# BlogAnalytics 2014-12-01 23:21:00

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__Hypothesis Testing for Two Populations__

Code : https://github.com/sahuvaibhav/Stats.git

App : https://sahuvaibhav.shinyapps.io/Stats/

Added a new functionality to my stats app – Hypothesis testing for comparing two population means.

There are various techniques to compare means of two populations based on the type available sample data and the assumptions on population variance.

– **Comparing two independent populations’ means using Z-test.** This test is applied when sample sizes are large or population variances are known.*This can be performed using “Hypothesis Testing” tab in the app.*

– **Comparing two independent populations’ means using t-test. **t-test is applied to compare two independent populations means when sample sizes are small or population variances are not known.

Based on assumptions on population variances two techniques are available.

– **Pooled Variance Test – **When population variances are unknown and are assumed equal, pooled variance test is applied. Pooled Variance and degree of freedom for test is

df = n1+n2–2

s = sqrt(((s1^2*(n1-1) + s2^2*(n2-1))/(n1+n2-2))*(1/n1+1/n2))

– **Unpooled Variance Test – **When population Variances are unknown and are assumed not equal.

Unpooled Variance and degree of freedom are

df = (s1^2/n1+s2^2/n2)/((s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1) )

s = sqrt(s1^2/n1 + s2^2/n2)

*Both these tests can be performed at “independent sample” tab in the app.***– Paired Sample Test – **When same sample is tested two times to observe the difference paired sample test is performed (Like before and after cases).*“Paired Sample” tab in the app***– Comparing two population Proportions: **Two populations can be compared when sample proportions are available.*“Proportions” tab in the app*

Shiny R provides a number of functionality to create such applications.

Feedback and comments are welcome!!!

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