Question

Below we have data on a group of individuals on a weight loss journey. A measure of self-esteem was taken at the start of the 3-month program (se1) and then again the end of the program (se2). Is there a significant difference in self-esteem?

se1	Se2
14	15
15	16
12	14
16	18
15	19
15	18

Sum of D-Score:

Mean of D-scores:

Variance of D-score:

df:

Standard error:

t obtained:

Decision:

d:

r-squared:

Answer 1

Solution:

se1	se2	D
14	15	1
15	16	1
12	14	2
16	18	2
15	19	4
15	18	3
	sum of D score	13
	mean of D score	2.166667
	variance of D score	1.138889

Sum of D-Score: 13

Mean of D-scores: 2.166667

Variance of D-score: 1.138889

We perform a paired sample t-test and obtain the following output:

Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	Se1	14.50	6	1.378	.563
	Se2	16.67	6	1.966	.803

Paired Samples Correlations
		N	Correlation	Sig.
Pair 1	Se1 & Se2	6	.812	.050

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	Se1 - Se2	-2.167	1.169	.477	-3.394	-.940	-4.540	5	.006

Value of the test statistics is t = -4.540.

The degrees of freedom df = 5.

The standard error is = 0.477.

We see the p-value is = 0.006.

As the p-value is = 0.006<0.05, we reject the null hypothesis and conclude that there is a significant difference in weight loss before and after the end of the 3-month program.

d = -2.965516

r-squared = 0.658802