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
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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 |
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