# Statistical Analysis Approach

Analyses were performed on SOCRATES to measure the significance of change. Upon exam- ining distributions of the data it became clear that they were not distributed normally and were at the ordinal level of measurement. The data distributions imply that for descriptive statistics the median should be used as a measure of central tendency with the interquartile range as a measure of dispersion (Hays, 1994). The data did not fit the assumptions for modeling through Repeated Measures Analysis of Variance (RM-ANOVA), which assumes normally distributed variables at the interval or ratio level of measurement (Hays, 1994; Keppel, 1991; Stevens, 1996). Fortunately alternative nonparametric procedures were developed that could be applied to these data.

The hypotheses were tested using the Friedman’s Test (also known as Friedman’s ANOVA). Assumptions of the Friedman’s Test include: (1) variables are related, or not independent of each other, (3) variables are at the ordinal level of measurement, and (4) three or more vari- ables are included in the analysis (Pett, 1997). When a within subjects repeated measures approach is used the analysis should also include bivariate step down procedures to more precisely determine the source of the results (Keppel, 1991; Stevens, 1996). The step down analyses were conducted using the Wilcoxon-Signed Rank Test, whose assumptions include: (1) variables are related, or not independent of each other, (2) the variables are at the ordinal level of measurement, and (3) two variables are included in the analysis (Pett, 1997). Two additional assumptions of any within subjects analysis are (1) that cases are independent of each other, which means that membership in a group for one participant is not dependent on any other participant’s membership in a group, and (2) that a common metric is used for all the variables (Keppel, 1991; Stevens, 1996). Because the SOCRATES data were at the ordinal level of measurement, the SOCRATES was used consistently to measure variables, and this study did not use approaches that violated the independence of cases, such as matched case control designs, the data met the assumptions of the analyses used.

Since multiple hypothesis tests were conducted a risk of increased family wise Type I error rates was very real. To maintain a true a = .05 significance criterion, Bonferroni adjustments to the alpha necessary for statistical significance were made (Keppel, 1991). Since the alco- hol and drug forms measure participants’ readiness for change relating to different substance classifications, data from these forms were treated as unique sets. Since recognition and taking steps are considered within the program theory of change to be part of the same continuum, data from the two scales within either alcohol or drug data sets were considered part of the same set or family. Within both the alcohol and drug form data there were two hypotheses tested using the Friedman’s Test, so these were evaluated at a level of a = .025 (a = .05 / 2 = .025). As described in the subsequent section on available cases, the alcohol form step down analyses used three Wilcoxon-Signed Rank Tests, so these were evaluated at a level of a = .008 (a = .025 / 3 = .008). The drug form step down analyses used five Wilcoxon-Signed Rank Tests, so these were evaluated at a level of a = .005 (a = .025 / 5 = .005).

# Idaho Pre-Treatment Program

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