This exerpt from a dissertation shows examples of two mixed-model ANOVAs. The study was a comparative analysis of three groups of students (students without learning disabilities, students with a reading disability, and students who had both a reading and math disability) on a math performance assessment. They were each tested under 6 conditions (a standard condition in which they received no accomodation, a condition in which the computer read the text of the test, a condition in which they watched a video that acted out the scenario in the assessment, a condition in which they constructed their responses on the computer rather than writing them on paper, a condition in which they chose any two accomodations, and a comprehensive condition in which they had access to all the accomodations). Both student achievement on the 6 tests and survey responses were compared for the three disability groups.

Student Achievement

The first ANOVA was a mixed-model ANOVA to compare the scores of students from each disability group (no disability, reading disability, reading and math disabilities) using test (accomodation condition) as the within-subjects variable and disability as the between-subjects variable. Significant differences were found for the main effects of test, F (4, 184) = 6.55, p < .001, and disability group, F (2, 46) = 23.27, p < .001, and for the interaction between the two variables, F (8, 184) = 2.54, p < .05. Table 5 shows mean scores and standard deviations for each disability group.

A series of one-way ANOVAs was run to follow-up the significant interaction between test condition and disability status. Four of the tests showed significant differences between the groups. Table 5 shows F-values for each test. Tukey HSD tests revealed that on each test that showed a significant difference, students without learning disabilities (LD) scored significantly higher than both students with RD and students with RMD, p < .01. Differences between students with RD and students with RMD were not significant on any test.

QUESTION:

1. What conclusion can you draw from the result for the Constructed Response test?

Table 5

Descriptive Statistics for Scores by Disability and Test Condition
	Disability
	NLD		RD		RMD	Marginal Means
Test	M	SD		M	SD		M	SD	Fa
Standard	30.88	13.23		14.14	9.75		9.70	6.21	18.33	23.16*
Computer-read text	33.28	13.22		14.92	11.32		9.77	8.65	19.34	19.02*
Video	34.28	16.44		11.89	8.64		10.33	8.78	19.72	20.73*
Constructed response	23.63	13.62		20.33	8.90		18.23	6.85	13.79	2.08
Two accommodations	20.56	11.22		16.87	7.64		17.81	5.47	18.02	1.34
Comprehensive	25.13	14.19		11.64	7.61		9.40	8.04	15.36	10.81*
Marginal means	29.44			12.78			8.49
aFollow-up one-way ANOVAs, df = 2, 46.
*p < .01.