Add Z tests (proportions & means)

[aurel-p]

Hi,

1. Intro

As mentioned in discussion #296, it would be convenient to have support for both proportion and mean z tests within pingouin.

statsmodels already provides several methods around those tests but in a confused and dispersed way, so you often end up writing some wrapper. Moreover, those methods sometimes have strange signatures, making it not really straightforward to use. A single and richer pandas output would be far more helpful. We are talking about basics here: in my opinion it would strengthen pingouin's position as a user-friendly but powerful and complete statistical package.

2. Ressources

• statsmodels

  • Proportions
    • z_stat and p_value: https://www.statsmodels.org/devel/generated/statsmodels.stats.proportion.proportions_ztest.html
    • diff CI: https://www.statsmodels.org/devel/generated/statsmodels.stats.proportion.confint_proportions_2indep.html
    • power: https://www.statsmodels.org/devel/generated/statsmodels.stats.proportion.power_proportions_2indep.html
    • effect size: https://www.statsmodels.org/dev/generated/statsmodels.stats.proportion.proportion_effectsize.html
  • Means
    • z_stat and p_value: https://www.statsmodels.org/stable/generated/statsmodels.stats.weightstats.ztest.html?highlight=ztest#statsmodels.stats.weightstats.ztest OR https://www.statsmodels.org/stable/generated/statsmodels.stats.weightstats.CompareMeans.ztest_ind.html#statsmodels.stats.weightstats.CompareMeans.ztest_ind
    • diff CI: https://www.statsmodels.org/stable/generated/statsmodels.stats.weightstats.zconfint.html?highlight=ztest OR https://www.statsmodels.org/stable/generated/statsmodels.stats.weightstats.CompareMeans.zconfint_diff.html#statsmodels.stats.weightstats.CompareMeans.zconfint_diff

• R

  • Means
    • Paired Z test: https://rpubs.com/nguyenminhsang/paired_z-test

3. Feature

• proportions_ztest()

  • parameters

    • x1: 2-column array_like, 1st column: number of trials, 2nd column: number of successes
    • x2: same or proportion value
    • alternative
    • paired
    • r
    • confidence
    • method: method for computing confidence interval, ‘newcomb’ (default), ‘wald’, ‘agresti-caffo’, ‘score’

  • returns

    • Z
    • alternative
    • p_val
    • CI95%: diff in proportion
    • cohen-d
    • BF10
    • power

• means_ztest()

  • parameters
    • x1: array_like
    • x2: same or mean value
    • alternative
    • paired
    • r
    • confidence
  • returns
    • Z
    • alternative
    • p_val
    • CI95%: diff in means
    • cohen-d
    • BF10
    • power

Thanks! Aurélien

[raphaelvallat]

Thanks for the detailed feature request @aurel-p! I won't have the time to implement this in the near future but I'll leave this issue open if anyone wants to give it a first go.