ANCOVA Research Scenario:

A church is operating a large substance abuse recovery program, and wants to know how they can be more effective in their work. Therefore, they hire a researcher to help them assess their effectiveness, and offer suggestions for improvements. Specifically, they want to know if different types of recovery training classes (traditional 12 step, Celebrate Recovery 12 step, uniquely designed nouthetic approach) have a different effect on a person's consumption of the substance. A pilot study was previously conducted using an ANOVA, with the three different teaching programs measured against the number of relapses in a six-month period. However, they wonder if a person's existing Bible knowledge may affect the scores. Therefore, the researcher decides to further study the teaching methods while considering the participants' biblical knowledge. The biblical knowledge is assessed by giving a general biblical knowledge test which is scored by percent of answers correct (0 to 100). Participants (N=99) are randomly assigned equally to one of the three teaching groups. Their biblical knowledge and number of relapses are scored to determine if there is covariance among these. Design this research based on the information given using an ANCOVA statistic. What is the critical value for the above scenario if it is a two-tailed test with a power of .05?