Compute z-statistic for z-test on proportions as the categorical variable (ZScoreForProportionZTest
)¶
-
class
cerebunit.statistics.stat_scores.zPropScore.
ZScoreForProportionZTest
(*args, **kwargs)¶ Compute z-statistic for z-Test of proportions.
For single population.
Definitions Interpretation \(n\) sample size \(p_0\) some specified value \(\hat{p}\) sample proportion (with characteristic of interest), i.e, sample statistic \(se_{H_0}\) standard error of \(\hat{p}\) if \(p_0\) is the true value of p \(se_{H_0} = \sqrt{\frac{p_0(1-p_0)}{n}}\) z-statistic, z z = \(\frac{ \hat{p} - p_0 }{ \sqrt{\frac{p_0(1-p_0)}{n}} }\) For two populations.
Definitions Interpretation \(n_1\) sample size for first population (experimental data) \(n_2\) sample size for second population (prediction data) \(x_1\) numbers in first population’s sample having the trait in question \(x_2\) numbers in second population’s sample having the trait in question \(p_0\) 0 \(\hat{p_1}\) sample 1 proportion:math:hat{p_1} = frac{x_1}{n} \(\hat{p_2}\) sample 2 proportion:math:hat{p_2} = frac{x_2}{n} \(\hat{p_1}-\hat{p_2}\) sample statistic (with characterisic of interest) \(\hat{p}\) - estimate of common population proportion; if \(H_0\) is true
- \(p_1 = p_2 = p\) and estimate \(\hat{p}\) is \(\hat{p} = \frac{n_1\hat{p_1} + n_2\hat{p_2}}{n_1 + n_2}\) \(\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}\)
\(se_{H_0}\) standard error of \(\hat{p_1}-\hat{p_2}\) if \(H_0\) is true \(se_{H_0} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n_1} + \frac{\hat{p}(1-\hat{p})}{n_2}}\) z-statistic, z z = \(\frac{ \hat{p_1} - \hat{p_2} - p_0 }{ se_{H_0} }\) Use Case:
x = ZScoreForProportionZTest.compute( observation, prediction ) score = ZScoreForProportionZTest(x)
Note: As part of the SciUnit framework this custom
TScore
should have the following methods,compute()
(class method)sort_key()
(property)__str__()
-
classmethod
compute
(observation, prediction)¶ Argument Value type first argument dictionary; observation/experimental data must have keys “sample_size” and “phat” second argument floating number or array Note:
- observation must have the key “raw_data” whose value is the list of numbers