Question

Consider the following data, which result from two independent samples:

• GroupA:1,4,7 • GroupB:5,2,8

We are interested in examining the difference in sums between the two groups (A minus B) by using a permutation test. The permutation distribution (for the 20 different possible permutations) is shown below (note that it only contains odd values).

a) (3 points) What is the observed value of the test statistic?

b) (2 points) What is the p-value for a one-sided greater alternative?

c) (2 points) What conclusion do you draw from this test at the α = 0.1 significance level?

Consider the following data, which result from two independent samples: • Group A: 1, 4, 7 • Group B: 5, 2,8 We are interested in examining the difference in sums between the two groups (A minus B) by using a permutation test. The permutation distribution (for the 20 different possible permutations) is shown below (note that it only contains odd values). count a) (3 points) What is the observed value of the test statistic? b) (2 points) What is the p-value for a one-sided greater altemative? c) (2 points) What conclusion do you draw from this test at the a = 0.1 significance level?

Answer 1

(a) The value is -0.408.

(b) The p-value is 0.6480.

(c) Since the p-value (0.6480) is greater than the significance level (0.1), we cannot reject the null hypothesis.

Therefore, we cannot support the claim.

The output is:

Group A	Group B
4.00	5.00	mean
3.00	3.00	std. dev.
3	3	n
	4	df
	-1.000	difference (Group A - Group B)
	9.000	pooled variance
	3.000	pooled std. dev.
	2.449	standard error of difference
	0	hypothesized difference
	-0.408	t
	.6480	p-value (one-tailed, upper)

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