## Friday, February 16, 2018

### Comparing Classical and Non-Parametric Tests with Outliers

The Classical  t-test versus the Wilcoxon Rank Sum Test

Question:   In a previous post, I discussed differences in sales growth for 35 growth firms and 35 value firms.

Previous Post is Here:

The raw data used to construct the statistics presented in this post can be found in a financial data spreadsheet found here.

Use the data to conduct the classical t-test of the null hypothesis that the mean sales growth variable for the growth firms is not equal to the mean sales growth value for the value firms.

Use the data to conduct the Wilcoxon Rank Sum test for differences in the rank sums of the two samples.

Why do the test results differ so starkly?

Analysis:   The t-statistic from the classical test on difference between mean sales growth for the two funds is t =   0.6580.   The p-value for the two-tailed alternative is Pr(|T| > |t|) = 0.5128.

We fail to reject the null hypothesis of identical means at any commonly accepted level of significance.

The chart below gives rank sum and expected rank sum for the two populations.

 Fund Sample Sizer Observed Rank Exepected Rank Difference Growth 35 1437.5 1242.5 195 Value 35 1047.5 1242.5 -195

The difference between actual and expected rank (195)  is divided by the standard error (85.1)  calculated in STATA to get a z-score of 2.3 and a p-value of 0.02.

Implications:   The classical t-test indicates the differences between means of revenue growth rates for growth and value funds are NOT significant.

The non-parametric Wilcoxon Rank Sum Test finds differences in the populations are highly significant.

The outliers in both samples is the reason why classical tests fail to find a significant relationship between revenue growth of growth and value funds.