Compute z-statistic for z-test on proportions as the categorical variable (ZScoreForProportionZTest)

class cerebstats.stat_scores.zPropScore.ZScoreForProportionZTest(*args: Any, **kwargs: Any)

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