1. What is the difference between a test of independent means and a test of depe
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Question
1. What is the difference between a test of independent means and a test of dependent means, and when is each appropriate?
2. In the following examples, indicate whether you would perform a t-test of independent means or dependent means.
Two groups were exposed to different levels of treatment for ankle sprains. Which treatment was most effective?
A researcher in nursing wanted to know if the recovery of patients was quicker when some received additional in-home care whereas others received the standard amount.
A group of adolescent boys was offered interpersonal skills counseling and then tested in September and May to see if there was any impact on family harmony.
One group of adult men was given instructions in reducing their high blood pressure whereas another was not given any instructions.
One group of men was provided access to an exercise program and tested two times over a 6-month period for heart health.
3. For Chapter 12 Data Set 2 (in the appendix), compute the t value manually or with SPSS and write a conclusion as to whether there was a change in tons of paper used as a function of the recycling program in 25 different districts. (Hint: Before and after become the two levels of treatment.) Test the hypothesis at the .01 level.
4. For Chapter 12 Data Set 3 (in the appendix), compute the t value using SPSS and write a conclusion as to whether there is a difference in satisfaction level, measured on a scale of 1 to 15, in a group of families’ use of service centers following a social service intervention. Do this exercise using SPSS and report the exact probability of the outcome.
5. Do this exercise the good old-fashioned way—by hand or with SPSS. A famous brand-name manufacturer wants to know whether people prefer Nibbles or Wribbles. Consumers get a chance to sample each type of cracker and indicate their like or dislike on a scale from 1 to 10. Which do they like the most?
Nibbles Rating Wribbles Rating
9 4
3 7
1 6
6 8
5 7
7 7
8 8
3 6
10 7
3 8
5 9
2 8
9 7
6 3
2 6
5 7
8 6
1 5
6 5
Statistics for People Who (Think They) Hate Sta Appendi 428 Ics Chapter 12 Data Set 2 per used before and after implementation of a recyclin Workers Tons of pa prograinm Before After After 23 8 Before 23 20 35 41 56 34 51 21 31 65 43 53 34 35 76 54 26 35 26 29 31 56 43 54 24 34 32 38 21 34 28 27 54 Bon Chapter 12 Data Set 3 Families' satisfaction levels with service centers before and after a social service intervention Before 1.30 2.50 2.30 8.10 5.00 7.00 7.50 5.20 4.40 7.60 After 6.50 8.70 9.80 10.20 7.90 6.50 8.70 7.90 8.70 9.10 Before 9.00 7.60 4.50 1.10 5.60 6.20 7.00 6.90 5.60 5.20 After 8.40 6.40 7.20 5.80 6.90 5.90 7.60 7.80 7.30 4.60Explanation / Answer
1)
Test of independent means is carried out when we want to calculate the test statistic when there are two different groups and our goal is to test hypothesis or form a confidence interval for the difference between two population means.
Test of dependent means, also called paired sample t-test is carried out whenever we have the same population before vs after a particular treatment or to put it in other words, we are testing means of two related populations which can be paired or matched samples, repeated measures (i.e. before/after a particular treatment)
2)
Two groups were exposed to different levels of treatment for ankle sprains. Which treatment was most effective?- Independent means
A researcher in nursing wanted to know if the recovery of patients was quicker when some received additional in-home care whereas others received the standard amount.- Dependent means
A group of adolescent boys was offered interpersonal skills counseling and then tested in September and May to see if there was any impact on family harmony.- Dependent means
One group of adult men was given instructions in reducing their high blood pressure whereas another was not given any instructions.- Independent means
One group of men was provided access to an exercise program and tested two times over a 6-month period for heart health.- Dependent means
3)
H0: D = 0
H1: D # 0
After
Diff (Di)
(Di-D)
(Di-D)^2
23
3
2.6
6.76
8
2
1.6
2.56
11
-1
-1.4
1.96
35
1
0.6
0.36
57
2
1.6
2.56
76
33
32.6
1062.76
54
0
-0.4
0.16
26
2
1.6
2.56
35
2
1.6
2.56
26
5
4.6
21.16
29
-5
-5.4
29.16
31
-2
-2.4
5.76
56
2
1.6
2.56
22
-1
-1.4
1.96
35
2
1.6
2.56
41
-3
-3.4
11.56
56
-9
-9.4
88.36
34
-9
-9.4
88.36
51
-2
-2.4
5.76
21
-1
-1.4
1.96
31
-3
-3.4
11.56
33
1
0.6
0.36
38
-6
-6.4
40.96
15
-2
-2.4
5.76
27
-1
-1.4
1.96
Avg
Sum
Sum
0.4
0.00
1402
D=ED/n=0.4
S.D=(E(Di-D)2/n-1)=1402/24=7.643
tSTAT=D-µ /S.D/n
Where tSTAT has n - 1 d.f
tSTAT=0.4-0/7.643/25
=0.26
tCRIT is +/-2.796
Hence cannot reject the null hypothesis
After
Diff (Di)
(Di-D)
(Di-D)^2
23
3
2.6
6.76
8
2
1.6
2.56
11
-1
-1.4
1.96
35
1
0.6
0.36
57
2
1.6
2.56
76
33
32.6
1062.76
54
0
-0.4
0.16
26
2
1.6
2.56
35
2
1.6
2.56
26
5
4.6
21.16
29
-5
-5.4
29.16
31
-2
-2.4
5.76
56
2
1.6
2.56
22
-1
-1.4
1.96
35
2
1.6
2.56
41
-3
-3.4
11.56
56
-9
-9.4
88.36
34
-9
-9.4
88.36
51
-2
-2.4
5.76
21
-1
-1.4
1.96
31
-3
-3.4
11.56
33
1
0.6
0.36
38
-6
-6.4
40.96
15
-2
-2.4
5.76
27
-1
-1.4
1.96
Avg
Sum
Sum
0.4
0.00
1402
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