30 May 2013

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Crim 320

February 5, 2013

Chi square analysis and measures of association

Objectives

- outline the steps involved in conducting a chi-square analysis

- conduct and interpret a chi-square analysis

- explain and interpret lambda

- explain and interpret gamma

- know when to use each of the tests

- chi square uses a nominal variable - names, labels, exhaustive and exclusive categories

- there are no mathematical qualities to nominal variables ex. male, female

- a nominal level variable could never be considered normal, it will never take on a normal curve

The basic idea and logic of chi square analysis

- are two variables related to one another?

- null hypothesis: the two variables are independent

- must understand 2 related concepts

1. expected counts - what would occur if no relationship

2. observed counts - what we actually see

- if the observed counts are sufficiently different from the expected counts, we reject the null hypothesis

- all we can tell from a chi sq analysis is whether or not two variables are related to one another - the association

- if the hypothesis is null, the variables are independent and there is no relationship

- we can make this claim premised on the idea of the difference between what we'd expect to happen if the variables were not related and

what we actually see happen in the dataset

- if there was no relationship, the numbers assigned to each category would expected to be random/arbitrary

- the difference between expected and observed is the chi square value

Online reading

- does showing up at a domestic violence assessment vary depending on who reported the crime

- two nominal variables:

1. dichotomous - yes/no, did he or she show up for assessment

2. categorical - no domestic violence, father reported, mother reported, both reported

- research question: is there a relationship between who reported domestic violence and whether somebody showed up for a domestic

violence assessment?

- null hypothesis: there is no such relationship (as with all chi square analysis)

Steps for chi square

1. calculate expected values (3 steps)

2. (observed - expected)2 / expected

3. sum across all cells

4. calculate degrees of freedom

5. determine if we can reject the null hypothesis

Table 2: Reported Domestic Violence and Showed Up for Assessment

DV Subcategory

No DV

Father

Reported

Mother

Reported

Both Reported

No

Yes

Step 1: Column and row marginals

70+7+10+0=87

Table 2.1: Reported Domestic Violence and Showed Up for Assessment

DV Subcategory

No DV

Father

Reported

Mother

Reported

Both Reported

Row Marginals

No

70

7

10

0

87

Yes

216

Column Marginals

163

67

56

17

303

Expected cell counts

row total x column total/grand total

87 x 163 / 303 = 46.801 (round to 1 decimal place)= 46.801

Table 2.2: Reported Domestic Violence and Showed Up for Assessment

DV Subcategory

No DV

Father

Reported

Mother

Reported

Both Reported

Row Marginals

No

Cell 1

87

Yes

Cell 7

216

Column Marginals

163

67

56

17

303

216 x 56 / 303 = 39.920 = 39.9

Step 2 - Final expected counts

Table 2.2: Reported Domestic Violence and Showed Up for Assessment

DV Subcategory

No DV

Father

Reported

Mother

Reported

Both Reported

Row Marginals

No

46.8

19.2

16.1

4.9

87

Yes

116.2

47.8

39.9

12.1

216

Column Marginals

163

67

56

17

303

Observed counts

Table 2.2: Reported Domestic Violence and Showed Up for Assessment

DV Subcategory

No DV

Father

Reported

Mother

Reported

Both Reported

Row Marginals

No

70

7

10

0

87

Yes

93

60

46

17

216

Column Marginals

163

67

56

17

303

Observed - expected counts