One-Way ANOVA
One-Way Analysis of Variance (ANOVA): Allows you to analyze the effects of multiple levels of a category (IV) on a test variable (DV). Whereas with the t test you are limited to 2 groups, with ANOVA you can have 2 or more groups (3 groups, 4 groups, etc.).
You can use the One-Way ANOVA for experimental and non-experimental data.
Assumptions of the One-Way ANOVA:
1) Groups are independent
2) IV or grouping variable is nominal (with two or more groups)
3) DV or test variable is interval or ratio
4) DV or test variable is normally distributed
5) Variability is approximately equal across groups
Overview of the Analyses required for a One-Way ANOVA:
· The ANOVA analysis will give you an F (instead of a t), although like the t:
F = Between group differences ¸ Within group differences (error)
When you report an F statistic, you need to report two types of df:
Between groups (treatment) df = Number of groups (G) – 1
Within groups (error) df = Number of Participants (N) – Number of Groups (G)
· You also need to report the effect size. Eta (h) is a correlation coefficient used to describe the magnitude of a relationship containing 2 or more levels. Eta2 (h2) tells you the proportion of variance in the test variable (DV) accounted for by the grouping variable (IV).
· If you find a statistically significant F, you will need to run post hoc tests.
A Multiple-Group Experiment Example:
A researcher hypothesizes that aerobic exercise will reduce anxiety. She randomly assigns 30 college students to three groups: 5 minutes of aerobics (low), 15 minutes of aerobics (medium), 30 minutes of aerobics (high). After the students are done with the aerobic exercise, she has each of them fill out a questionnaire rating their level of anxiety.
Data Entry:
To run a one-way ANOVA, you need at least two variables. One variable is the grouping variable or IV, the other is the test variable or DV.
Data entry for the one-way ANOVA is very similar to the independent-samples t test except that your IV will have 2 or more levels.
In the multiple-group experiment example, we would have a variable called “group” that is coded as 1=low, 2=medium, 3=high. We would also have a variable called “anxiety” that is scored on an interval scale.
Conducting a One-Way ANOVA:
First, you want to find out if there is a significant difference between your groups and the magnitude of this difference.
On SPSS Menu Bar, Click
Analyze à Compare Means à Means
The options box will appear:
SPSS OUTPUT
Means
If the F is statistically significant, this only tells you that differences exist among the groups. It doesn’t tell you which groups differ.
To find this out, you need to do post hoc comparisons.
Post Hoc Comparisons
You only do these if you have a statistically significant F from your ANOVA analysis. Post Hocs compare 1 level of the IV to all the other levels (pair wise comparisons). There are a ton of post hoc tests, we’ll use LSD (least significant difference).
On SPSS Menu Bar, Click
Analyze à Compare Means à One-Way ANOVA
The Post hoc box will appear:
The options box will appear:
SPSS OUTPUT
Oneway
Post Hoc Tests
Means Plots
Writing up Results
Include the following:
Ø The type of analysis(es) conducted and the variable examined.
Ø The mean and SD for each group.
Ø The F value, dfs, p value, and proportion of variance accounted for.
Ø A statement about whether or not the difference between the groups was statisitically significant.
Ø If the F was significant, report the results of the post hoc tests. Indicate which groups were significantly different from each other and the direction of the difference.