Crim 320.Week 5 February 5.docx

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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
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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
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