One-Way Analysis of Variance Flashcards
For a one-way analysis of variance (one-way ANOVA), each individual or case must have scores on…
two variables: a factor and a dependent variable.
The factor divides individuals into…
two or more groups or levels, whereas the dependent variable differentiates individuals on a quantitative dimension.
The ANOVA F test evaluates whether
the population means on the dependent variable differ across the levels of the factor.
A one-way ANOVA can be used to analyze data from different types of studies:
Experimental studies, Quasi-experimental studies, Field studies
An overall analysis-of-variance test is conducted to…
assess whether means on a dependent variable are significantly different among groups
If the overall ANOVA is significant and a factor has more than two levels:
follow-up tests are usually conducted. (These follow-up tests frequently involve comparisons between pairs of group means)
if a factor has three levels what might be conducted?
three pairwise comparisons might be conducted to compare the means of groups 1 and 2, the means of groups 1 and 3, and the means of groups 2 and 3. SPSS calls these follow-up tests post hoc multiple comparisons
Assumption 1:
The Dependent Variable Is Normally Distributed for Each of the Populations as Defined by the Different Levels of the Factor
Assumption 2:
The Variances of the Dependent Variable Are the Same for All Populations
Assumption 3:
The Cases Represent Random Samples from the Populations and the Scores on the Test Variable Are Independent of Each Other
The General Linear Model procedure computes an effect size index of…
eta squared
eta square ranges in value from 0 to 1 which mean…
value of 0 indicates that there are no differences in the mean scores among groups, a value of 1 indicates that there are differences between at least two of the means on the dependent variable and that there are no differences on the dependent variable scores within each of the groups (i.e., perfect replication)
eta squared is interpreted as…
the proportion of variance of the dependent variable that is related to the factor.
One-way ANOVA assumes…
equality of population variances. If this assumption is violated, use the Browne-Forsythe or the Welch statistic available within One-Way ANOVA in Compare Means
Writing APA Results, 1. Describe the statistical test(s
Describe the statistical test(s), the variables, and the purpose of the statistical test(s), Describe the factor or factors, Indicate the number of levels of each factor (description of each level), Describe what the dependent variables are.
- Report the results of the overall test(s).
Describe any decisions about which test was chosen based on assumptions (for a one-way within-subjects ANOVA, justify the choice of using a traditional univariate test instead of a multivariate test), Report the test value and significance level, Report statistics that allow the reader to make a judgment about the magnitude of the effect for each overall test (eta squared),
- Report the descriptive statistics
efer the reader to a table or figure that presents the relevant descriptive statistics (e.g., means and standard deviations for ANOVA designs)
- Describe and summarize the general conclusions of the analysis.
For example, “The results of the one-way ANOVA supported the hypothesis that different types of vitamin C treatment had a differential effect on the reduction of cold symptoms in individuals.”
- Report the results of the follow-up tests
Describe the procedures used to conduct the follow-up tests. Explain any decisions you made about the choice of tests based on their assumptions., Report the method used to control for Type I error across the multiple tests (e.g., Dunnett’s C)., Summarize the results of the follow-up procedures. It may be useful to present the results of the significance tests among pairwise comparisons with a table of means and standard deviations. When possible, report confidence intervals for pairwise comparisons.
Describe and summarize the general conclusions of the follow-up analyses. Make sure to include in your description the directionality of the test. For example, the mean for one treatment group is higher or lower than the mean for another group.
- Report the distributions of the dependent variable for levels of the factor(s)
Report the distributions of the dependent variable for levels of the factor(s) in a graph, if space is available. The graph should be inserted in the text where appropriate. For example, if the graph pertains to assumptions, you would insert it in the section where assumptions are discussed. Likewise, if the graph reflects the means and standard deviations, it should be presented with the delineation of these statistics.
