Illustrated Example

Mixed-Factorial ANOVA

 

Example

 

This example is based on the work of Dr. Shawnna Helf. [Download Data Here]

 

Purpose

The purpose of this study was to compare two grouping conditions (i.e., one tutor to one student [1:1] and one tutor to three students [1:3]) on the reading achievement of first grade students identified at-risk for reading failure.

 

Participants

All first-grade students enrolled in three elementary schools will serve as the group from which the final 54 participants will be selected. The 54 students who participate in the study will be randomly selected from a pool of all of the students who meet the following criteria: (a) students will place into the instructional level labeled “Strategic - Additional Intervention” due to a combination of their scores on the DIBELS subtests, (b) written parental consent will be obtained for participating students, (c) students will be native speakers of English, (d) students will have no identified disability, and (e) students will be in classrooms where Open Court is the primary reading program. Before the intervention phase begins, the students will be distributed evenly among the two grouping conditions. The 1:1 grouping condition will be composed of 27 students and the 1:3 grouping condition will be composed of 27 students.

 

Variables

The independent variables were (a) type of grouping condition (1:1 or 1:3) and (b) time from pretest to posttest. The dependent variable was Oral Reading Fluency (ORF).


 

Analysis

 

Determine the analysis--there are two independent variables with one between subjects factor (grouping conditions) and one within subjects factor (pretest and posttest), and one dependent variable (ORF).

 

A 2X2 mixed-factorial ANOVA was conducted to examine the effects of grouping conditions on the pretest/posttest ORF means.

 

Analyze the data


 

 

 

 

 

 

 


Output

 

 
 

 

 

 


Results

 

The purpose of this study was to compare two grouping conditions (i.e., one tutor to one student [1:1] and one tutor to three students [1:3]) on the reading achievement of first grade students identified at-risk for reading failure. A 2X2 mixed-factorial ANOVA was conducted to examine the effects of grouping conditions on the pretest/posttest oral reading fluency (ORF) means. There were two independent variables with one between subjects factor (grouping conditions) and one within subjects factor (pretest and posttest and one dependent variable oral reading fluency (ORF). If there is a differential effect between the grouping conditions, we hypothesize the there should be a significant interaction. The means and standard deviations for the pretest and posttest ORF scores by grouping conditions are reported in Table 1.

 

Table 1

Means and Standard Deviations for Pretest and Posttest Oral Reading Fluency by Type of Grouping (1:1 or 1:3)

 

 

group

M

SD

N

Pretest

1:1

13.8800

8.98295

25

 

1:3

12.7083

11.11786

24

 

Total

13.3061

9.99626

49

Posttest

1:1

23.7600

11.33681

25

 

1:3

23.7083

11.56261

24

 

Total

23.7347

11.32802

49

 

The assumption of homogeneity of covariance matrixes was tenable (Box's M=5.94, p=.13). The results of the ANOVA are reported in Table 2. There was a statistically significant difference between pretest means to posttest means on the ORF, but there was not a significant interaction or significant between subjects effect.

 

Table 2

Results of the Mixed-Factorial ANOVA

 

Source

df

F

 

Partial Eta Squared

Within Subjects

 

 

 

 

Pre/Post

1

60.19

**

.56

Interaction

1

0.17

 

<.01

Error

47

 

 

 

Between Subjects

 

 

 

 

Grouping Type

1

0.05

 

<.01

Error

47

188.40

 

 

 

Summary

While there was a statistically significant change from pretest to posttest, there was not a significant interactions for the groups by pretest/posttest. These results suggest that the method of grouping students does not have an effect on the oral reading fluency of students.