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

PlanCollectProcessDiscuss Start screen PlanCollectProcessDiscuss Start screen How safe is the area you live in?

What sort of area do you live in? CollectPlanProcessDiscuss Start screen How safe do you think it is?

Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach You can build on the first try by continuing here... First we decide what problem to solve and what data we need Then we collect suitable data. Then we examine our data and make it easier to understand.

Discuss Process PlanCollectProcessDiscuss Plan Collect DHCycle The Problem Solving Approach

How safe is your neighbourhood? TV, radio and newspapers regularly report crimes and crime statistics. CollectProcessDiscuss Crime in the Media Plan

CollectProcessDiscuss Set the problem How safe is your neighbourhood? Are the crime figures as bad as some of the newspapers suggest? What are the crime figures like in your neighbourhood? Are crime figures increasing each year? Should people be more/less concerned about certain crimes? Where in the UK is the ‘safest’ place to live? Where is the ‘crime capital’ of the UK? In which areas of the UK is crime increasing? Which places are improving?

PlanCollectProcessDiscuss Start screen How can you find out? Who should you ask? What proportion of students worried about safety? Do most freshers live in safe neighbourhoods? What should you ask them? Plan

CollectProcessDiscuss Crime in the Media Plan Is there any association between university town and attitude to safety? Do freshers choose ‘safe’ neighbourhoods to live in? A r e s t u d e n t s a t a l l u n i v e r s i t i e s w o r r i e d ? Use a questionnaire? What crimes worry students most?

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 university town and concern about being mugged There is an association

Collect ProcessDiscuss Plan The questionnaire

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 University and scale of worry are INDEPENDENT P(B and fairly worried) = P(B) х P(2)

Process PlanCollectDiscuss Which processes How does this compare with P(B and 2) P(B and 2) = How close are they??

Expected frequencies How many would we have expected to be B and 2? P(B and 2) If B and 2 are independent Expected frequency = row total х column total overall total х (total number) Process PlanCollectDiscuss

Process PlanCollectDiscuss Which processes H0:H0: H1:H1: There is no association between university and worry about being mugged 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) Process PlanCollectDiscuss

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 Process PlanCollectDiscuss

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

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

Process PlanCollectDiscuss Which processes Example H0:H0: H1:H1: α = 0.05 There is no association between university and worry about being mugged There is an association DECISION RULE Reject H 0 if d.f. = (3-1)Χ(5-1) = 8

Process PlanCollectDiscuss Which processes

Process PlanCollectDiscuss Which processes Example H 0 : H 1 : α = 0.05 There is no association between university and worry about being mugged There is an association DECISION RULE Reject H 0 if d.f. = (3-1)Χ(5-1) = 8 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 university attended and fear of being mugged H 1 : there is an association α = 0.05 DECISION rule Reject H 0 if DISCUSS d.f. = (r-1)Χ(c-1) = 8 REJECT Do not reject From sample data 8 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?