Question

2. Take data sets A and B and delete duplicated values such that each value is unique even when pooling the two data sets. Just like with the previous problem, treat data sets A and B as hypothetical data on the weights of children whose parents smoke cigarettes, and those whose parents do not, respectively. Conduct a Wilcoxon Rank-Sum test on the data.

	Dataset A	Dataset B+0.5
	48.79	53.32
	49.72	51.74
	49.71	51.98
	49.59	52.02
	49.59	51.91
	51.12	51.62
	50.67	50.93
	51.02	50.08
	50.94
	51.19
Mean	50.234	51.7
S.D	0.847128	0.931557835
Variance	0.717626	0.8678

Answer 1

Two sample mann-whitney u, using Normal tables (n=10.0000) (two-tailed)

The normal approximation is used,the data contains ties, identical values, it is recommended to use the normal approximation that uses a ties correction.

H0: Group1 = Group2 V s H1: Group1 ≠ Group2

Z=(U-μ+c)/6

C - continuity correction, when U > μ: C = -0.5, when U < μ: C = 0.5

U=9.00

α=0.05

The test statistic Z equals -2.711396, is not in the 95% critical value accepted range: [-1.9600 : 1.9600].
U=9.00, is not in the 95% accepted range: [17.9500 : 0.09600].
The statistic S' equals 11.249

P-value

0.00670006, ( p(x≤Z) = 0.00335003 )

This means that the chance of type1 error (rejecting a correct H0) is small: 0.006700 (0.67%).
The smaller the p-value the more it supports H1.

4. Effect size
The observed standardized effect size, Z/√(n1+n2) ,is large (0.64). That indicates that the magnitude of the difference between the probability to choose bigger value from Group1 and the probability to choose bigger value from Group2 is large.
The common language effect size, U1/(n1n2), is: 0.11, this is the probability that a random value from Group1 is greater than a random value from Group2.