Statistical methods in psychology

Mathematics problems can be particularly difficult, especially for primary-grade children. A recent study investigated a combination of techniques for teaching students to master these problems (Fuchs, Fuchs, Craddock, Hollenbeck, Hamlett, & Schatschneider, 2008). The study investigated the effectiveness of small-group tutoring (sessions with or without tutoring) and the effectiveness of a classroom instruction technique known as “hot-math” (compared to traditional instruction). The hot-math program teaches students to recognize types or categories of problems so that they can generalize skills from one problem to another. Students were randomly assigned to the study conditions. The dependent variable is a math test score for each student after 16 weeks in the study. The results of the similar hypothetical study are presented in the summary table below. (25 points)
Source SS df MS Between Treatments 114 3 Tutoring 54 1 54 F(1, 20) = 12.56 Instruction 54 1 54 F(1, 20) = 12.56 Tutor x Instr. 6 1 6 F(1, 20) = 1.40 Within Treatments 86 20 4.3 Total 200 23
a. Describe the design of this study: how many factors and what are they? How many levels per factor? Is this a between or within study design? Is this an experiment? What type of analysis did researchers use to test their hypothesis? (7 points) b. How many students participated in the study total? (2 point) c. Is it possible to have an equal number of students in each sample? If yes, how many students would be in each sample? (2 points) d. Is there a significant main effect for any of the factors? (2 points) e. Is there a significant interaction? (2 point) f. Calculate and evaluate the effect size for significant factors and interaction (if significant). (4 points) g. Using the answers for the questions above, write a paragraph describing the study and its results in APA style. Make sure to report all relevant statistics. (6 points)