stated. The d |
1,868 | What is meant by a "random variable"? | A random variable, usually denoted X, is a variable where the outcome is uncertain. The observation of a particular outcome of this variable is called a realisation. More concretely, it is a function which maps a probability space into a measurable space, usually called a state space. Random variables are discrete (can... | What is meant by a "random variable"? | A random variable, usually denoted X, is a variable where the outcome is uncertain. The observation of a particular outcome of this variable is called a realisation. More concretely, it is a function | What is meant by a "random variable"?
A random variable, usually denoted X, is a variable where the outcome is uncertain. The observation of a particular outcome of this variable is called a realisation. More concretely, it is a function which maps a probability space into a measurable space, usually called a state spa... | What is meant by a "random variable"?
A random variable, usually denoted X, is a variable where the outcome is uncertain. The observation of a particular outcome of this variable is called a realisation. More concretely, it is a function |
1,869 | What is meant by a "random variable"? | From Wikipedia:
In mathematics (especially probability
theory and statistics), a random
variable (or stochastic variable) is
(in general) a measurable function
that maps a probability space into a
measurable space. Random variables
mapping all possible outcomes of an
event into the real numbers are
fr... | What is meant by a "random variable"? | From Wikipedia:
In mathematics (especially probability
theory and statistics), a random
variable (or stochastic variable) is
(in general) a measurable function
that maps a probability space | What is meant by a "random variable"?
From Wikipedia:
In mathematics (especially probability
theory and statistics), a random
variable (or stochastic variable) is
(in general) a measurable function
that maps a probability space into a
measurable space. Random variables
mapping all possible outcomes of an
... | What is meant by a "random variable"?
From Wikipedia:
In mathematics (especially probability
theory and statistics), a random
variable (or stochastic variable) is
(in general) a measurable function
that maps a probability space |
1,870 | What is meant by a "random variable"? | The sample space may be a set of arbitrary elements, e.g. $\{\color{red} {\text{red}}, \color{green} {\text{green}}, \color{blue} {\text{blue}}\}$.
But this freedom of possible outcomes is difficult to work with. So someone invented the idea of working not with arbitrary elements, but only with real numbers.
To reach i... | What is meant by a "random variable"? | The sample space may be a set of arbitrary elements, e.g. $\{\color{red} {\text{red}}, \color{green} {\text{green}}, \color{blue} {\text{blue}}\}$.
But this freedom of possible outcomes is difficult t | What is meant by a "random variable"?
The sample space may be a set of arbitrary elements, e.g. $\{\color{red} {\text{red}}, \color{green} {\text{green}}, \color{blue} {\text{blue}}\}$.
But this freedom of possible outcomes is difficult to work with. So someone invented the idea of working not with arbitrary elements, ... | What is meant by a "random variable"?
The sample space may be a set of arbitrary elements, e.g. $\{\color{red} {\text{red}}, \color{green} {\text{green}}, \color{blue} {\text{blue}}\}$.
But this freedom of possible outcomes is difficult t |
1,871 | What is meant by a "random variable"? | In the my non-math university studies, we were told that random variable is a map from values that variable can take to the probabilities. This allowed to draw the probability distributions
Recently, I have realized how different is that from what mathematicians do have in mind. It turns out that by the random variabl... | What is meant by a "random variable"? | In the my non-math university studies, we were told that random variable is a map from values that variable can take to the probabilities. This allowed to draw the probability distributions
Recently, | What is meant by a "random variable"?
In the my non-math university studies, we were told that random variable is a map from values that variable can take to the probabilities. This allowed to draw the probability distributions
Recently, I have realized how different is that from what mathematicians do have in mind. I... | What is meant by a "random variable"?
In the my non-math university studies, we were told that random variable is a map from values that variable can take to the probabilities. This allowed to draw the probability distributions
Recently, |
1,872 | What is meant by a "random variable"? | A random variable is a measurable function defined on a probability space:
If $\left(\Omega,\mathcal F, \mathbb P\right)$ is a probability space and $\left(S, \mathcal A \right)$ a measurable space, then any $\mathcal F/\mathcal A$-measurable function $Y: \Omega \to S$ is called a ($S$-valued) random variable.
