StatisticsProblems

StatisticsProblems

Question1

Table1

Glucose content

Group

Rank with correction

119

A

1

120

A

2

123

A

3

124

A

4

125

B

5

126

A

6.5

126

B

6.5

128

A

8

129

B

9

130

A

10.5

130

B

10.5

131

A

12

132

B

13

133

A

14

134

B

15

135

B

16

136

B

17

137

A

18

138

B

19

139

A

20

140

A

21

142

B

22.5

142

B

22.5

143

B

24

144

B

25

145

A

26

146

B

27

147

B

28

148

B

29

149

B

30

Fromtable 1:

Sumof ranks for group A (R1) =146

Sumof ranks for group B (R2) =319

Countfor group A (n1) =13

Countfor group B (n2) =17

UMann Whitney test

U1=n1*n2+[n1 (n1+1)/2]-R1

U1=13*17+[13(13+1)/2]-146

U1=166

U2=n1*n2+ [n2 (n2+1)/2]-R2

U2=13*17[17(17+1)/2]-319

U2=55

Min(U1, U2) =55

TheMann Whitney critical value =63

Min(u1, u2) =55 is less than The Mann Whitney critical value of 63 andhence we reject the null hypothesis and say that the sum of ranks forgroup A is significantly different from the sum of ranks of group B.Hence we conclude that the glucose content of prediabetic patientsare significantly different between group A and group B.

Question2

PartA

Chisquare=Sum ((O-E)/E)

Chisquare= (0.5/0.5) + (1.1/2.1) + (0.9/4.1) + (1/3) + (0.1/0.9)

Chisquare=1+0.5238+0.2195+0.3333+0.1111

Chisquare=2.1877

Chisquare (approximate) = 2.376

PartB

Theobtained chi square of 2.376 is less than the chi square critical of9.488 hence we conclude that the data doesn’t depart from normalitythat is the data follows a normal distribution.

Question3

Comparingthe one group pre-posttest with the Randomized classical test inaccordance with their threats

  1. History threat is only a threat in the one group pre-posttest. This is whereby unanticipated event occurs while the experiment is in progress and it has an effect on the dependent variable.

  2. Selection threat is only a threat in the randomized classical test. In random sampling each subject has an equal chance of being selected but if the subjects are self-selected into the experiment then this could affect the dependent variable.

  3. Experimental mortality is only a threat in the randomized classical test. This occurs when some participants drop out while the experiment is in progress and this might affect the results.

  4. Statistical regression threat occurs in one group pre-posttest. This is when the participant scores are in the either extremes. This means when the scores of these participants are taken in the post test they will tend to regress towards the mean (Verstappen et al., 2004).

  5. Diffusion of treatment threat occurs in randomized classical test. This is where the control group and the test group interact. The control group is contaminated making the results of the dependent variable might be the same for the two groups.

References

Verstappen,W. H., van der Weijden, T., ter Riet, G., Grimshaw, J., Winkens, R.,&amp Grol, R. P. (2004). Block design allowed for control of theHawthorne effect in a randomized controlled trial of test ordering.Journalof clinical epidemiology,57(11),1119-1123.