IV = Learning Method (Levels: lecture, turtorial, reading).
In the Variable View, under the Values column, "Lecture" was assigned a value of "1", "Tutorial" was assigned a value of "2", and "Reading" was assigned a value of "3"
DV = Test Score
Analyze > General Linear Model > Univariate...
In the Univariate dialogue box, move the IV into the Fixed Factor(s) box and the DV into the Dependent Variable box.
Step 4: Look at the Output
The main tables you need to look at are the "Descriptives Statistics" table, "Tests of Between-Subjects Effects" table, and "Multiple Comparisons" table.
The means in the "Descriptives Statistics" table can be used in the write-up of the descriptive statistics. However, to get the upper and lower bounds of the Confidence Intervals you will need to go to Analyze > Descriptive Statistics > Explore...
The "Tests of Between-Subjects Effects" table displays the results of ANOVA analysis, which shows whether there are significant differences between the groups as a whole.
The "Multiple Comparisons" table displays the results of the post-hoc tests, telling us which groups differed from each other. In this case, the significant differences lie between the tutorial group and the lecture group, and between the tutorial group and the reading group. There was no significant difference between the reading and the lecture groups.
ANOVA stands for Analysis of Variance. It is used to determine whether there is a significant difference between the means of three or more groups. It is an omnibus test, which means that it cannot tell you where the significant difference lies, such as whether group A is significantly different from group B or group C. You determine which groups were significantly different from each other by carrying out post-hoc tests, which will also be covered here.
There are two types:
A between-subjects/independent samples One-Way ANOVA
A within-subjects/repeated measures One-Way ANOVA
A mixed ANOVA
We will be looking at the first type.
The dependent variable (DV) should be scale data (either interval or ratio)
The independent variable (IV) should consist of two categorical groups
There should be no obvious outliers
The data should be roughly normally distributed for each group of the independent variable
Between-Subjects One-Way ANOVA(example)
Step 5: Calculate the Effect Sizes
The effect size of the ANOVA will be calulcated for you (Partial Eta Squared), but the effect sizes for the differences revealed by the post-hoc tests will need to be calculated by hand.
To calculate the effect size (Cohen's d), you need the means (x) and standard deviations (SD).
d = (x1 - x2) ÷ ((SD1 + SD2) ÷ 2)
Very Small < 0.3
Small-Medium > 0.3; < 0.5
Medium-Large > 0.5; < 0.8
Large > 0.8
Step 6: Write up
Figure 1. Mean Test Score and Confidence Intervals for the lecture group, the tutoruial group, and the reading group
Students had higher test scores for tutorial-based learning than lecture-based learning and reading-based learning. The mean test score for those in the tutorial group was 81.7 compared to 60.75 in the lecture group and 55.2 in the reading group. The confidence intervals show that the means are reasonably close to the population mean. *Report upper and lower bounds of the confidence intervals from Analyze > Descriptive Statistics > Explore ...*
A One-Way Between-Subjects ANOVA revealed a significant difference between the means [f(2, 57) = 15.288, p < 0.001]. The Global Effect Size using Partial Eta Squared was 0.349 which is small, and the Observed Power was 0.999 which is very strong. A Scheffé post hoc test revealed a significant difference between the lecture group and the tutorial group (p = 0.001) with a very large effect size (d = 1.44), and between the reading group and tutorial group (p < 0.001), also with a very large effect size (d = 1.79). The difference between the lecture group and the reading group was not significant (p = 0.551).
Click on Post Hoc... and move the IV to the Post HocTests for: box, and then check Scheffe. Another popular post-hoc test for between-subjects ANOVAs is Tukey. Click Continue.
Now click on Options... and move the IV to the Display MEans for: box, and then check Descriptive statistics, Estimates of effect size, and Observed power (and Parameter estimates if you want).
Click "OK" to get the output.