Where do chi squared p-value lookup tables come from?
$begingroup$
I'm doing a lot of labs in science and my teacher always wants us to find the chi-squared values of our data and find the probability of that occurring from a lookup table. Where do these probabilities come from in the lookup table? Is there a function or functions that output these numbers?
chi-squared
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I'm doing a lot of labs in science and my teacher always wants us to find the chi-squared values of our data and find the probability of that occurring from a lookup table. Where do these probabilities come from in the lookup table? Is there a function or functions that output these numbers?
chi-squared
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
the lookup tables your teacher mentions are the distribution tables. For example, you can get your p value for z score from normal distribution table while chi squared p-values would come from corresponding chi squared distribution. There are lots of online websites that replaced the traditional tables. for example see here
$endgroup$
– V. Aslanyan
3 hours ago
add a comment |
$begingroup$
I'm doing a lot of labs in science and my teacher always wants us to find the chi-squared values of our data and find the probability of that occurring from a lookup table. Where do these probabilities come from in the lookup table? Is there a function or functions that output these numbers?
chi-squared
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm doing a lot of labs in science and my teacher always wants us to find the chi-squared values of our data and find the probability of that occurring from a lookup table. Where do these probabilities come from in the lookup table? Is there a function or functions that output these numbers?
chi-squared
chi-squared
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
asked 4 hours ago
whackamadoodle3000whackamadoodle3000
1062
1062
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
whackamadoodle3000 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
the lookup tables your teacher mentions are the distribution tables. For example, you can get your p value for z score from normal distribution table while chi squared p-values would come from corresponding chi squared distribution. There are lots of online websites that replaced the traditional tables. for example see here
$endgroup$
– V. Aslanyan
3 hours ago
add a comment |
$begingroup$
the lookup tables your teacher mentions are the distribution tables. For example, you can get your p value for z score from normal distribution table while chi squared p-values would come from corresponding chi squared distribution. There are lots of online websites that replaced the traditional tables. for example see here
$endgroup$
– V. Aslanyan
3 hours ago
$begingroup$
the lookup tables your teacher mentions are the distribution tables. For example, you can get your p value for z score from normal distribution table while chi squared p-values would come from corresponding chi squared distribution. There are lots of online websites that replaced the traditional tables. for example see here
$endgroup$
– V. Aslanyan
3 hours ago
$begingroup$
the lookup tables your teacher mentions are the distribution tables. For example, you can get your p value for z score from normal distribution table while chi squared p-values would come from corresponding chi squared distribution. There are lots of online websites that replaced the traditional tables. for example see here
$endgroup$
– V. Aslanyan
3 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
A little about statistics and statistical tests.
When you use the data to compute these chi-square values, we idealize whatever you compute as coming from a probability distribution. The distribution is called the chi-square distribution.
The chi-square distribution depends on a parameter called "the degrees of freedom". Since probability distributions are just functions (you know about functions), I can plot them. I've plotted the chi-square under a couple of degrees of freedom below.
[![]](https://i.stack.imgur.com/ZedHl.png)
Now, onto p-values. Let's say you conduct your experiment and get a chi-square value. You go to your table and find the corresponding p-value. Those p-values in those tables are what we call "tail probabilities". So for example, let's say your experiment has 2 degrees of freedom (corresponding to the top left picture). You get a chi-square value of 2. Then, your p-value is the area under the curve to the right of 2 (the shaded region).
What those tables do is tell you the area under the curve for a variety of chi-square values. We obtain the values in the table by computing the area under the curve. It is easier to compute the areas under the curves once and put them in a table rather than have you compute the areas yourself, hence why you look up values in tables.
Math, if you are interested...
The function for the chi-square distribution is
$$f(x) = begin{cases} dfrac{x^{k/2 - 1}e^{-x/2}}{2^{k/2} Gamma(k/2)} quad x>0 \
0 qquadqquad text{else} end{cases}$$
Here, $k$ is the degrees of freedom. Suppose you get a chi-square value of $chi$. Then the p-value is
$$ lim_{srightarrow infty} int_{chi}^s f(x) , dx$$
We know this integral converges, and that it is less than 1 unless $chi=0$. The table is created by computing this integral for various $k$ and $chi$.
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "65"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
whackamadoodle3000 is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f388864%2fwhere-do-chi-squared-p-value-lookup-tables-come-from%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A little about statistics and statistical tests.
When you use the data to compute these chi-square values, we idealize whatever you compute as coming from a probability distribution. The distribution is called the chi-square distribution.
The chi-square distribution depends on a parameter called "the degrees of freedom". Since probability distributions are just functions (you know about functions), I can plot them. I've plotted the chi-square under a couple of degrees of freedom below.
[
Now, onto p-values. Let's say you conduct your experiment and get a chi-square value. You go to your table and find the corresponding p-value. Those p-values in those tables are what we call "tail probabilities". So for example, let's say your experiment has 2 degrees of freedom (corresponding to the top left picture). You get a chi-square value of 2. Then, your p-value is the area under the curve to the right of 2 (the shaded region).
What those tables do is tell you the area under the curve for a variety of chi-square values. We obtain the values in the table by computing the area under the curve. It is easier to compute the areas under the curves once and put them in a table rather than have you compute the areas yourself, hence why you look up values in tables.
Math, if you are interested...
The function for the chi-square distribution is
$$f(x) = begin{cases} dfrac{x^{k/2 - 1}e^{-x/2}}{2^{k/2} Gamma(k/2)} quad x>0 \
0 qquadqquad text{else} end{cases}$$
Here, $k$ is the degrees of freedom. Suppose you get a chi-square value of $chi$. Then the p-value is
$$ lim_{srightarrow infty} int_{chi}^s f(x) , dx$$
We know this integral converges, and that it is less than 1 unless $chi=0$. The table is created by computing this integral for various $k$ and $chi$.
