The Classical ttest 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 ttest 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 tstatistic from the classical test on
difference between mean sales growth for the two funds is t = 0.6580.
The pvalue for the twotailed 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 zscore of 2.3 and a pvalue of 0.02.
Implications: The classical ttest indicates the
differences between means of revenue growth rates for growth and value funds
are NOT significant.
The nonparametric 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.