Some aut... | What is meant by a "random variable"? | A random variable is a measurable function defined on a probability space:
If $\left(\Omega,\mathcal F, \mathbb P\right)$ is a probability space and $\left(S, \mathcal A \right)$ a measurable space, t | What is meant by a "random variable"?
A random variable is a measurable function defined on a probability space:
If $\left(\Omega,\mathcal F, \mathbb P\right)$ is a probability space and $\left(S, \mathcal A \right)$ a measurable space, then any $\mathcal F/\mathcal A$-measurable function $Y: \Omega \to S$ is called a ... | What is meant by a "random variable"?
A random variable is a measurable function defined on a probability space:
If $\left(\Omega,\mathcal F, \mathbb P\right)$ is a probability space and $\left(S, \mathcal A \right)$ a measurable space, t |
1,873 | Locating freely available data samples | Also see the UCI machine learning Data Repository.
http://archive.ics.uci.edu/ml/ | Locating freely available data samples | Also see the UCI machine learning Data Repository.
http://archive.ics.uci.edu/ml/ | Locating freely available data samples
Also see the UCI machine learning Data Repository.
http://archive.ics.uci.edu/ml/ | Locating freely available data samples
Also see the UCI machine learning Data Repository.
http://archive.ics.uci.edu/ml/ |
1,874 | Locating freely available data samples | The following list contains many data sets you may be interested:
America's Best Colleges - U.S. News & World Reports
American FactFinder
The Baseball Archive
The Bureau of Justice Statistics
The Bureau of Labor Statistics
The Bureau of Transportation Statistics
The Census Bureau
Data and Story Library (DASL)
Data Set... | Locating freely available data samples | The following list contains many data sets you may be interested:
America's Best Colleges - U.S. News & World Reports
American FactFinder
The Baseball Archive
The Bureau of Justice Statistics
The Bur | Locating freely available data samples
The following list contains many data sets you may be interested:
America's Best Colleges - U.S. News & World Reports
American FactFinder
The Baseball Archive
The Bureau of Justice Statistics
The Bureau of Labor Statistics
The Bureau of Transportation Statistics
The Census Bureau... | Locating freely available data samples
The following list contains many data sets you may be interested:
America's Best Colleges - U.S. News & World Reports
American FactFinder
The Baseball Archive
The Bureau of Justice Statistics
The Bur |
1,875 | Locating freely available data samples | See my response to "Datasets for Running Statistical Analysis on" in reference to datasets in R. | Locating freely available data samples | See my response to "Datasets for Running Statistical Analysis on" in reference to datasets in R. | Locating freely available data samples
See my response to "Datasets for Running Statistical Analysis on" in reference to datasets in R. | Locating freely available data samples
See my response to "Datasets for Running Statistical Analysis on" in reference to datasets in R. |
1,876 | Locating freely available data samples | World Bank offers quite a lot of interesting data and has been recently very active in developing nice API for it.
Also, commugrate project has an interesting list available.
For US health related data head for Health Indicators Warehouse.
Daniel Lemire's blog points to few interesting examples (mostly tailored toward... | Locating freely available data samples | World Bank offers quite a lot of interesting data and has been recently very active in developing nice API for it.
Also, commugrate project has an interesting list available.
For US health related dat | Locating freely available data samples
World Bank offers quite a lot of interesting data and has been recently very active in developing nice API for it.
Also, commugrate project has an interesting list available.
For US health related data head for Health Indicators Warehouse.
Daniel Lemire's blog points to few inter... | Locating freely available data samples
World Bank offers quite a lot of interesting data and has been recently very active in developing nice API for it.
Also, commugrate project has an interesting list available.