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
$endgroup$
add a comment |
$begingroup$
A little about statistics and statistical tests.
When you use the data to compute these chi-square values, we idealize whatever you compute as coming from a probability distribution. The distribution is called the chi-square distribution.
The chi-square distribution depends on a parameter called "the degrees of freedom". Since probability distributions are just functions (you know about functions), I can plot them. I've plotted the chi-square under a couple of degrees of freedom below.
[
Now, onto p-values. Let's say you conduct your experiment and get a chi-square value. You go to your table and find the corresponding p-value. Those p-values in those tables are what we call "tail probabilities". So for example, let's say your experiment has 2 degrees of freedom (corresponding to the top left picture). You get a chi-square value of 2. Then, your p-value is the area under the curve to the right of 2 (the shaded region).
What those tables do is tell you the area under the curve for a variety of chi-square values. We obtain the values in the table by computing the area under the curve. It is easier to compute the areas under the curves once and put them in a table rather than have you compute the areas yourself, hence why you look up values in tables.
Math, if you are interested...
The function for the chi-square distribution is
$$f(x) = begin{cases} dfrac{x^{k/2 - 1}e^{-x/2}}{2^{k/2} Gamma(k/2)} quad x>0 \
0 qquadqquad text{else} end{cases}$$
Here, $k$ is the degrees of freedom. Suppose you get a chi-square value of $chi$. Then the p-value is
$$ lim_{srightarrow infty} int_{chi}^s f(x) , dx$$
We know this integral converges, and that it is less than 1 unless $chi=0$. The table is created by computing this integral for various $k$ and $chi$.
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
$endgroup$
add a comment |
$begingroup$
A little about statistics and statistical tests.
When you use the data to compute these chi-square values, we idealize whatever you compute as coming from a probability distribution. The distribution is called the chi-square distribution.
The chi-square distribution depends on a parameter called "the degrees of freedom". Since probability distributions are just functions (you know about functions), I can plot them. I've plotted the chi-square under a couple of degrees of freedom below.
[
Now, onto p-values. Let's say you conduct your experiment and get a chi-square value. You go to your table and find the corresponding p-value. Those p-values in those tables are what we call "tail probabilities". So for example, let's say your experiment has 2 degrees of freedom (corresponding to the top left picture). You get a chi-square value of 2. Then, your p-value is the area under the curve to the right of 2 (the shaded region).
What those tables do is tell you the area under the curve for a variety of chi-square values. We obtain the values in the table by computing the area under the curve. It is easier to compute the areas under the curves once and put them in a table rather than have you compute the areas yourself, hence why you look up values in tables.
Math, if you are interested...
The function for the chi-square distribution is
$$f(x) = begin{cases} dfrac{x^{k/2 - 1}e^{-x/2}}{2^{k/2} Gamma(k/2)} quad x>0 \
0 qquadqquad text{else} end{cases}$$
Here, $k$ is the degrees of freedom. Suppose you get a chi-square value of $chi$. Then the p-value is
$$ lim_{srightarrow infty} int_{chi}^s f(x) , dx$$
We know this integral converges, and that it is less than 1 unless $chi=0$. The table is created by computing this integral for various $k$ and $chi$.
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
$endgroup$
A little about statistics and statistical tests.
When you use the data to compute these chi-square values, we idealize whatever you compute as coming from a probability distribution. The distribution is called the chi-square distribution.
The chi-square distribution depends on a parameter called "the degrees of freedom". Since probability distributions are just functions (you know about functions), I can plot them. I've plotted the chi-square under a couple of degrees of freedom below.
[
Now, onto p-values. Let's say you conduct your experiment and get a chi-square value. You go to your table and find the corresponding p-value. Those p-values in those tables are what we call "tail probabilities". So for example, let's say your experiment has 2 degrees of freedom (corresponding to the top left picture). You get a chi-square value of 2. Then, your p-value is the area under the curve to the right of 2 (the shaded region).
What those tables do is tell you the area under the curve for a variety of chi-square values. We obtain the values in the table by computing the area under the curve. It is easier to compute the areas under the curves once and put them in a table rather than have you compute the areas yourself, hence why you look up values in tables.
Math, if you are interested...
The function for the chi-square distribution is
$$f(x) = begin{cases} dfrac{x^{k/2 - 1}e^{-x/2}}{2^{k/2} Gamma(k/2)} quad x>0 \
0 qquadqquad text{else} end{cases}$$
Here, $k$ is the degrees of freedom. Suppose you get a chi-square value of $chi$. Then the p-value is
$$ lim_{srightarrow infty} int_{chi}^s f(x) , dx$$
We know this integral converges, and that it is less than 1 unless $chi=0$. The table is created by computing this integral for various $k$ and $chi$.
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
answered 3 hours ago
Demetri PananosDemetri Pananos
974317
974317
add a comment |
add a comment |
whackamadoodle3000 is a new contributor. Be nice, and check out our Code of Conduct.
whackamadoodle3000 is a new contributor. Be nice, and check out our Code of Conduct.
whackamadoodle3000 is a new contributor. Be nice, and check out our Code of Conduct.
whackamadoodle3000 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Cross Validated!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f388864%2fwhere-do-chi-squared-p-value-lookup-tables-come-from%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
the lookup tables your teacher mentions are the distribution tables. For example, you can get your p value for z score from normal distribution table while chi squared p-values would come from corresponding chi squared distribution. There are lots of online websites that replaced the traditional tables. for example see here
$endgroup$
– V. Aslanyan
3 hours ago