Repeated Measures ANOVA factorial withinsubjects designs OneWay Repeated
Repeated Measures ANOVA factorial within-subjects designs
One-Way Repeated Measures l 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 l The same subjects are assessed on pre, mid, and post treatment occasions. l The same subjects are given three different types of medication. l The same subjects rate three different aspects of school climate.
Factorial Designs l Between-subjects terms can be completely crossed within-subjects terms to form factorial designs. l 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 l Subjects are assessed on pre, mid, and post treatment occasions, AND are randomly assigned to two different treatments.
Examples - TREATMENT l Male and female participants each receive three different treatment conditions. Participants are randomly assigned to receive the treatments in different orders.
Examples - MEASURE l 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 l 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 l Factorial designs with multiple completely crossed within-subjects terms can also be used but are relatively rare in educational research. l “Split plot” designs are very common, with one within-subjects term (time) and one between-subjects term (group). Why?
Examples l Suppose you are charged with evaluating different delivery models for staff development in your school district. l The question is whether some use of computer based instruction would be helpful.
Examples l You are interested in evaluating knowledge, job satisfaction, and teaching effectiveness gains over time. l 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 l l A possible research design: What are some of the potential issues with this design?
Examples l What are some of the potential issues with this design? – – 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 l 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 l Null and Alternative Hypotheses for Multiple Main Effects l Null and Alternative Hypotheses for Interaction Terms l Graphing the data and post-hoc comparisons are essential as interpretation aids.
Hypotheses l Main Effect for Time (MEASURE or l Main Effect for Group l TREATMENT) Interaction Effects – different patterns of growth or rates of growth between the groups
Our Research Design
Differences l Sphericity Assumption with the Univariate case. l Homogeneity of Variance-Covariance Matrices in the Multivariate case. l Data from individual subjects occurs in multiple cells rather than only one cell.
Special Considerations l 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 betweensubjects terms l Consider the interactions first l Graph the results l Look at Height, Slope, Parallelism l Use Tukey Post Hoc test to help explain the results l
Interpretation l Height = difference between groups l Slope = growth over time l Parallelism = differential rates of growth between the groups
Graphs
- Slides: 23