Chapter 11, Problem 7P

The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n = 9 participants before and after they receive the treatment.

a. Calculate the difference scores and M_D.

b. Compute SS, sample variance, and estimated standard error.

c. Is there a significant treatment effect? Use α = .05, two tails.

Participant	Before Treatment	After Treatment
A	8	7
B	7	5
C	6	6
D	7	6
E	9	7
F	8	5
G	5	4
H	9	4
I	7	4

To determine

Difference scores and $M_D$.

Answer to Problem 7P

Difference scores obtained are $\begin{array}{ccccccccc}-1& -2& 0& -1& -2& -3& -1& -5& -3\end{array}$ and $M_D=-2$.

Explanation of Solution

Given info:

Scores of $n=9$ participants before and after the treatment are given.

Participant	Before Treatment	After Treatment
A	8	7
B	7	5
C	6	6
D	7	6
E	9	7
F	8	5
G	5	4
H	9	4
I	7	4

Calculation:

Difference of scores are given by the subtracting the scores before different treatment from the scores after treatment.

Step-by-step procedure to obtain the difference scores using the SPSS software is.

• Enter the name of four variables in variable view>Participants, Before_Treatment, After_Treatment, and Difference.
• Enter the values of given variables.
• Go to Transform>Choose Compute variable>Write Difference in Target Variable.
• Choose variable After_Treatment and move it to numeric expression> Choose $(-)$ sign and move it to numeric expression>Choose variable Before_Treatment and move it to numeric expression.
• Choose OK.
• Choose Yes.

Output using the SPSS software is given below:

From the SPSS output difference scores are $\begin{array}{ccccccccc}-1& -2& 0& -1& -2& -3& -1& -5& -3\end{array}$.

Step-by-step procedure to obtain the $M_D$ using the SPSS software:

• Choose Analyze > Descriptive Statistics> choose Descriptive.
• Select Difference and move it under variable(s)>Choose Options>Select Mean.
• Choose Continue> choose OK.

Output using the SPSS software is given below:

From the SPSS output, $M_D=-2$.

To determine

Difference scores are and $M_D$.

Answer to Problem 7P

The value of SS, variance and standard error obtained are 18, 2.25 and 0.5 respectively.

Explanation of Solution

Calculation:

Difference of scores are given by the subtracting the scores before different treatment from the scores after treatment.

Step-by-step procedure to obtain the difference scores using the SPSS software is.

• Enter the name of four variables in variable view>Participants, Before_Treatment, After_Treatment, and Difference.
• Enter the values of given variables.
• Go to Transform>Choose Compute variable>Write Difference in Target Variable.
• Choose variable After_Treatment and move it to numeric expression> Choose $(-)$ sign and move it to numeric expression>Choose variable Before_Treatment and move it to numeric expression.
• Choose OK.
• Choose Yes.

Output using the SPSS software is given below:

From the SPSS output difference scores are $\begin{array}{ccccccccc}-1& -2& 0& -1& -2& -3& -1& -5& -3\end{array}$.

Step-by-step procedure to obtain the variance using the SPSS software:

• Choose Analyze > Descriptive Statistics> choose Descriptive.
• Select Difference and move it under variable(s)>Choose Options>Select Variance.
• Choose Continue> choose OK.

Output using the SPSS software is given below:

From the SPSS output variance is 2.25.

Let $s^2$ denotes the variance of difference scores. Then,

$s^2=2.25$

Then SS is given as:

$\begin{array}{c}{s}^2=\frac{SS}{n-1}\\ SS=s^2\times \left(n-1\right)\\ =2.25\times \left(9-1\right)\\ =18\end{array}$

Step-by-step procedure to obtain the standard error using the SPSS software:

• Choose Analyze > Descriptive Statistics> choose Descriptive.
• Select Difference and move it under variable(s)>Choose Options>Select S.E. mean.
• Choose Continue> choose OK.

Output using the SPSS software is given below:

From the SPSS standard error is 0.5.

Thus, the value of SS, variance and standard error obtained are 18, 2.25 and 0.5 respectively.

To determine

Treatment has a significant effect.

Answer to Problem 7P

Treatment has significant effect on the participants.

Explanation of Solution

Calculation:

State the hypotheses:

Null Hypothesis:

$H_0:{\mu }_D=0$

That is, the treatment does not have a significant effect on the participants.

Alternate Hypothesis:

$H_1:{\mu }_D\ne 0$

That is, the treatment has a significant effect on the participants.

Step-by-step procedure to obtain the p value for given test using the SPSS software:

• Choose Analyze > Compare means> choose Paired Samples T test.
• Select Before_treatment and move it under variable1> Select After_treatment and move it under variable2.
• Choose OK.

Output using the SPSS software is given below:

From the SPSS output t statistic and p value obtained are 4 and 0.004 respectively.

Since p value obtained is less than level of significance $\alpha =0.05$, therefore we reject null hypothesis and conclude that treatment has significant effect on participants.

Conclusion:

The treatment has significant effect on participants.