Exercise 1

1. Exercise 1 • Use Transform  Compute variable to calculate weight lost by each person • Calculate the overall mean weight lost • Calculate the means and standard deviation by group and complete the table on the next slide (hint: can use Analyse  Explore to obtain stats) • Which diet resulted in the greatest weight lost and are the group standard deviations similar? • Use Graphs  Legacy Dialogs  Box-plot to produce a boxplot of weight lost by diet

2. Exercise 1: Summary statistics • Fill in the table • Which diet was best? • Are the standard deviations similar?

3. Exercise 2: Discuss the results Discuss the results and how you would interpret the table. Is there a difference between the groups?

4. Exercise 3: What are the significant differences between diets? Write up the results and conclude with which diet is the best

5. Exercise 3: Pairwise comparisons Results: Report:

6. Exercise 4: Can normality be assumed? From your histogram of the standardised residuals can normality be assumed? Should you: Use ANOVA Use Kruskall-Wallis

7. Exercise 4: Use Levene’s test to examine whether equal variances can be assumed? Null: p= Decision: Reject / do not reject Conclusion:

8. Exercise 5: Interaction Is there an interaction between gender and diet?

9. Exercise 6: Two way ANOVA with interaction • Run a two way ANOVA for gender and diet. Don’t forget to click on the Options box and request the estimated marginal means for Diet and Gender • Check the assumptions • Levene’s test for homogeneity of variance / look at the SDs within each group • Save the residuals and plot them – does they look normally distributed • Are the main effects of gender and diet significant? • Is the interaction between the two significant?

10. Exercise 7: ANOVA by gender • Split the file by group as described on the previous slide • Run the ANOVA again (removing gender from the Fixed Factor list) • Is there a diet effect for males and/ or females? • If there is, what is it and which diets are different?

11. Exercise 7: Post hoc tests and reporting results If the ANOVA is significant, produce suitable post hoc tests and summarise differences using summary statistics by diet/ gender

12. Exercise 1: Summary statistics • Which diet was best? Diet 3 with an average weight loss of 5.15kg per person • Are the standard deviations similar? Yes. The spread of weight loss within groups is similar

13. Exercise 2: Discuss the results There was a significant difference in mean weight lost [F(2,75)=6.197, p = 0.003] between the diets. The average weight lost in groups 1 and 2 was similar (3.3 kg and 3.03 respectively), but was much larger in group 3 (5.15kg)

14. Exercise 3: Pairwise comparisons Results: Report: There is no significant difference between diets 1 and 2 but there is between diet 3 and diet 1 (p = 0.02) and diet 2 and diet 3 (p = 0.005). Participants lost weight on all diets. The mean weight lost on diets 1 and 2 were similar (3.3 kg and 3 kg respectively) but the weight loss was more effective for diet 3 (5.15kg) compared to either diets 1 or 2.

15. Exercise 4: Can normality be assumed? Histogram of standardised residuals From your histogram of the standardised residuals can normality be assumed? Yes the residuals look approximately normally distributed Should you: Use ANOVA Use Kruskall-Wallis

16. Exercise 4: Use Levene’s test to examine whether equal variances can be assumed? Null: the variances of the groups are equal p= 0.52 Decision: Reject / do not reject Conclusion: Equality of variances can be assumed

17. Exercise 5: Interaction Is there an interaction between gender and diet? Yes it appears there is. The response to the different diets varies by gender

18. Exercise 6: Assumption of homogeneity Has the assumption of homogeneity been met?Yes the test is not significant. Could also look at the standard deviations by group

19. Exercise 6: Assumption of normality Has the assumption of normality been met? Looks like it

20. Exercise 6: ANOVA table What are the significant effects? Main effect of diet is significant • Main effect for gender is not significant • Interaction between diet and gender is significant

21. Exercise 7: ANOVA for diet by gender • Diet is only significant for females: type of diet is only important for women but not for men

22. Exercise 7: ANOVA for diet by gender • Diet is only significant for females, it appears that the type of diet is only important for women but not for men Gender was missing for two individuals For women weight loss is similar for diets 1 & 2 and both of these are different from diet 3 For men the diet type does not have an impact on weight loss as the loss is similar for all diets

23. Exercises 7: Post hoc tests and reporting the results • Participants lost weight on all diets. • For men the type of diet did not have an impact on weight loss as it was similar in all diet groups with an average weigh loss of about 4kg. • For women diet type did have an impact on the amount of weight lost. The mean weight loss on diets 1 and 2 were similar (3.3 kg and 3 kg respectively) but the weight loss was more effective for diet 3 (5.15kg) compared to either diets 1 or 2. Post hoc comparisons using the Tukey HSD test were carried out. There was no significant difference between diets 1 and 2 but there was between diet 3 and both diet 1 (p = 0.02) and diet 2 (p = 0.005) As part of the Post Hoc procedure SPSS subsets the groups. In this example it groups the women into two subsets consisting of diets 1 & 2 and diet 3 alone. For men as all diets gave similar results it forms a single ‘subset’ that consists of all diet groups