For US health related dat |
1,877 | Locating freely available data samples | Gapminder has a number (430 at the last look) of datasets, which may or may not be of use to you. | Locating freely available data samples | Gapminder has a number (430 at the last look) of datasets, which may or may not be of use to you. | Locating freely available data samples
Gapminder has a number (430 at the last look) of datasets, which may or may not be of use to you. | Locating freely available data samples
Gapminder has a number (430 at the last look) of datasets, which may or may not be of use to you. |
1,878 | Locating freely available data samples | MLComp has quite a few interesting datasets, and as a bonus your algorithm will get ranked if you upload it. | Locating freely available data samples | MLComp has quite a few interesting datasets, and as a bonus your algorithm will get ranked if you upload it. | Locating freely available data samples
MLComp has quite a few interesting datasets, and as a bonus your algorithm will get ranked if you upload it. | Locating freely available data samples
MLComp has quite a few interesting datasets, and as a bonus your algorithm will get ranked if you upload it. |
1,879 | Locating freely available data samples | A good place to look is Carnegie Mellon University's Data and Story Library or DASL, which contains data files that "illustrate the use of basic statistics methods... A good example can make a lesson on a particular statistics method vivid and relevant. DASL is designed to help teachers locate and identify datafiles fo... | Locating freely available data samples | A good place to look is Carnegie Mellon University's Data and Story Library or DASL, which contains data files that "illustrate the use of basic statistics methods... A good example can make a lesson | Locating freely available data samples
A good place to look is Carnegie Mellon University's Data and Story Library or DASL, which contains data files that "illustrate the use of basic statistics methods... A good example can make a lesson on a particular statistics method vivid and relevant. DASL is designed to help te... | Locating freely available data samples
A good place to look is Carnegie Mellon University's Data and Story Library or DASL, which contains data files that "illustrate the use of basic statistics methods... A good example can make a lesson |
1,880 | Locating freely available data samples | Start R and type data(). This will show all datasets in the search path.
Many additional datasets are available in add-on packages.
For example, there are some interesting real-world social science datasets in the AER package. | Locating freely available data samples | Start R and type data(). This will show all datasets in the search path.
Many additional datasets are available in add-on packages.
For example, there are some interesting real-world social science da | Locating freely available data samples
Start R and type data(). This will show all datasets in the search path.
Many additional datasets are available in add-on packages.
For example, there are some interesting real-world social science datasets in the AER package. | Locating freely available data samples
Start R and type data(). This will show all datasets in the search path.
Many additional datasets are available in add-on packages.
For example, there are some interesting real-world social science da |
1,881 | Locating freely available data samples | NIST provides a Reference Dataset archive. | Locating freely available data samples | NIST provides a Reference Dataset archive. | Locating freely available data samples
NIST provides a Reference Dataset archive. | Locating freely available data samples
NIST provides a Reference Dataset archive. |
1,882 | Locating freely available data samples | http://www.reddit.com/r/datasets and also, http://www.reddit.com/r/opendata both contain a constantly growing list of pointers to various datasets. | Locating freely available data samples | http://www.reddit.com/r/datasets and also, http://www.reddit.com/r/opendata both contain a constantly growing list of pointers to various datasets. | Locating freely available data samples
http://www.reddit.com/r/datasets and also, http://www.reddit.com/r/opendata both contain a constantly growing list of pointers to various datasets. | Locating freely available data samples
http://www.reddit.com/r/datasets and also, http://www.reddit.com/r/opendata both contain a constantly growing list of pointers to various datasets. |
1,883 | Locating freely available data samples | The Stack Exchange network now has a new site, Open Data (in beta as of March 5th, 2015), dedicated to data. It describes itself as:
Open Data Stack Exchange is a question and answer site for developers and researchers interested in open data. It's built and run by you as part of the Stack Exchange network of Q&A s... | Locating freely available data samples | The Stack Exchange network now has a new site, Open Data (in beta as of March 5th, 2015), dedicated to data. It describes itself as:
Open Data Stack Exchange is a question and answer site for deve | Locating freely available data samples
The Stack Exchange network now has a new site, Open Data (in beta as of March 5th, 2015), dedicated to data. It describes itself as:
Open Data Stack Exchange is a question and answer site for developers and researchers interested in open data. It's built and run by you as part... | Locating freely available data samples
