Yuen's Test Of Heteroscedasticity

The third problem was chosen to demonstrate the use of a method described in Rand Wilcox’s book [4] and implemented as a Minitab® macro in the diskette accompanying the book [5]. In class discussions lead to my interest in Yuen’s test of trimmed means which is appropriate for situations when there is evidence of non-normality and heteroscedasticity [4]. If there is no violation of normality but there’s is heteroscedasticity, the Yuen’s test without trimming, which is actually the classical Welch’s test, is appropriate. Therefore for this example, unlike the previous two, I first picked the method that I wanted to use and then looked for data where its application would be warranted.
The problem deals with comparison of hourly wages between …show more content…
Two variables from the original data were retained for analysis. These were Wage (hourly wage of the person) and College (binary variable indicating whether or not the person had a 4 year college degree, 1 for yes and 0 for no). The random sample contained the hourly wage data for 148 college graduates and 52 non college educated people.
The dataset containing the random sample of 200 observations used in the analysis is attached as a separate file, Wages.csv.
HYPOTHESIS
The goal was to compare the hourly wages of college-educated and non-college educated people. The null and alternative hypothesis is specified below:
Null Hypothesis, H0: There is no difference in the average hourly wages between college graduates and non-college educated people.
Alternative Hypothesis, H1: There is a difference the average hourly wages between college graduates and non-college educated people
It is clear from the specification of the alternative hypothesis that a two sided test would be performed since the concern was not in the direction of the difference but to test if at all there was a …show more content…
Therefore I used Yuen’s test for trimmed means which is considered most suited in terms of power and controlling Type I error rate when dealing with unequal variances and non-normality [4]. In order to use the Yuen’s test, the null and alternative hypothesis may be re-written as:
H0: The trimmed means are equal in the two groups, µt1 = µt1
H1: The trimmed means are equal in the two groups, µt1 ≠ µt1
Essentially we are testing for a shift in location with trimmed means being used as the measures of location in the two groups. The details about how to calculate the statistic and it’s standard error are given on pages of Rand Wilcox’s book [4].
REJECTION REGIONS
Once again, instead of relying on critical values, a pre-defined p value cut-off of 0.05 was used to determine significance i.e. it was determined before looking at the data that the significance level of the test would be 0.05.