Anderson – Darling goodness-of-fit test

This test is useful when some values in the data are quite smaller or larger compared to the sample mean, in other words data has several outliers.

Example Problems

The following problems have been formulated from the travel data collected from the elderly people (more than 60 years old) of Shimla, Himachal Pradesh. In these problems, travel related aspects of female and male travelers, like average walking time, average number of trips in terms of mean and the variability, have been compared.

Average Walking Time:

	Average Walking Time (in min) to Shimla downtown	Standard Deviation
Men	32.61	12.76
Women	35.85	14.78
Total Sample	33.95	13.71

Hypotheses testing for variance inequality between avg. walking time of elderly male and female trip makers

This problem deals with the testing of the variability in the walking times of elderly male and female trip makers in the Shimla town. Here, the two populations are the elderly male and female trip makers. Sample size collected from the male population is 297 and from the female population it is 210.

Variable 1 = Walking time for men

Variable 2 = Walking time for women

Hypotheses formulation for this problem is as follows;

H₀: σ₁² = σ₂²

H₁: σ₁² ≠ σ₂²

Sample means are 32.6 and 35.9 minutes for male and female travelers, respectively. Sample variances are 162.8 and 218.4 for both the variables respectively.

As discussed earlier the test statistic in this case follows F- distribution.

Test on the Variances
	Variable 1	Variable 2
Mean	32.6	35.9
Variance	162.8	218.4
Observations	297	210
df	296	209
F calculated	0.745
P(F<=f) one-tail	0.0102
F Critical one-tail	0.812

p-value of 0.01091484 (< 0.05) indicates that the variances are not equal so we will go for t-test for unequal variances for avg. walking time for men and women.