Assume that a statistical consultant has been called in to assist the police dep
ID: 3355941 • Letter: A
Question
Assume that a statistical consultant has been called in to assist the police department of a large city in evaluating its human relations course for new officers. The independent variables are type of beat to which the officers are assigned during the course, treatment A, and the length of the course, treatment B. Treatment A has three levels: upper-class beat, a1, middle-class beat, a2, and inner-city beat, a3. Treatment B also has three levels, 5 hours of human relations training, b1, 10 hours, b2, and 15 hours b3. The dependent variable is attitude toward minority groups following the course. A test developed and validated previously by the consultant is used to measure the dependent variable.
1. If the Main Effect of Beat is Significant conduct subsequent pairwise comparisons using Tukey and LSD.If it is not significant state that below. Make sure I can easily see what the critical difference(s) are. Write your specific conclusions below.
2. If the Main Effect of Hours is significant conduct subsequent pairwise comparisons using Tukey and LSD.If it is not significant state that below. Make sure I can easily see what the critical difference(s) are. Write your specific conclusions below.
Tukey Test Critical Difference
(1) Tukey CD =
Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
3. Interaction of Beat x Hours is significant
I choose to look at whether the simple effects of training change depending upon the type of beat that the officer patrols
Effect of Hours at Upper:
Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
Effect of Hours at Middle:
Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
Effect of Hours at Lower:
Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
Simple Effects Test of Hour At Each level of SES Beat
1 way anova just at upper leads to MSbet =
1 way anova just at middle leads to MSbet =
1 way anova just at lower leads to MSbet =
(1) F at upper = X /62.5 =
(1) F at middle = X/62.5 =
(1) F at lower = X /62.5 =
NOTE: replace X above with the appropriate number and compute the correct F test
(1) Critical F needed for significance at 2, 36 DF =
Conclusions
A1 a1 a1 a2 a2 a2 a3 a3 a3 B1 b2 b3 b1 b2 b3 b1 b2 b3 24 44 38 30 35 26 21 41 42 33 36 29 21 40 27 18 39 52 37 25 28 39 27 36 10 50 53 29 27 47 26 31 46 31 36 49 42 43 48 34 22 45 20 34 641. If the Main Effect of Beat is Significant conduct subsequent pairwise comparisons using Tukey and LSD.If it is not significant state that below. Make sure I can easily see what the critical difference(s) are. Write your specific conclusions below.
2. If the Main Effect of Hours is significant conduct subsequent pairwise comparisons using Tukey and LSD.If it is not significant state that below. Make sure I can easily see what the critical difference(s) are. Write your specific conclusions below.
Tukey Test Critical Difference
(1) Tukey CD =
Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
3. Interaction of Beat x Hours is significant
I choose to look at whether the simple effects of training change depending upon the type of beat that the officer patrols
Effect of Hours at Upper:
33 35 38 33 2 5 35 3 38Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
Effect of Hours at Middle:
30 31 36 30 1 6 31 5 36Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
Effect of Hours at Lower:
20 40 52 20 20 32 41 12 51Conclusions from Tukey=
LSD Test Critical Difference
(1) LSD =
Conclusions from LSD=
Simple Effects Test of Hour At Each level of SES Beat
1 way anova just at upper leads to MSbet =
1 way anova just at middle leads to MSbet =
1 way anova just at lower leads to MSbet =
(1) F at upper = X /62.5 =
(1) F at middle = X/62.5 =
(1) F at lower = X /62.5 =
NOTE: replace X above with the appropriate number and compute the correct F test
(1) Critical F needed for significance at 2, 36 DF =
Conclusions
Explanation / Answer
The independent variables are type of beat to which the officers are assigned during the course, treatment A, and the length of the course, treatment B. Treatment A has three levels: upper-class beat, a1, middle-class beat, a2, and inner-city beat, a3. Treatment B also has three levels, 5 hours of human relations training, b1, 10 hours, b2, and 15 hours b3.
Here Factor1 is “A” and Factor2 is “B”
Between-Subjects Factors
Value Label
N
Factor1
.00
a1
15
1.00
a2
15
2.00
a3
15
Factor2
.00
b1
15
1.00
b2
15
2.00
b3
15
Descriptive Statistics
Dependent Variable: V1
Factor1
Factor2
Mean
Std. Deviation
N
a1
b1
33.0000
6.96419
5
b2
35.0000
8.80341
5
b3
38.0000
9.51315
5
Total
35.3333
8.14745
15
a2
b1
30.0000
6.96419
5
b2
31.0000
6.96419
5
b3
36.0000
9.51315
5
Total
32.3333
7.80720
15
a3
b1
20.0000
7.51665
5
b2
40.0000
6.20484
5
b3
52.0000
7.96869
5
Total
37.3333
15.22998
15
Total
b1
27.6667
8.77225
15
b2
35.3333
7.84371
15
b3
42.0000
11.14194
15
Total
35.0000
10.89203
45
Levene's Test of Equality of Error Variancesa
Dependent Variable: V1
F
df1
df2
Sig.
