# 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

http://www.globalslaveryindex.org/

were used in this workbook.

As found in their methodology paper

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:

https://public.tableau.com/views/Z-TestProportionsSampleSize/Dashboard7

Hope it could help someone.

Yours,

Yuri

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

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3672437

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.

More subjects on a topic:

1. G*Power : statistical power analysis tool

Universität Düsseldorf: G*Power