Question

Consider the data below of inches of rainfall per month for three different regions in the Northwestern United States:

Plains Mountains Forest

April 24.6 12.9 9.6

May 16.9 17.8 16.4

June 18.5 15.4 18.3

July 17.4 11.2 12.7

August 16.1 13.7 15.2

Using SPSS, perform an ANOVA test the hypothesis that there is not the same amount of rainfall in every region in the Northwestern United States with a significance level of 0.10. What are the two degrees of freedom of your test statistic? In a written analysis, explain what your conclusion is and why.

Answer 1

We used SPSS for One-way testing:

Following Steps we follows:

1. Click Analyze > Compare Means > One-Way ANOVA... on the top menu

2. You will be presented with the One-Way ANOVA dialogue box

3. Transfer the dependent variable, "Rainfall", into the Dependent List: box and the independent variable, "Region", into the Factor: box using the appropriate   buttons (or drag-and-drop the variables into the boxes).

4. Click the button. Tick the Tukey checkbox.

5. Click the button.

6. Click the button. Tick the Descriptive checkbox in the –Statistics– area

7. Click the button.

8. Click the button.

Following is the output we obtained using SPSS:

Degrees of Freedom

The total sample size is N =15. Therefore, the total degrees of freedom are:

df_total​ = 15−1=14

Also, the between-groups degrees of freedom are df_between​ = 3−1 = 2, and the within-groups degrees of freedom are:

df_within​ = df_total​−df_between ​= 14−2 = 12

The two degrees of freedom of your test statistic are df_between​ = 2 and df_within​ = 12.

Conclusion

The p-value is p=0.074, and since p=0.074 < 0.10, we reject null hypothesis. Therefore, there is enough evidence to claim that there is not the same amount of rainfall in every region in the Northwestern United States, at the α=0.10 significance level. This is great to know, but we do not know which of the specific regions differed. We can find this out in the Multiple Comparisons table which contains the results of the Tukey post hoc test.

From the Tukey post hoc test table, we can see that there is a statistically significant difference between rainfall between Plain and Mountain regions (p = 0.099 < 0.10).