Interactions & Simple Effects finding the differences

Case Study

Case Study – Teacher Burnout 3

Case Study – Teacher Burnout b vs. a effect size = 1.259 d vs. c effect size = 0.706 b vs. c effect size = 1.817 4

Factorial Designs Factorial Designs are used when: a study includes more than one categorical IV. the researcher is interested in examining the relationship between several IVs and the DV. the researcher is interested in the combined effects of the IVs. 5

Two-Way ANOVA Two-Way ANOVA is a statistical term that refers to a specific type of factorial design. Two-Way ANOVA design includes two categorical IVs. Both IVs are Between-Subjects terms. They are completely crossed.

Hypotheses Two-Way ANOVA includes three sets of null and alternative hypotheses. There is a null and alternative hypothesis for each of the two main effects. There is also a null and alternative hypothesis for the interaction between the two IVs.

Interactions An interaction effect tests for the combined effects of several IVs. It examines whether the patterns to the means within the rows or columns are similar.  It examines whether any cell mean is out of the pattern that would be expected given the pattern of the main effects.

Interactions As we learned from the book, an interaction focuses on the differences in the differences.

Interactions

Interactions

Differences in the Differences This means that within any given column in the factorial design, the differences in row means are similar to those found in the other columns. This also means that within any given row in the factorial design, the differences in column means are similar to those found in the other rows.

Interpretation Guidelines 1. Interpret the significance test for interaction effects first. 2. Next, examine the main effects. 3. You may need to qualify your interpretation of the main effects based on the interactions.

Interpretation Guidelines 4. Graph the cell means both ways. This means allowing each IV to be the “line” and “column” variable in the graph, keeping the scaling the same. 5. Height – Line Main Effect Slope – Column Main Effect Parallelism – Interaction Effect

Enhancing Interpretation 6. Post Hoc Comparisons following Main Effects (3+ levels), which are important only if there is not an interaction effect. SPSS will perform these tests for you. Click on Post Hoc.

Enhancing Interpretation 7. Simple Main Effects, the effects within Rows or Columns, using Post Hoc Comparisons as needed. 8. Post Hoc Comparisons at the cell mean level. Steps 7 & 8 can be performed using a spreadsheet on the website. 16

Effect Sizes 9. Calculate Effect Sizes for the Cell Mean differences that best illustrate the patterns in your results.

Example Stress levels by Location and Intention to return   Example Stress levels by Location and Intention to return  

Example Main Effect 1: Location of School   Example Main Effect 1: Location of School Main Effect 2: Teacher Intention to Return Interaction: Combined Effects of Location and Intention to Return  

  SPSS Output  

  SPSS Output  

  SPSS Output  

  SPSS Output  

  SPSS Output  

HSD Post Hoc Tests for Cell Means

Mean square error comes from here   Mean square error comes from here  

Cell sizes come from here Cell means come from here