Z-test : Proportions : Sample Size

Version 3



    The workbook is a recipe for calculating a required Sample Size

    for two independent Proportions given Alpha, Power (1-Beta) and Effect Size.

    It is applied to a binary (categorical) outcome measure,

    such as web-ad click-through rate (CTR), or child mortality rate.


    A common case is a split-test (A/B test).

    When designing such tests (experiments)

    one should define a-priori minimal sample size(s)

    for a test group (A) and a control group (B) to get a result

    which is both statistically significant (defined by Alpha parameter)

    and has enough statistical power (defined by Beta parameter).


    But this calculation could also be applied Post-hoc --

    to estimate which groups (test cells) have been designed

    to have sample sizes well enough to validate differences

    in measured binary outcome(s) between them.


    As an example of a latter approach,

    data from The Global Slavery Index 2014


    were used in this workbook.


    As found in their methodology paper

    http://d1p5uxokz2c0lz.cloudfront.net/wp-content/uploads/2015/01/GSI2014_full_methodology_new-op.pdf ,

    data for the seven countries (including Russia) had been obtained from the Gallup World Poll 2014 survey.

    And the poll sample sizes are seen in Table 2 on page 5 of this document.


    So I combined these data together with the main GSI-2014 results

    in an Excel spreadsheet and use it as a Tableau datasource (in the attached).


    Link to a workbook on Tableau Public:




    Hope it could help someone.







    PS   The logic behind the calculations could be found in this article:


    General definitions are in Box 1, and the exact calculations and definitions

    for a categorical outcome measure are shown in Box 3 of the article.


    One could download a PDF version of the article here:



    More subjects on a topic:


    1. G*Power : statistical power analysis tool

    Universität Düsseldorf: G*Power


    2. G*Power Data Analysis Examples: Two independent proportions power analysis


    3. How large should your A/B test sample size be? - VWO Blog