ANOVA or Analysis of Variance is conducted to determine the significant differences between the means of three or more independent variables. Specifically, this test is conducted to test the Null hypothesis.
When to use ANOVA?
When a group is randomly split into 3 or smaller groups, in order to undertake different tasks and measure the outcome of the dependent variables. For example, we are studying the Marathon running speed of a group of individuals who belong to 3 different ‘Course’ levels: Beginner, Intermediate, and Advanced. Now if the researcher wants to know the outcome of different pacing strategies with respect to the course, then he/she would randomly divide the group of individuals participating in the marathon into three different groups with different speeds. The time taken by different groups to complete the marathon would indicate the outcome of the study (i.e. time) which is regarded as the dependent variable (because time is dependent on ‘Course’ and Speed).
One way ANOVA in SPSS
- Step 1: In Menu, Click Analyze -> Compare Means -> One way ANOVA (figure 1)
- Step 2: Once clicked, the One-Way ANOVA dialogue box will open as shown in Figure 2 given below:
- Step 3: Next transfer the “Dependent List” i.e. Time is taken to complete the Marathon; and the Independent variable i.e. course (Beginner, Intermediate and Advanced) into “FACTOR” (Figure 3)
- Step 4: Once that is done Click on the Post Hoc button and select “Tukey” and Click on Continue (Figure 4).
- Step 5: Next Click on Options, and a new dialogue box would open. In this dialogue box, check ‘Descriptive’ as shown below. Click Continue and then click OK (Figure 5).
Output and Results
The Descriptives Table is given below (Table 1) provides useful information about the descriptive statistics including Mean, Median, Standard Deviation and 95% confidence interval with respect to Dependent variable i.e. Time for three groups i.e. Beginners, Intermediate and Advanced. Here “N” reflects the sample size for each group. Mean is the average time taken to complete the marathon within the individual group. This reflects that the average time taken by advanced course individuals was the least although, in comparison to Intermediate, we can see that there is not much difference in the average meantime. 95% confidence interval for Mean reflects the minimum and maximum time taken by the individual at 95% significance.
- N: Number of respondents in the sample size
- Mean: Average Time taken by respondents within the sample
- Standard Deviation: Deviation in an average time of each pacer within the sample.
- 95% Confidence Interval for Mean: It estimates the mean response for each group level i.e. Beginner, Intermediate and Advanced at a 95% confidence interval. The difference in Upper Bound and Lower Bound values (i.e. since they are not overlapping) indicates that there is a difference in population means between the three group levels.
- Maximum/Minimum: Simply reflects the maximum and minimum time scored by pacers within each group i.e. Beginner, Intermediate and Advanced
Interpretation of ANOVA table
Table 2 shown below reflects the results of the ANOVA analysis which would enable the researcher to determine the difference between the group means. The results reflect a statistically significant p-value i.e. p=0.021 (p< 0.05) and show that the difference between the course taken is significantly related to the mean length of time. However, this table does not give the measure of difference for different runners within the individual groups and therefore the results of Post Hoc will be analyzed for the same.
The previous results indicate that there is a significant difference between groups. Now Table 3 shows the Multiple Comparison Table which reflects the differences between individual groups.
Tukey is considered to be the preferred test for Post Hoc analysis in the case of One Way ANOVA. As can be seen in Table 3 given below, there is a significant difference in time to complete the marathon between the group which took intermediate and beginner courses to complete the marathon (p =0.046). Also, the significant difference is reflected between groups who took beginner and advanced courses (p =0.034). However, there is no difference between groups who took the intermediate and advanced courses (p =0.989)
Inference: On the basis of the above results, one can interpret that there is a statistically significant difference between groups as one-way ANOVA shows (F = 4.467, p = .021). A Tukey posthoc test revealed that the time to complete the race was statistically significantly lower after taking the intermediate (23.6 ± 3.3 min, p = .046) and advanced (23.4 ± 3.2 min, p = .034) course compared to the beginner’s course (27.2 ± 3.0 min). There were no statistically significant differences between the intermediate and advanced groups (p = .989).