Beyond the ANOVA

The Analysis of Variance is a powerful statistical technique for analyzing data. But what happens when we have conditions that go beyond the ANOVA and we need more?

2-way ANOVA

A two-way ANOVA is used when each participant in a study has scores on three variables: two independent variables (IV) with two or more levels and a dependent variable (DV). For example, a two-way ANOVA can be used to evaluate the effects of three different methods of math instruction on math achievement scores for boys and girls. In this example the first IV is gender which has two levels: male and female; the second IV is math instruction which has three levels: Method 1, Method 2, and a Control; the third variable is the DV-math achievement scores. The two-way ANOVA starts with an omnibus test to determine if there are any significant effects on the DV based on each IV and the interaction of the IV's. If the omnibus test indicates significance, then follow-up tests are required to specifically identify where the significant differences exist. A two-way ANOVA can be used to analyze data from experimental studies, quasi-experimental studies, and field studies.

contributed by Helen Knudsen

Repeated Measures ANOVA

Repeated measures ANOVA, as in any ANOVA, compares the means of different groups. What a repeated measures ANOVA allows the researcher to do, however, is to compare data on the same characteristic when samples are collected at different times (i.e. within a longitudinal study).

A repeated measures ANOVA can also be used when members of a random sample are matched based upon some criteria. The data collected at various points by the matched pairs in the study can then be analyzed with this method.

Submitted by Karen A. Fildes

ANCOVA

ANCOVA Steps in SPSS

→ Select Analyze

→ General Linear Model

→ Univariate

→ Put the DV in the Dependent Variable box and the IV in the Fixed Factors box. Proceed to put the covariates of interest in the Covariate(s) box.

→ Click on the Options button and move the IV over to the Display Means For box.

→ Click on Compare Main Effects and select Bonferroni from the Confidence interval adjustment menu to request post hoc tests.

→ Select Descriptive Statistics, Estimate of effect size and homogeneity tests from the display options.

When writing up the results, it is common to report certain figures from the ANCOVA table. F(df between, df within)= Test Statistic, p =

File:Https://www.sheffield.ac.uk/polopoly fs/1.531229!/file/MASH ANCOVA SPSS.pdf

contributed by Britany Kuslis, WCSU Cohort 8

Reference:

Rothwell, Joanne. “ANCOVA in SPSS.” www.statstutor.ac.uk, University of Sheffield, www.sheffield.ac.uk/polopoly_fs/1.531229!/file/MASH_ANCOVA_SPSS.pdf.

MANOVA

The Multivariate Analysis of Variance, also known as the MANOVA, is used when there are multiple dependent variables and you are looking at multiple factors. The only difference between an ANOVA and a MANOVA is that the ANOVA has the limitation of only allowing for a single dependent variable while the MANOVA allows for more. For example, using the MANOVA analysis, a researcher could examine Math Achievement and Reading Achievement scores.

An example research question for a MANOVA would be: Is there a significant difference in Math Achievement (computation, problem solving and numeracy) and Math Self Efficacy for students who participate in an after school treatment program for either one day per week (Program A), three days per week (Program B), or the traditional math curriculum.

DV 1: Math Achievement
Level 1: Computation
Level 2: Problem Solving
Level 3: Numeracy

DV 2: Self Efficacy

1V 1: Math Program
Level 1: Program A
Level 2: Program B
Level 3: Comparison/Control

contributed by Karen Fildes