The Stack Exchange network now has a new site, Open Data (in beta as of March 5th, 2015), dedicated to data. It describes itself as:
Open Data Stack Exchange is a question and answer site for deve |
1,884 | Locating freely available data samples | Timetric provides a web interface to data and provide a list of the publicly available data sets they use. | Locating freely available data samples | Timetric provides a web interface to data and provide a list of the publicly available data sets they use. | Locating freely available data samples
Timetric provides a web interface to data and provide a list of the publicly available data sets they use. | Locating freely available data samples
Timetric provides a web interface to data and provide a list of the publicly available data sets they use. |
1,885 | Locating freely available data samples | Adding a couple to the list:
Lots of in-depth financial data on publicly-traded companies, going back many decades: http://www.mergent.com/servius
Rich information on 16+ million businesses in the US: http://compass.webservius.com
Both available via a REST API and have free trial plans. | Locating freely available data samples | Adding a couple to the list:
Lots of in-depth financial data on publicly-traded companies, going back many decades: http://www.mergent.com/servius
Rich information on 16+ million businesses in the US | Locating freely available data samples
Adding a couple to the list:
Lots of in-depth financial data on publicly-traded companies, going back many decades: http://www.mergent.com/servius
Rich information on 16+ million businesses in the US: http://compass.webservius.com
Both available via a REST API and have free tria... | Locating freely available data samples
Adding a couple to the list:
Lots of in-depth financial data on publicly-traded companies, going back many decades: http://www.mergent.com/servius
Rich information on 16+ million businesses in the US |
1,886 | Locating freely available data samples | This is probably the most complete list you'll find: Some Datasets Available on the Web | Locating freely available data samples | This is probably the most complete list you'll find: Some Datasets Available on the Web | Locating freely available data samples
This is probably the most complete list you'll find: Some Datasets Available on the Web | Locating freely available data samples
This is probably the most complete list you'll find: Some Datasets Available on the Web |
1,887 | Locating freely available data samples | Peter Skomoroch maintains a list of datasets at http://www.datawrangling.com/some-datasets-available-on-the-web. Many of the links provided as to places that list datasets. | Locating freely available data samples | Peter Skomoroch maintains a list of datasets at http://www.datawrangling.com/some-datasets-available-on-the-web. Many of the links provided as to places that list datasets. | Locating freely available data samples
Peter Skomoroch maintains a list of datasets at http://www.datawrangling.com/some-datasets-available-on-the-web. Many of the links provided as to places that list datasets. | Locating freely available data samples
Peter Skomoroch maintains a list of datasets at http://www.datawrangling.com/some-datasets-available-on-the-web. Many of the links provided as to places that list datasets. |
1,888 | Locating freely available data samples | I highly recommend checking out quandl.com. This is a data programmers dream. It provides one very easy API to access any of the over 10 million different data sits. You are looking for bi-modial or multi-variate data, so I would suggest checking out the various sets of population data eg this world population chart... | Locating freely available data samples | I highly recommend checking out quandl.com. This is a data programmers dream. It provides one very easy API to access any of the over 10 million different data sits. You are looking for bi-modial o | Locating freely available data samples
I highly recommend checking out quandl.com. This is a data programmers dream. It provides one very easy API to access any of the over 10 million different data sits. You are looking for bi-modial or multi-variate data, so I would suggest checking out the various sets of populat... | Locating freely available data samples
I highly recommend checking out quandl.com. This is a data programmers dream. It provides one very easy API to access any of the over 10 million different data sits. You are looking for bi-modial o |
1,889 | Locating freely available data samples | Data sets from seminal book A handbook of small data sets are available
here. | Locating freely available data samples | Data sets from seminal book A handbook of small data sets are available
here. | Locating freely available data samples
Data sets from seminal book A handbook of small data sets are available
here. | Locating freely available data samples
Data sets from seminal book A handbook of small data sets are available
here. |
1,890 | Locating freely available data samples | Here's another list that might be of help. | Locating freely available data samples | Here's another list that might be of help. | Locating freely available data samples
Here's another list that might be of help. | Locating freely available data samples
Here's another list that might be of help. |
1,891 | Locating freely available data samples | Searching for an appropriate data set for my needs I have just stumbled across two sites that are pertinent to this discussion.
