Test for Normality Assumption

A shapiro-wilks test for normality was used to evaluate the data. Graphical displays were used to further assess normality in the event that the shapiro-wilk test was sensitive to violations of normality due to the large sample size. The data consisted of total scores for the Pre and Post assessments for items B3 a-j related to employment skills and items D1 a-f which assessed individual distress. Gain scores were also calculated using the total scores from these sets of items. Items C1a and C1b were not evaluated for normality since these are four point likert style items and are therefore ordinal in nature.

Employment Skills


Pre-Test Total Score


Control Group


The shapiro-wilk test resulted in a p-value of 7.312e-09 providing evidence that the Pre-test score for the control group is not a normal distribution. The histogram confirms that this distribution is very right skewed. The QQ plot further demonstrates how these data do not conform to a normal distribution. Note that the gray area is the theoretical range of an appoximately normal distribution.


statistic p.value method
0.939 7.312e-09 Shapiro-Wilk normality test



Treatment Group


The shapiro-wilk test resulted in a p-value of 2.757e-09 providing evidence that the distribution is also not normal. The histogram confirms that this distribution is very right skewed as well. The QQ plot further demonstrates how these data do not conform to a normal distribution.

statistic p.value method
0.9381 2.757e-09 Shapiro-Wilk normality test




Post-Test Total Score


Control Group


The shapiro-wilk test resulted in a p-value of 1.426e-10 providing evidence that the distribution is also not normal. The histogram confirms that this distribution is also right skewed. The QQ plot also shows major deviations from what is expected of a normal distribution.

statistic p.value method
0.9197 1.426e-10 Shapiro-Wilk normality test



Treatment Group


The shapiro-wilk test resulted in a p-value of 1.208e-07 providing evidence that the distribution is also not normal. The histogram confirms that this distribution is also right skewed. The QQ plot also shows some deviation from what is expected of a normal distribution.

statistic p.value method
0.9535 1.208e-07 Shapiro-Wilk normality test



Gain Scores


Control Group


The shapiro-wilk test resulted in a p-value of 7.978e-09 providing evidence that the distribution is not normal. The histogram confirms that this distribution is quite leptokuritic. The QQ plot also shows major deviation from what is expected of a normal distribution.

statistic p.value method
0.9394 7.978e-09 Shapiro-Wilk normality test



Treatment Group


The shapiro-wilk test resulted in a p-value of 0.007085 providing evidence that the distribution is not normal. The histogram confirms that this distribution is somewhat leptokuritic. The QQ plot also shows some deviation for what is expected in a normal distribution.

statistic p.value method
0.9854 0.007085 Shapiro-Wilk normality test




Individual Distress


Pre-Test Total Score


Control Group


The shapiro-wilk test resulted in a p-value of 4.657e-09 providing evidence that the Pre-test score for the Control group is not a normal distribution. The histogram confirms that this distribution is very right skewed. The QQ plot further demonstrates that these data do not conform to a normal distribution.


statistic p.value method
0.9406 4.657e-09 Shapiro-Wilk normality test



Treatment Group


The shapiro-wilk test resulted in a p-value of 7.622e-09 providing evidence that the distribution is not normal. The histogram confirms that this distribution is very right skewed as well. The QQ plot further demonstrates that these data do not conform to a normal distribution.

statistic p.value method
0.9451 7.622e-09 Shapiro-Wilk normality test




Post-Test Total Score


Control Group


The shapiro-wilk test resulted in a p-value of 3.552e-10 providing evidence that the distribution is also not normal. The histogram confirms that this distribution is also right skewed. The QQ plot also shows major deviations from what is expected of a normal distribution.

statistic p.value method
0.9289 3.552e-10 Shapiro-Wilk normality test



Treatment Group


The shapiro-wilk test resulted in a p-value of 2.741e-13 providing evidence that the distribution is not normal. The histogram confirms that this distribution is also right skewed. The QQ plot also shows some deviation from what is expected of a normal distribution.

statistic p.value method
0.8935 2.741e-13 Shapiro-Wilk normality test



Gain Scores


Control Group


The shapiro-wilk test resulted in a p-value of 6.459e-07 providing evidence that the distribution is not normal. The histogram confirms that this distribution is quite leptokuritic. The QQ plot also shows major deviation from what is expected of a normal distribution.

statistic p.value method
0.9596 6.459e-07 Shapiro-Wilk normality test



Treatment Group


The shapiro-wilk test resulted in a p-value of 2.853e-09 providing evidence that the distribution is not normal. The histogram confirms that this distribution is leptokuritic. The QQ plot also shows deviation from what is expected of a normal distribution.

statistic p.value method
0.9411 2.853e-09 Shapiro-Wilk normality test




Analysis

The data are unsuitable for parametric analysis because they do not meet the normality assumption; however, the data do meet the assumptions for non-parametric analysis. The unpaired two-sample Wilcoxon test is the most approptiate procedure. The unpaired Wilcoxon is the cognate of the unpaired T-test with the chief difference being less stringent assumptions and a null hypothesis of equal population medians instead of means.


Only employment skills (items B3) gain scores and marriage beliefs (item C1a) were found to have significant desired differences in the median location for control and treatment groups. The effects of both can be assecertained by reference to the esitmate and the confindence intervals.


Employment Skills


Pre-Test

estimate statistic p.value conf.low conf.high alternative
-1 32472 0.1194 -1 2.96e-05 two.sided

Post-Test

estimate statistic p.value conf.low conf.high alternative
1.21e-05 35468 0.4433 -1 Inf greater

Gain Scores

estimate statistic p.value conf.low conf.high alternative
0.9999 38856 0.01925 1.972e-05 Inf greater



Individual Distress


Pre-Test

estimate statistic p.value conf.low conf.high alternative
-1 36499 0.16 -1 7.266e-05 two.sided

Post-Test

estimate statistic p.value conf.low conf.high alternative
-2.688e-06 38918 0.555 -1 Inf greater

Gain Scores

estimate statistic p.value conf.low conf.high alternative
7.557e-05 40277 0.2825 -5.184e-05 Inf greater



Marriage Beliefs


Pre-Test C1a

estimate statistic p.value conf.low conf.high alternative
2.369e-05 44384 0.9189 -8.837e-06 3.642e-05 two.sided

Post-Test C1a

estimate statistic p.value conf.low conf.high alternative
4.142e-05 48072 0.02194 5.824e-06 Inf greater

Gain Score C1a

estimate statistic p.value conf.low conf.high alternative
5.25e-05 47877 0.01969 6.524e-06 Inf greater



Pre-Test C1b

estimate statistic p.value conf.low conf.high alternative
-3.081e-05 43950 0.9834 -9.385e-05 5.92e-05 two.sided

Post-Test C1b

estimate statistic p.value conf.low conf.high alternative
-1.843e-05 41060 0.933 -5.668e-05 Inf greater

Gain Score C1b

estimate statistic p.value conf.low conf.high alternative
-4.533e-05 40817 0.9543 -6.853e-06 Inf greater