CROSSTABULATION
The following crosstabulation examines the relationship between being abused as a child and committing sex offenses as an adult. It tests for the presence of a relationship by using a chi-square test. It examines how strong the relationship is by looking at the difference between the percentage of the non-abused who were sex offenders versus the percentage of the abused who were sex offenders.

                           Not 
                          Abused       Abused 
                           N     %    _N     %   TOTAL

No Sex Offense 56   70%   16   40%   72 60%

Sex Offense       24   30%   24   60%   48 40% 
TOTAL             80 100%   40 100% 120 100%
     chi ² = 10.47, d.f.=1, p<.01, alpha level cutoff=.05

The chi-square test is significant. If you look up the critical ratio for a chi-square in a table for one degree of freedom, the chi-square in the crosstabulation is larger than the critical value. Also, the "p" value is small than the alpha level criteria..

The percentage difference is 30% (60-30). Values less than 30% are weak relationships. This is a moderate relationship. If it had been greater than 50%, it would be a strong relationship.

T-TEST
The following t-test examines the relationship between mental illness and gender. It tests the presence of a relationship by using a t-test on the mean score for a scale of mental adjustment given to 50 men and 50 women. A score below 30 is clinically significant maladjustment. A 10 point difference in mean scores is clinically significant if this differences is also statistically significant.

          Men Women
Mean     35       45
Score
N          50       50 
 t = 1.91, d.f.=48, p=.06, alpha level=.05.

If one looks up the critical ratio for t in a t-test table for 48 degrees of freedom, we see the t value in the above table is smaller than the value in the critical ratio table. It is not statistically significant. The p-value is greater than the alpha level, which also indicates that the difference in the mean scores for men and women are not statistically significant. Since the difference is not statistically significant, one cannot say that the 10 point difference in their mean scores has clinical implications.
 

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