Datacite.org which describes itself as...
We are an international organisation which aims to:
establish easier access to research data
increase acceptance of research data as legitimate cont... | Locating freely available data samples | Searching for an appropriate data set for my needs I have just stumbled across two sites that are pertinent to this discussion.
Datacite.org which describes itself as...
We are an international organ | Locating freely available data samples
Searching for an appropriate data set for my needs I have just stumbled across two sites that are pertinent to this discussion.
Datacite.org which describes itself as...
We are an international organisation which aims to:
establish easier access to research data
increase accepta... | Locating freely available data samples
Searching for an appropriate data set for my needs I have just stumbled across two sites that are pertinent to this discussion.
Datacite.org which describes itself as...
We are an international organ |
1,892 | Locating freely available data samples | Usage Over Time
A very large Excel spreadsheet available for download containing data points for all online activities, with user demographics, over time. Please read Tip Sheet (below) before downloading or using this spreadsheet.
http://pewinternet.org/Trend-Data/Usage-Over-Time.aspx | Locating freely available data samples | Usage Over Time
A very large Excel spreadsheet available for download containing data points for all online activities, with user demographics, over time. Please read Tip Sheet (below) before downloa | Locating freely available data samples
Usage Over Time
A very large Excel spreadsheet available for download containing data points for all online activities, with user demographics, over time. Please read Tip Sheet (below) before downloading or using this spreadsheet.
http://pewinternet.org/Trend-Data/Usage-Over-Time... | Locating freely available data samples
Usage Over Time
A very large Excel spreadsheet available for download containing data points for all online activities, with user demographics, over time. Please read Tip Sheet (below) before downloa |
1,893 | Locating freely available data samples | http://www.ckan.net has a number of datasets too.
http://www.biotorrents.net/browse.php is also starting to have quite a large amount of BIG datasets. | Locating freely available data samples | http://www.ckan.net has a number of datasets too.
http://www.biotorrents.net/browse.php is also starting to have quite a large amount of BIG datasets. | Locating freely available data samples
http://www.ckan.net has a number of datasets too.
http://www.biotorrents.net/browse.php is also starting to have quite a large amount of BIG datasets. | Locating freely available data samples
http://www.ckan.net has a number of datasets too.
http://www.biotorrents.net/browse.php is also starting to have quite a large amount of BIG datasets. |
1,894 | Locating freely available data samples | Here's a list of quantitative social science data: https://f.briatte.org/teaching/quanti
I update it every 3-4 months or so.
At the very end, I cite the "Data is Plural" newsletter, which has tons of interesting stuff. It's my favourite newsletter ever. | Locating freely available data samples | Here's a list of quantitative social science data: https://f.briatte.org/teaching/quanti
I update it every 3-4 months or so.
At the very end, I cite the "Data is Plural" newsletter, which has tons of | Locating freely available data samples
Here's a list of quantitative social science data: https://f.briatte.org/teaching/quanti
I update it every 3-4 months or so.
At the very end, I cite the "Data is Plural" newsletter, which has tons of interesting stuff. It's my favourite newsletter ever. | Locating freely available data samples
Here's a list of quantitative social science data: https://f.briatte.org/teaching/quanti
I update it every 3-4 months or so.
