Start screen

1. Plan Start screen Collect Process Discuss What sort of place do you live in?

2. Plan Start screen Collect Process Discuss Where do your friends live? What sort of place do you live in?

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

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

5. Crime in the Media Collect Process Discuss Plan Do third years live in hall? Do freshers prefer private accommodation? Do students pay a lot of rent? Use a questionnaire? Does the average rent paid depend on type of accommodation?

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

7. Process Discuss Plan Collect The questionnaire

8. Which data Process Discuss Plan Collect

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

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

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

12. Plan Which processes Collect Discuss Process Analysis of variance • Testing for • Differences between means AN O VA ANOVA If we want to detect differences between means why do we look at variances?

13. Plan Which processes Collect Discuss Assume the variance σ2 is the same for all Process H0 true The null hypothesis is H0 : the means are all equal or μ1 = μ2 = μ3 …… = μk The alternative hypothesis is H1 : the means are not all equal or μi ≠ μj for some i and j H1 true Assume H0 true when H1 true

14. Plan Which processes Collect Discuss ANOVA Process H0 : μ1 = μ2 = μ3 …… = μk Average the variances from these H1 : μi ≠ μj for some i and j And compare it with the variance from this

15. Plan Collect Discuss ANOVA Process H0 : μ1 = μ2 = μ3 …… = μk Average the variances from these H1 : μi ≠ μj for some i and j Within groups And compare it with the variance from this Between groups A big difference would support H1

16. Plan Which processes Collect Discuss ANOVA Process • Measuring the variability within groups • Calculate individual sample means • Calculate sum of squared deviations from these sample means for each group • 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. Plan Which processes Collect Discuss ANOVA Process • Measuring the variability between groups • Calculate individual sample means • Calculate the overall sample mean To estimate we would use because So to estimate σ2 we use • Calculate the between groups sum of squares as 4. Then divide by the degrees of freedom k-1 The between groups mean square

18. Plan Which processes Collect Discuss The test statistic Process We have two estimates of σ2 The within group mean square The between groups mean square If H0 is true they should be similar The test statistic We look at k-1 numerator AND F has an F distribution with n-k denominator degrees of freedom

19. Plan Which processes Collect Discuss Different F distributions Process 3 and 179 d.f. 3 and 10 d.f. 10 and 10 d.f. 100 and 179 d.f.

20. Plan Collect Discuss Process Discussion H0 : μ1 = μ2 = μ3 H1 : μi ≠ μj for some i and j α = 0.05 2 and 232 df The decision rule is Reject if Do not reject Can obtain this from Minitab Reject H0

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

22. Plan Collect Discuss Process Which processes From Minitab Rent versus type between groups mean square MSB within group mean square MSW

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

24. Plan Collect Process Discuss DISCUSS Discussion H0 : μ1 = μ2 = μ3 H1 : μi ≠ μj for some i and j α = 0.05 2 and 232 df The decision rule is Reject if From sample data Do not reject Reject H0

25. Plan Discussion Collect Process Discuss Can we say why? 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 What about students living at home? Have we asked the right questions?

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

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