Question

Problem Set 3: One-Way randomized ANOVA

Research Scenario: A health psychologist is looking into the effects of different kinds of exercise on stress. She divides volunteers into three exercise groups: high-intensity interval training (HIIT) (n=8), yoga (n=8), or running (n=8). The volunteers participate in a set number of hours of the exercise for a month, after which the psychologist measures their stress levels on a scale of 1-40 where lower scores = lower stress, and higher scores = higher stress. The scores for each group are shown in the table below. Input the data into SPSS (remember you will enter the data only using 2 columns - one for group (make sure you label the values) and one fore stress. Conduct a one-way ANOVA to determine the effect of these different exercises on stress levels.

HIIT	16	25	19	11	17	11	15	27
YOGA	19	21	22	23	14	24	27	15
RUNNING	19	28	33	24	26	30	17	21

11) Paste relevant SPSS output

12) Create an appropriate graph to display this data.

13) Write an APA-style Results section based on your analysis. All homework "Results sections" should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and if relevant, effect size and/or post hoc analyses. Don't forget to include a decision about the null hypothesis.

Answer 1

11)

Using SPSS,

Entering the given data in 2 columns:

Following are the assumptions for conducting ANOVA:

- Dependent Variable (Stress) is continuous.

- Factor or Group is categorical, here, 3 categories- HIIT, Yoga, Running.

-Independence of Observations

And, to check the following assumptions,

-No significant outliers present

Since, the above box plot contains no point lying beyond the whiskers, we may conclude that there are no significant outliers.

- Stress scores are normally distributed accross each category and homogeneity of variance.

Since the p values (sig) of normality test and homogeneity of variance test are greater than 0.05, we may conclude that both the assumptions are satisfied.

To perform One way ANOVA,

The output obtained is as follows:

Since the p value obtained for the test is 0.045<0.05, we may conclude that the mean scores accross the three groups are significantly different.

The post hoc test reveals that the difference in mean occurs mainly in the 1st and 3rd group, namely, HIIT and Running.

12)

An appropriate graph to display the given data would be the box plot, given by,

From the graph, it is evident that the stress level of people under the running exercise group are comparatively higher than the rest.

13) One Way ANOVA

To test:

H₀ : Mean Stress Level is same for all the three groups.

Vs H₁ :  Mean Stress level is not same for the three groups.

The test conducted is one way ANOVA, which is used to compare means of two or more groups.

One way ANOVA test conducted, yielded significant results (p value = 0.045<0.05) which implies that there is not sufficient evidence to conclude that the mean stress level is same for all groups.Hence, we reject H₀ at 5% level of significance.

Hence, we may conclude that the mean stress level of the three groups are significantly different.

In order to determine, which among the pairs significantly differ, tukey's post hoc test is conducted.Its result reveals that the mean stress level of the group HIIT and Running are significantly different.