Question

The data set EF1.SAV contains percentages of fractional fraction, made by 34 subjects in an imaginary clinical study. The efficacy fraction (EF) was calculated before and after treatment, given with the baseline and post variables, while ID is patient number.

1- Check if Baseline is a normally distributed variable.

2- Calculate average and standard deviation for Baseline, and find a 95% confidence interval for the Baseline average.

3- Repeat Points 1 and 2 for the Post variable.

4- Is there a significant difference between the Baseline and Post average? Make an analysis based on both confidence and p-value.

5- Write a short summary of what you found.

A researcher who has not had any course in statistics analyzes the same data using a two-sample method. He considers the data from before and after treatment as if they came from two random sample of patients.

Here you can use the dataset ef2.sav; The data represents the ejaculation fraction before and after a treatment. The measurements are the same as in ef1.sav, but the data structure is slightly different and the ID variable has been removed.

6- Perform the test performed by the researcher. What conclusion do you get? Compare these conclusions you received when analyzing the data in point 4.

7- What's wrong with this method? Why do you get different conclusions when using the two different methods? Consider this based on the effectiveness goals and the uncertainty of the effect goals you get when using the two methods.

EF1 SPSS FILES

ID

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34

BASELINE

55
54
57
47
54
57
62
54
51
51
59
47
54
54
53
54
56
59
55
57
58
51
42
58
55
61
54
58
55
57
54
60
48
55

Post baseline

60
54
59
48
54
59
64
53
52
50
61
45
54
55
54
57
57
62
57
57
59
55
42
61
57
64
56
59
57
60
55
59
49
55

THE ABOVE THREE SPSS VARIABLES ID, BASELINE AND POST BASELINE, ARE PART OF EF1 FILE

EF2 SPSS FILE

TIME

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2

EF (ejection fraction)

54
57
47
54
57
62
54
51
51
59
47
54
54
53
54
56
59
55
57
58
51
42
58
55
61
54
58
55
57
54
60
48
55
60
54
59
48
54
59
64
53
52
50
61
45
54
55
54
57
57
62
57
57
59
55
42
61
57
64
56
59
57
60
55
59
49
55

THESE ABOVE TWO VARIABLES, TIME AND EF(ejection fraction) ARE PART OF EF2 SPSS FILE.

Answer 1

Answered for part 1

The data set EF1.SAV contains percentages of fractional fraction, made by 34 subjects in an imaginary clinical study. The efficacy fraction (EF) was calculated before and after treatment, given with the baseline and post variables, while ID is patient number.

1. Check if Baseline is a normally distributed variable.

Tests of Normality
	Kolmogorov-Smirnova			Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
Baseline	0.209	34	0.001	0.935	34	0.044
a. Lilliefors Significance Correction

Kolmogorov-Smirnov test value 0.209, P=0.001 which is < 0.05 level. The test is significant. The data is not normally distributed.

2- Calculate average and standard deviation for Baseline, and find a 95% confidence interval for the Baseline average.

Descriptives
			Statistic	Std. Error
Baseline	Mean		54.59	0.723
	95% Confidence Interval for Mean	Lower Bound	53.12
		Upper Bound	56.06
	5% Trimmed Mean		54.78
	Median		55.00
	Variance		17.765
	Std. Deviation		4.215
	Minimum		42
	Maximum		62
	Range		20
	Interquartile Range		4
	Skewness		-0.911	0.403
	Kurtosis		1.429	0.788

95% CI = (53.12, 56.06).

3- Repeat Points 1 and 2 for the Post variable.

Descriptives
			Statistic	Std. Error
Post baseline	Mean		55.88	0.848
	95% Confidence Interval for Mean	Lower Bound	54.16
		Upper Bound	57.61
	5% Trimmed Mean		56.13
	Median		57.00
	Variance		24.471
	Std. Deviation		4.947
	Minimum		42
	Maximum		64
	Range		22
	Interquartile Range		5
	Skewness		-0.859	0.403
	Kurtosis		1.037	0.788

95% CI= (54.16, 57.61)

Tests of Normality
	Kolmogorov-Smirnova			Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
Post baseline	0.146	34	0.064	0.945	34	0.089
a. Lilliefors Significance Correction

Kolmogorov-Smirnov test value 0.146, P=0.064 which is > 0.05 level. The test is not significant. The data is approximately normally distributed

4- Is there a significant difference between the Baseline and Post average? Make an analysis based on both confidence and p-value.

Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	Baseline	54.59	34	4.215	0.723
	Post baseline	55.88	34	4.947	0.848

Paired Samples Test
		Paired Differences					t	df	Sig. (2-tailed)
		Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
					Lower	Upper
Pair 1	Baseline - Post baseline	-1.294	1.528	0.262	-1.827	-0.761	-4.938	33	0.000

5- Write a short summary of what you found.

The data are paired. Paired sample t test is used. Calculated t=-4.938, P=0.000 which is < 0.05 level. Ho is rejected. We conclude that there is a significant difference between the Baseline and Post average.