# CRIM 320 Lecture Notes - Lecture 9: Analysis Of Variance, John Tukey, Perfective Aspect

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24 Nov 2016

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ANOVA – analysis of variance

-t tests will have 5 percent risk of error (15 percent for three tests)

-ANOVA maintains 5 percent risk

-compares groups means when we have more than 2 independent groups

-factor is the categorical variable containing our groups

-null: the population means for all groups is the same

-how do we test to see if there are differences in groups means?

-F statistic and probability

-more difference within our groups then between our groups

-if there are significant group differences, how do we determine which groups are different

from each other?

-post hoc comparisons

-Tukey (equal variances assumed)

-Dunnett C (equal variances not assumed)

online reading – Lane and Meeker article

Table 2

ANOVA results

Ethnicity

Indicators of social disorganization

Gang Risk

Gang Fear

Behavioral precautions

Disorder

Diversity

Avoidance

Arming

Whites N

595

605

611

621

623

620

Latinos N

252

250

261

272

276

278

Vietnamese N

70

98

83

95

94

101

Whites

x¯

(SD)

1.77 (.75)

1.83 (.75)

1.50 (.58)

2.05 (1.00)

.42 (.35)

.10 (.25)

Latinos

x¯

(SD)

2.43 (.98)

2.08 (.89)

2.09 (.88)

2.51 (.99)

.48 (.37)

.07 (.21)

Vietnamese

x¯

(SD)

3.35 (.58)

2.44 (.84)

2.47 (.70)

3.11 (.80)

.48 (.40)

.11 (.24)

F

154.93***

28.91***

56.15***

58.72***

3.556*

1.647

df

2,914

2,950

2,952

2,985

2,990

2,996

Significant contracts

Tukey HSD

L>W

L>W

L>W

L>W

L>W

V>W

V>W

V>W

V>W

V>L

V>L

V>L

V>L

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Lecture 9: Correlation

-measures association between two interval level variables

preliminaries – plotting data

Country

Democracy

Index (X)

Terrorist

Incidents (Y)

1

68

2

2

65

5

3

70

1

4

62

10

5

60

9

6

55

13

7

58

10

8

65

3

9

69

4

10

63

6

68, 2

0

2

4

6

8

10

12

14

50 55 60 65 70 75

Terrorist Incidents (Y)

Democracy Index (X)

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-summary of where those values fall

-purpose of correlation: trying to understand the line

correlation

-used to measure the degree of association between two interval level variables

-formal name – Pearso’s orrelatio oeffiiet r

-standardized – make things directly comparable

-r ranges from -1 to +1

direction and magnitude of r

-size, relative strength and direction of relationship

-if r is positive – positive relationship

-two variables are moving in the same direction

-as one variable increases, the other variable also increases

-as one variable decreases, so does the other

-if r is negative – negative relationship

-variables moving in opposite directions

-as one variable increases, the other decreases

-the closer r gets to 0 – the weaker the association is

-if r = 0 – there is no relationship

-only time you can say there is no association between the variables

-otherwise there is always a relationship, whether it is significant or not

-null: there is no relationship (correlation) between variable a and variable b

-the correlation coefficient is equal to zero

a note of causality

-correlation does not equal causation

-there is no specification of dependent and independent variables (like chi-square)

-only seeing if variables are associated or not, significant or not

examples of perfect correlation

0

2

4

6

8

10

12

14

16

18

50 55 60 65 70 75

Terrorist Incidents (Y)

Democracy Index (X)

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