Standardize binomial variable for non-constant meta-population - binomial z-scores
$begingroup$
Let's say I'm doing a meta-analysis of a general experimental protocol that has been applied to some experiments (with 1,0 type outcomes) across a variety of experiment-type sub-groups. I want to test the hypothesis that experiments using the protocol are more likely to achieve their endpoint (x=1) than do other experiments of the same type sub-group that do not utilize the protocol. There may be only one or two experiments that utilized the protocol in each sub-group. All the experiments across all sub-groups are basically similar, except that the probability of success (p) can vary a fair amount across sub-groups (though p is constant within a sub-group). My instinct is to standardize each of the instances of the protocol-experiment outcomes (x) by calculating a Bernoulli z-score for each as z = (x - p) / sqrt{ p (1 - p) }, where p refers to the measured success-ratio across the entire sub-group that the (protocol-using) experiment x was drawn from. Then using this collection of standardized z values, what would be the test for my hypothesis? Would the (squared) standardized values follow a chi-squared distribution, as per the K-proportions theorem? Let me say, the populations of each sub-group are large (>3000), but the number of subgroups / protocol-using experiments is relatively small (10-20, depending), which means I'd be using small degrees of freedom despite having standardized on large sets ... ? Am I at all on the right track? Thanks for your help.
probability-theory statistical-inference binomial-distribution hypothesis-testing
asked Jan 1 at 16:34
fvcfvc
43
$endgroup$
add a comment |
$begingroup$
Let's say I'm doing a meta-analysis of a general experimental protocol that has been applied to some experiments (with 1,0 type outcomes) across a variety of experiment-type sub-groups. I want to test the hypothesis that experiments using the protocol are more likely to achieve their endpoint (x=1) than do other experiments of the same type sub-group that do not utilize the protocol. There may be only one or two experiments that utilized the protocol in each sub-group. All the experiments across all sub-groups are basically similar, except that the probability of success (p) can vary a fair amount across sub-groups (though p is constant within a sub-group). My instinct is to standardize each of the instances of the protocol-experiment outcomes (x) by calculating a Bernoulli z-score for each as z = (x - p) / sqrt{ p (1 - p) }, where p refers to the measured success-ratio across the entire sub-group that the (protocol-using) experiment x was drawn from. Then using this collection of standardized z values, what would be the test for my hypothesis? Would the (squared) standardized values follow a chi-squared distribution, as per the K-proportions theorem? Let me say, the populations of each sub-group are large (>3000), but the number of subgroups / protocol-using experiments is relatively small (10-20, depending), which means I'd be using small degrees of freedom despite having standardized on large sets ... ? Am I at all on the right track? Thanks for your help.
probability-theory statistical-inference binomial-distribution hypothesis-testing
asked Jan 1 at 16:34
fvcfvc
43
$endgroup$
add a comment |
$begingroup$
Let's say I'm doing a meta-analysis of a general experimental protocol that has been applied to some experiments (with 1,0 type outcomes) across a variety of experiment-type sub-groups. I want to test the hypothesis that experiments using the protocol are more likely to achieve their endpoint (x=1) than do other experiments of the same type sub-group that do not utilize the protocol. There may be only one or two experiments that utilized the protocol in each sub-group. All the experiments across all sub-groups are basically similar, except that the probability of success (p) can vary a fair amount across sub-groups (though p is constant within a sub-group). My instinct is to standardize each of the instances of the protocol-experiment outcomes (x) by calculating a Bernoulli z-score for each as z = (x - p) / sqrt{ p (1 - p) }, where p refers to the measured success-ratio across the entire sub-group that the (protocol-using) experiment x was drawn from. Then using this collection of standardized z values, what would be the test for my hypothesis? Would the (squared) standardized values follow a chi-squared distribution, as per the K-proportions theorem? Let me say, the populations of each sub-group are large (>3000), but the number of subgroups / protocol-using experiments is relatively small (10-20, depending), which means I'd be using small degrees of freedom despite having standardized on large sets ... ? Am I at all on the right track? Thanks for your help.
probability-theory statistical-inference binomial-distribution hypothesis-testing
asked Jan 1 at 16:34
fvcfvc
43
$endgroup$
Let's say I'm doing a meta-analysis of a general experimental protocol that has been applied to some experiments (with 1,0 type outcomes) across a variety of experiment-type sub-groups. I want to test the hypothesis that experiments using the protocol are more likely to achieve their endpoint (x=1) than do other experiments of the same type sub-group that do not utilize the protocol. There may be only one or two experiments that utilized the protocol in each sub-group. All the experiments across all sub-groups are basically similar, except that the probability of success (p) can vary a fair amount across sub-groups (though p is constant within a sub-group). My instinct is to standardize each of the instances of the protocol-experiment outcomes (x) by calculating a Bernoulli z-score for each as z = (x - p) / sqrt{ p (1 - p) }, where p refers to the measured success-ratio across the entire sub-group that the (protocol-using) experiment x was drawn from. Then using this collection of standardized z values, what would be the test for my hypothesis? Would the (squared) standardized values follow a chi-squared distribution, as per the K-proportions theorem? Let me say, the populations of each sub-group are large (>3000), but the number of subgroups / protocol-using experiments is relatively small (10-20, depending), which means I'd be using small degrees of freedom despite having standardized on large sets ... ? Am I at all on the right track? Thanks for your help.
probability-theory statistical-inference binomial-distribution hypothesis-testing
probability-theory statistical-inference binomial-distribution hypothesis-testing
asked Jan 1 at 16:34
fvcfvc
43
asked Jan 1 at 16:34
fvcfvc
43
edited Jan 2 at 14:00
fvc
asked Jan 1 at 16:34
fvcfvc
43
asked Jan 1 at 16:34
fvcfvc
43
asked Jan 1 at 16:34
fvcfvc
43
43
add a comment |
add a comment |
0
active
oldest
votes
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: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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%2fmath.stackexchange.com%2fquestions%2f3058627%2fstandardize-binomial-variable-for-non-constant-meta-population-binomial-z-scor%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- 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%2fmath.stackexchange.com%2fquestions%2f3058627%2fstandardize-binomial-variable-for-non-constant-meta-population-binomial-z-scor%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
