# 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 oeffiiet 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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