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

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

Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach

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

CollectProcessDiscuss Crime in the Media Plan Is there any association between year of course and 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?

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: There is no association between year of course and type of accommodation There is an association

Collect ProcessDiscuss Plan The questionnaire

Collect ProcessDiscuss Which data Plan

Collect ProcessDiscuss Which data Plan

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

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

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

Process PlanCollectDiscuss Which processes If year and accommodation type are INDEPENDENT P(year 1 and Uni) = P(year 1) х P(Uni)

Process PlanCollectDiscuss Which processes How does this compare with P(year1 and Uni) P(year 1 and Uni) = How close are they??

Expected frequencies How many would we have expected to be year 1 and Uni? P(year 1 and Uni) If defective and B are independent Expected frequency = row total х column total overall total х (total number)

Process PlanCollectDiscuss Which processes H0:H0: H1:H1: There is no association between year of course and type of accommodation There is an association We also need to choose the level α Recall that α = P(reject H 0 when H 0 true) What is the test statistic?

The test statistic Expected frequency = row total х column total overall total i is row number j is column number e ij is expected frequency for cell (i, j) o ij is the observed (sample) frequency for cell (i, j) TEST STATISTIC X 2 has a distribution that is approximately The approximation is good when all of e ij ≥5 or when 80% of e ij ≥ 5 and all e ij ≥ 1 (Chi squared)

The distribution has a chi-squared distribution with (r-1)(c-1) degrees of freedom (r-1)(c-1) = rc – r – c + 1 number of o ij frequencies number of row totals number of column totals (r-1)(c-1) df Remove double counting

Different  2 distributions 2 d.f. 5 d.f. 50 d.f. 100 d.f.

The decision rule If o ij close to e ij (r-1)(c-1) df will be close to zero and X 2 will be small If o ij very different from e ij, and X 2 will be large DECISION RULE Reject H 0 if X 2 is too big

Process PlanCollectDiscuss Which processes Example H0:H0: H1:H1: α = 0.05 There is no association between year and accommodation type There is an association DECISION RULE Reject H 0 if d.f. = (3-1)Χ(3-1) = 4

Process PlanCollectDiscuss Which processes

Process PlanCollectDiscuss Which processes Example H 0 : H 1 : α = 0.05 There is no association between year and accommodation type There is an association DECISION RULE Reject H 0 if d.f. = (3-1)Χ(3-1) = 4 From sample data …

Process PlanCollectDiscuss Which processes From Minitab Expected frequencies Contribution to test statistic Test statistic

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

H 0 : there is no association between year and accommodation type H 1 : there is an association α = 0.05 DECISION rule Reject H 0 if DISCUSS d.f. = (r-1)Χ(c-1) = 4 REJECT Do not reject From sample data 4 df Discuss PlanCollectProcess

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

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?