Introduction to Biostatistics

Introduction to Biostatistics
Assignment 2
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Question 1
a) Using R Commander, the requisite graphs for the distributions of income for males and
females has been presented separately.
Figure 1: Histogram of Income for Males and Females
Histograms for income of males as well as females are highly left skewed. High left skewness
in distribution reflected few outlier observations in high income category. Income above
8000 can be considered as unusually higher, and those observations made the distribution of
income as left skewed.
Figure 2: Histogram of Log_Income for Males and Females
Histograms for Log_income of males as well as females are almost normally distributed. The
bell shape of the histograms reflects the normal nature of the distributions.
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b) An independent sample t-test requires some assumptions to be satisfied. One of the
assumptions of independent t-test is normality of distribution of the sample. In this case
Log_income for both male and females are almost normally distributed. Hence, Log_income
are more appropriate compared to income for t-test.
c) Using R Commander, the results have been presented.
Null hypothesis: H0 : ( μLM =μLF ) There is no difference in average Log_income between
male and females.
Alternate hypothesis: H A : ( μLM ≠μLF ) There is statistically significant difference in
average Log_income between male and females.
Level of significance: α=0 . 05 or 5% level of significance is considered for this test.
Test statistics: Mean of Log_income for males = 7.31, and mean for females = 7.24. The t-
statistics = 1.089, p-value = 0.277, 95% confidence interval for difference between average
Log_income of males and females is [-0.058, 0.201].
Conclusion: As the p-value > 0.05, the null hypothesis failed to get rejected at 5% level of
significance. Hence, there is no statistically significant difference in Log_income between
males and females.
d) A non-parametric hypothesis test, Wilcoxon rank sum test (which ranks the data) will give
the same answer (Perolat, Couso, Loquin, & Strauss, 2015).
Null hypothesis: H0 : ( M LM =M LF ) There is no difference in distribution of medians of
Log_income between male and females.
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