1. PlanCollectProcessDiscuss Start screen What sort of place do you live in?

2. PlanCollectProcessDiscuss Start screen What sort of place do you live in? Where do your friends live?

3. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach

4. PlanCollectProcessDiscuss Start screen How can you find out? Who should you ask? What proportion of students are freshers? Do most freshers live in university accommodation? What should you ask them? Plan

5. CollectProcessDiscuss Crime in the Media Plan Does the average rent paid depend on type of accommodation? Do freshers prefer private accommodation? D o t h i r d y e a r s l i v e i n h a l l ? Use a questionnaire? Do students pay a lot of rent?

6. CollectProcessDiscuss Eight categories Plan  Develop a model of the population.  One variable may depend on another.  Turn the model into precise statistical hypotheses (null and alternative). H0:H0: H1:H1: The average rent is the same for all types of accommodation The average rents differ

7. Collect ProcessDiscuss Plan The questionnaire

8. Collect ProcessDiscuss Which data Plan

9. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You are now here.

10. Collect ProcessDiscuss Which data Plan You did this in your first seminars Students at three other UK universities have completed the questionnaire

11. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You are now here.

12. Process PlanCollectDiscuss Which processes Analysis of variance Testing for –Differences between means ANOVA ANOVA If we want to detect differences between means why do we look at variances?

13. Process PlanCollectDiscuss Which processes H 1 true H 0 true Assume H 0 true when H 1 true The null hypothesis is H 0 : the means are all equal or μ 1 = μ 2 = μ 3 …… = μ k The alternative hypothesis is H 1 : the means are not all equal or μ i ≠ μ j for some i and j Assume the variance σ 2 is the same for all

14. Process PlanCollectDiscuss Which processes ANOVA H 0 : μ 1 = μ 2 = μ 3 …… = μ k H 1 : μ i ≠ μ j for some i and j Average the variances from these And compare it with the variance from this

15. Process PlanCollectDiscuss ANOVA H 0 : μ 1 = μ 2 = μ 3 …… = μ k H 1 : μ i ≠ μ j for some i and j Average the variances from these And compare it with the variance from this A big difference would support H 1 Within groups Between groups

16. Process PlanCollectDiscuss Which processes ANOVA Measuring the variability within groups 1.Calculate individual sample means 2.Calculate sum of squared deviations from these sample means for each group 3.Calculate the total sum of squares across all groups the within groups sum of squares 4. Then divide by the degrees of freedom n-k The within group mean square

17. Process PlanCollectDiscuss Which processes ANOVA Measuring the variability between groups 1.Calculate individual sample means 2.Calculate the overall sample mean 3.Calculate the between groups sum of squares as To estimate we would use because So to estimate σ 2 we use 4. Then divide by the degrees of freedom k-1 The between groups mean square

18. Process PlanCollectDiscuss Which processes The test statistic We have two estimates of σ 2 The within group mean square The between groups mean square If H 0 is true they should be similar We look at The test statistic F has an F distribution with k-1 numeratorAND n-k denominator degrees of freedom

19. Process PlanCollectDiscuss Which processes Different F distributions 3 and 179 d.f. 3 and 10 d.f. 10 and 10 d.f. 100 and 179 d.f.

20. Discussion H 0 : μ 1 = μ 2 = μ 3 H 1 : μ i ≠ μ j for some i and j α = 0.05 The decision rule is Reject if Can obtain this from Minitab Reject H 0 Do not reject 2 and 232 df Process PlanCollectDiscuss

21. Process PlanCollectDiscuss Which processes ANOVA table for rent versus type of accommodation A random sample of n=235 students across 3 universities was taken Type of accommodation classified as home, university or private Numerator df = k - 1 = 2 Denominator df = n - k = 232

22. Process PlanCollectDiscuss Which processes From Minitab Rent versus type within group mean square MS W between groups mean square MS B

23. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You are now here.

24. DISCUSS Discuss PlanCollectProcess Discussion H 0 : μ 1 = μ 2 = μ 3 H 1 : μ i ≠ μ j for some i and j α = 0.05 The decision rule is Reject if From sample data Reject H 0 Do not reject 2 and 232 df

25. Discuss PlanCollectProcess Discussion Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ----+---------+---------+---------+----- Home 5 319.60 251.78 (----------------*----------------) Private 117 248.36 85.78 (---*--) Uni 113 292.82 94.34 (---*--) ----+---------+---------+---------+----- 250 300 350 400 Pooled StDev = 95.23 Can we say why? What about students living at home? Have we asked the right questions?

26. Discuss PlanCollectProcess Discussion Other questions? about what is this due to about other questions/relationships What can we conclude?

27. Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You are now here. You can build on the first try by continuing here... Have you got all the evidence you want?