Question

The effect of social competence training is tested. 12 Subjects are tested before and after the training for social competence on a seven point scale. Data are ordinal scaled and not normally distributed. The question is, if social competence is enhanced by the training. Use Sign Test. Raw data are listed in the following table:

Before 5 3 4 2 1 6 7 3 2 3 5 1

After 6 2 4 4 3 6 7 5 3 5 5 3

Answer 1

Calculation

Positive sign count = 1
Negative sign count = 7
Total count = 8

Z-score Calculation

z = (X - pn) / ?npq

z = (7 - 4) / ?2

z = 2.12132

The z-value is 2.12132. The p-value is .016947. The result is significant at p < 0.05.

So social compentency is enhanced by the traning

Answer 2

SOLUTION :

Before training                   5    3   4     2    1   6   7    3   2   3   5   1

 

After training                      6    2    4    4    3   6   7    5   3   5   5   3

 

Difference                          1  - 1    0    2    2   0   0    2   1   2   0   2

(After - Before)

Sign                                   +    -           +     +             +    +   +       +

There are 8 signs, 1 negative and 7 positive. Difference of zero means no sign.

Probability of either sign, p = 0.5 

Total number of signs, n = 8

So, 

mean, m = n p = 8*0.5 = 4

SD = sqrt(n p q) = sqrt(8 *0.5*(1 - 0.5)) = sqrt(2) 

For 7 point scale,

z = (X - m)/SD = (7 - 4)/sqrt(2) = 2.12132

For this value of z, p-value (one tail)  = 1 - 0.98305 = 0.01695 

At significance level of p-value of 0.05, the obtained p-value is outside the limit. 

Hence, difference is significant.

This means training enhances social competence level. (ANSWER).