.618
8
36
.757
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.a
a. Design: Intercept + VAR00001 + VAR00002
Pairwise Comparisons
Dependent Variable: V1
(I) Factor1
(J) Factor1
Mean Difference (I-J)
Std. Error
Sig.a
95% Confidence Interval for Differencea
Lower Bound
Upper Bound
a1
a2
3.000
3.409
.384
-3.890
9.890
a3
-2.000
3.409
.561
-8.890
4.890
a2
a1
-3.000
3.409
.384
-9.890
3.890
a3
-5.000
3.409
.150
-11.890
1.890
a3
a1
2.000
3.409
.561
-4.890
8.890
a2
5.000
3.409
.150
-1.890
11.890
Based on estimated marginal means
a. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Univariate Tests
Dependent Variable: V1
Sum of Squares
df
Mean Square
F
Sig.
Contrast
190.000
2
95.000
1.090
.346
Error
3486.667
40
87.167
The F tests the effect of Factor1. This test is based on the linearly independent pairwise comparisons among the estimated marginal means.
2. Factor2
Estimates
Dependent Variable: V1
Factor2
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
b1
27.667
2.411
22.795
32.539
b2
35.333
2.411
30.461
40.205
b3
42.000
2.411
37.128
46.872
Pairwise Comparisons
Dependent Variable: V1
(I) Factor2
(J) Factor2
Mean Difference (I-J)
Std. Error
Sig.b
95% Confidence Interval for Differenceb
Lower Bound
Upper Bound
b1
b2
-7.667*
3.409
.030
-14.557
-.777
b3
-14.333*
3.409
.000
-21.223
-7.443
b2
b1
7.667*
3.409
.030
.777
14.557
b3
-6.667
3.409
.058
-13.557
.223
b3
b1
14.333*
3.409
.000
7.443
21.223
b2
6.667
3.409
.058
-.223
13.557
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Univariate Tests
Dependent Variable: V1
Sum of Squares
df
Mean Square
F
Sig.
Contrast
1543.333
2
771.667
8.853
.001
Error
3486.667
40
87.167
The F tests the effect of Factor2. This test is based on the linearly independent pairwise comparisons among the estimated marginal means.
Post Hoc Tests
Factor1
Multiple Comparisons
Dependent Variable: V1
(I) Factor1
(J) Factor1
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
95% Confidence Interval
Lower Bound
Upper Bound
Tukey HSD
a1
a2
3.0000
3.40914
.656
-5.2976
11.2976
a3
-2.0000
3.40914
.828
-10.2976
6.2976
a2
a1
-3.0000
3.40914
.656
-11.2976
5.2976
a3
-5.0000
3.40914
.318
-13.2976
3.2976
a3
a1
2.0000
3.40914
.828
-6.2976
10.2976
a2
5.0000
3.40914
.318
-3.2976
13.2976
LSD
a1
a2
3.0000
3.40914
.384
-3.8901
9.8901
a3
-2.0000
3.40914
.561
-8.8901
4.8901
a2
a1
-3.0000
3.40914
.384
-9.8901
3.8901
a3
-5.0000
3.40914
.150
-11.8901
1.8901
a3
a1
2.0000
3.40914
.561
-4.8901
8.8901
a2
5.0000
3.40914
.150
-1.8901
11.8901
Factor2
Multiple Comparisons
Dependent Variable: V1
(I) Factor2
(J) Factor2
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
95% Confidence Interval
Lower Bound
Upper Bound
Tukey HSD
b1
b2
-7.6667
3.40914
.075
-15.9642
.6309
b3
-14.3333*
3.40914
.000
-22.6309
-6.0358*
b2
b1
7.6667
3.40914
.075
-.6309
15.9642
b3
-6.6667
3.40914
.137
-14.9642
1.6309
b3
b1
14.3333*
3.40914
.000
6.0358
22.6309*
b2
6.6667
3.40914
.137
-1.6309
14.9642
LSD
b1
b2
-7.6667*
3.40914
.030
-14.5568
-.7765*
b3
-14.3333*
3.40914
.000
-21.2235
-7.4432*
b2
b1
7.6667*
3.40914
.030
.7765
14.5568*
b3
-6.6667
3.40914
.058
-13.5568
.2235
b3
b1
14.3333*
3.40914
.000
7.4432
21.2235*
b2
6.6667
3.40914
.058
-.2235
13.5568
Between-Subjects Factors
Value Label
N
Factor1
.00
a1
15
1.00
a2
15
2.00
a3
15
Factor2
.00
b1
15
1.00
b2
15
2.00
b3
15