Descriptive Statistics: Value a.)Looking at the median housing values for highly
ID: 3159589 • Letter: D
Question
Descriptive Statistics: Value
a.)Looking at the median housing values for highly and lesser educated towns we generate the descriptive statistics and graphs of the data are given above. Does it seem reasonable to compare the median housing values by using a two-sample t-test analysis? If not, what procedure would you suggest in order to continue using the t-test?
b.)Which non-parametric test do you suggest as an alternative to this two-sample t-test?
Variable Education Total Count Mean St.Dev Value 0 118 151.60 35.53 1 48 295.7 167.8 Histogram of Value Boxplot of Value vs Education 900 800 700 600 500 400 300 200 100 100 200 300 400 500 600 700 800 80 70 60 E 50 & 40 30 20 10 100 200 300 400 500 600 700 800 Value Education Panel variable: EducationExplanation / Answer
a) Looking at the median housing values for highly and lesser educated towns, it doesn't seem reasonable to compare the median housing values by using a two-sample t-test analysis. As the following assumptions of the two-sample t-test are not met:-
We have to use two-sample t-test for unequal variances, where there is no assumption of equal variance.
b) For the two-sample t test, the most common nonparametric alternative tests are the Wilcoxon rank-sum test (equivalent to the Mann-Whitney U test), and the Median test. Although the rank-sum test does not assume normality of the distributions for the two sample populations, it does assume that the two populations have the same distribution, except for a possible difference in the two population medians. Thus the rank-sum test will not address the problem of inequality of variances. Also, as with the t test, it is assumed that the two samples are independent of each other, and that there is independence within each sample.