Repeated Measures ANOVA factorial within-subjects designs

One-Way Repeated Measures One-way Repeated Measures Designs are used when: One-way Repeated Measures Designs are used when: – the same subjects are measured on 3 or more occasions (TIME) – the same subjects are exposed to 3 or more treatments (TREATMENT) – the same subjects provide three or more ratings that are measured on the same scale (MEASURE)

Examples The same subjects are assessed on pre, mid, and post treatment occasions. The same subjects are assessed on pre, mid, and post treatment occasions. The same subjects are given three different types of medication. The same subjects are given three different types of medication. The same subjects rate three different aspects of school climate. The same subjects rate three different aspects of school climate.

Factorial Designs Between-subjects terms can be completely crossed with within-subjects terms to form factorial designs. Between-subjects terms can be completely crossed with within-subjects terms to form factorial designs. All three uses of within-subjects terms, TIME, TREATMENT, and MEASURE, can be combined with between-subjects terms to form a variety of completely crossed factorial designs. All three uses of within-subjects terms, TIME, TREATMENT, and MEASURE, can be combined with between-subjects terms to form a variety of completely crossed factorial designs.

Examples - TIME Subjects are assessed on pre, mid, and post treatment occasions, AND are randomly assigned to two different treatments. Subjects are assessed on pre, mid, and post treatment occasions, AND are randomly assigned to two different treatments.

Examples - TREATMENT Male and female participants each receive three different treatment conditions. Participants are randomly assigned to receive the treatments in different orders. Male and female participants each receive three different treatment conditions. Participants are randomly assigned to receive the treatments in different orders.

Examples - MEASURE Teachers rate three different aspects of school climate, AND are randomly assigned to a treatment or control group. The treatment group gets a particular model of administrator support. Teachers rate three different aspects of school climate, AND are randomly assigned to a treatment or control group. The treatment group gets a particular model of administrator support.

Examples - MEASURE Subjects are randomly assigned to three different types of medication, AND asked to rate two different aspects of the effects of the drug. Subjects are randomly assigned to three different types of medication, AND asked to rate two different aspects of the effects of the drug.

Educational Evaluation Factorial designs with multiple completely crossed within-subjects terms can also be used but are relatively rare in educational research. Factorial designs with multiple completely crossed within-subjects terms can also be used but are relatively rare in educational research. “Split plot” designs are very common, with one within-subjects term (time) and one between-subjects term (group). Why? “Split plot” designs are very common, with one within-subjects term (time) and one between-subjects term (group). Why?

Examples Suppose you are charged with evaluating different delivery models for staff development in your school district. Suppose you are charged with evaluating different delivery models for staff development in your school district. The question is whether some use of computer based instruction would be helpful. The question is whether some use of computer based instruction would be helpful.

Examples You are interested in evaluating knowledge, job satisfaction, and teaching effectiveness gains over time. You are interested in evaluating knowledge, job satisfaction, and teaching effectiveness gains over time. You consider the following three specific delivery models for staff development in your school district: You consider the following three specific delivery models for staff development in your school district: – Traditional format – Computer-based tutorials – The combination of the two

Examples A possible research design: A possible research design: What are some of the potential issues with this design? What are some of the potential issues with this design?

Examples – Randomization of schools, teachers, classes, etc. – Difficulty of content – Time of the year the instruction takes place – Availability of computer technology

Our Research Design

Factorial Designs Just like the One-way ANOVA is analogous to the One-Way Repeated Measures procedure, Split plot factorial designs share many of the same properties with completely crossed Between- Subjects Factorial designs. Just like the One-way ANOVA is analogous to the One-Way Repeated Measures procedure, Split plot factorial designs share many of the same properties with completely crossed Between- Subjects Factorial designs.

Similarities Null and Alternative Hypotheses for Multiple Main Effects Null and Alternative Hypotheses for Multiple Main Effects Null and Alternative Hypotheses for Interaction Terms Null and Alternative Hypotheses for Interaction Terms Graphing the data and post-hoc comparisons are essential as interpretation aids. Graphing the data and post-hoc comparisons are essential as interpretation aids.

Hypotheses Main Effect for Time (MEASURE or TREATMENT) Main Effect for Time (MEASURE or TREATMENT) Main Effect for Group Main Effect for Group Interaction Effects – different patterns of growth or rates of growth between the groups Interaction Effects – different patterns of growth or rates of growth between the groups

Our Research Design

Differences Sphericity Assumption with the Univariate case. Sphericity Assumption with the Univariate case. Homogeneity of Variance-Covariance Matrices in the Multivariate case. Homogeneity of Variance-Covariance Matrices in the Multivariate case. Data from individual subjects occurs in multiple cells rather than only one cell. Data from individual subjects occurs in multiple cells rather than only one cell.

Special Considerations Additional potential threats to the validity of this type of design: Additional potential threats to the validity of this type of design: – practice effects – order effects – fatigue effects – carry-over effects

Interpretation Follow the same steps we used for factorial designs with only between- subjects terms Follow the same steps we used for factorial designs with only between- subjects terms Consider the interactions first Consider the interactions first Graph the results Graph the results Look at Height, Slope, Parallelism Look at Height, Slope, Parallelism Use Tukey Post Hoc test to help explain the results Use Tukey Post Hoc test to help explain the results

Interpretation Height = difference between groups Height = difference between groups Slope = growth over time Slope = growth over time Parallelism = differential rates of growth between the groups Parallelism = differential rates of growth between the groups

Graphs