At the very end, I cite the "Data is Plural" newsletter, which has tons of |
1,895 | Locating freely available data samples | SODA POP at Penn State;
Simple Online Data Archive for POPulation studies. | Locating freely available data samples | SODA POP at Penn State;
Simple Online Data Archive for POPulation studies. | Locating freely available data samples
SODA POP at Penn State;
Simple Online Data Archive for POPulation studies. | Locating freely available data samples
SODA POP at Penn State;
Simple Online Data Archive for POPulation studies. |
1,896 | Locating freely available data samples | I'm gonna go ahead and bump an old topic because I just found this mother lode:
http://vincentarelbundock.github.io/Rdatasets/ | Locating freely available data samples | I'm gonna go ahead and bump an old topic because I just found this mother lode:
http://vincentarelbundock.github.io/Rdatasets/ | Locating freely available data samples
I'm gonna go ahead and bump an old topic because I just found this mother lode:
http://vincentarelbundock.github.io/Rdatasets/ | Locating freely available data samples
I'm gonna go ahead and bump an old topic because I just found this mother lode:
http://vincentarelbundock.github.io/Rdatasets/ |
1,897 | Locating freely available data samples | Singapore announces Open Data initiative. Check out data.gov.sg similar to data.gov in the US. | Locating freely available data samples | Singapore announces Open Data initiative. Check out data.gov.sg similar to data.gov in the US. | Locating freely available data samples
Singapore announces Open Data initiative. Check out data.gov.sg similar to data.gov in the US. | Locating freely available data samples
Singapore announces Open Data initiative. Check out data.gov.sg similar to data.gov in the US. |
1,898 | What's the difference between correlation and simple linear regression? | What's the difference between the correlation between $X$ and $Y$ and a linear regression predicting $Y$ from $X$?
First, some similarities:
the standardised regression coefficient is the same as Pearson's correlation coefficient
The square of Pearson's correlation coefficient is the same as the $R^2$ in simple linea... | What's the difference between correlation and simple linear regression? | What's the difference between the correlation between $X$ and $Y$ and a linear regression predicting $Y$ from $X$?
First, some similarities:
the standardised regression coefficient is the same as Pea | What's the difference between correlation and simple linear regression?
What's the difference between the correlation between $X$ and $Y$ and a linear regression predicting $Y$ from $X$?
First, some similarities:
the standardised regression coefficient is the same as Pearson's correlation coefficient
The square of Pea... | What's the difference between correlation and simple linear regression?
What's the difference between the correlation between $X$ and $Y$ and a linear regression predicting $Y$ from $X$?
First, some similarities:
the standardised regression coefficient is the same as Pea |
1,899 | What's the difference between correlation and simple linear regression? | Here is an answer I posted on the graphpad.com website:
Correlation and linear regression are not the same. Consider these differences:
Correlation quantifies the degree to which two variables are related. Correlation does not fit a line through the data.
With correlation you don't have to think about cause and effec... | What's the difference between correlation and simple linear regression? | Here is an answer I posted on the graphpad.com website:
Correlation and linear regression are not the same. Consider these differences:
Correlation quantifies the degree to which two variables are re | What's the difference between correlation and simple linear regression?
Here is an answer I posted on the graphpad.com website:
Correlation and linear regression are not the same. Consider these differences:
Correlation quantifies the degree to which two variables are related. Correlation does not fit a line through t... | What's the difference between correlation and simple linear regression?
Here is an answer I posted on the graphpad.com website:
Correlation and linear regression are not the same. Consider these differences:
Correlation quantifies the degree to which two variables are re |
1,900 | What's the difference between correlation and simple linear regression? | In the single predictor case of linear regression, the standardized slope has the same value as the correlation coefficient. The advantage of the linear regression is that the relationship can be described in such a way that you can predict (based on the relationship between the two variables) the score on the predict... | What's the difference between correlation and simple linear regression? | In the single predictor case of linear regression, the standardized slope has the same value as the correlation coefficient. The advantage of the linear regression is that the relationship can be des | What's the difference between correlation and simple linear regression?
In the single predictor case of linear regression, the standardized slope has the same value as the correlation coefficient. The advantage of the linear regression is that the relationship can be described in such a way that you can predict (based... | What's the difference between correlation and simple linear regression?
In the single predictor case of linear regression, the standardized slope has the same value as the correlation coefficient. The advantage of the linear regression is that the relationship can be des |
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