HUDM 5123 - Linear Models and Experimental Design
HW 02 - One-Way ANOVA
Inst ructions.
You are encouraged to discuss problems with classmates, but all work you submit must be your own.
If applicable, any plots should have appropriate axis and overall labels.
In general, do not include computer output (either SPSS or R) in your write-up. Instead, summarize relevant points using text, tables, or plots.
When in doubt about formatting issues (e.g., for references, tables, notes, etc.), use APA style.
Background. The goal in Gomes-Koban et al (2017) is to test the efficacy of two vocabulary training programs adapted for Spanish-speaking children as compared with the read-aloud met hod.
Outcome variables were measures at three timepoints: baseline (Tl; at beginning of school year before intervention), posttest (T2; immediately after the intervention ended) and follow-up (T3; five months later at the end of the school year). Five outcome measures were assessed: taught words, control words, receptive vocabulary, expressive vocabulary, and reading comprehension.
Given the design of this experiment (multiple outcomes measured over time), two extensions would improve the analysis. First, we could use a multivariate ANovA technique to test all five outcomes at the same time for a treatment effect overall. This approach can have more power than testing the outcomes individually when they are correlated. Second, we could run a repeated measures analysis or mixed effects analysis that would allow us to analyze baseline, posttest, and follow-up data in the same analysis. In this course, we will cover repeated measures analyses but not multivariate methods.
For this assignment.
We will focus on a single outcome: Y = taught words, at posttest (T2) for simplicity and so that we can run the one-way ANOVA omnibus test.
X= Group is the treatment group variable where 1 = definition group, 2 = context group, and 3control group.
Your Tasks.
2 point 1. Baseline balance. Using the Gomes-Koban data, check baseline balance on age and baseline taught words score (T1_Taught Words). Group is the treat ment group variable where 1-definition group, 2-context group, and 3-control group. Report Cohen's d and variance ratios for each pair of group comparisons and comment on whether the results cause you to be concerned about lack of balance or not and why. Refer to the benchmark values discussed in lab.
1 point 2. Normality. Discuss the tenability of the assumption of normally dist ributed residuals (or, equivalently, normally distributed outcome within groups). Be sure to reference visual evidence based on QQ-plots as well as the results of the Kolmogorov-Smirnov and Shapiro-Wilk tests.
1 point 3. Given your conclusions about the tenability of the normality assumption, are you concerned about the validity of results? Why or why not? Be sure to discuss group sample sizes in your response.
1 point 4. Constant variance. Use the rule of thumb from MDK discussed in lab as well asvisual evidence from parallel boxplots and results from Levene's test of homogeneity of variances to comment on the tenability of this assumption.
1 point 5. Given your conclusions about the tenability of the constant variance assumption, are you concerned about the validity of results? Why or why not? Be sure to discuss group sample sizes in your response.
1 point 6. Independence. Is there any reason to be concerned about the tenability of the assumption of independence of observations here? Discuss this and refer to the paper.
2 point 7. ANOVA table. Regardless of what you decided about the tenability of the assumptions required for valid inferences above, go ahead and run the one-way ANOVA omnibus test for taught words at posttest (T2). Report the null and alternative hypotheses and create an ANOVAtable with Source, SS, df, MS, F, and p-value. This table should not be copy/pasted from SPSS. Create your own table in whatever word processing program you are using.
1 point 8. ANOVA results. Interpret the results of the omnibus test in context of the problem.