T-test for Paired Dependent Samples

1. The dataset meets all the assumptions of a paired (dependent) T-test. The data distributions are measured through interval or ratio scale and are continuous; the distribution of the scores is normally distributed; the repeated measures data is extracted from the same participants giving paired values. Also, there is independence among the differences between every paired score.
2. Considering the normality test, the Shapiro-Wilk value is 0.953 and 0.91 for the baseline and post-treatment scores respectively. The resulting a p-values are 0.705 and 0.292, respectively and are all above alpha (0.05) indicating that the shapes are normal.

Tests of Normality
	group	Kolmogorov-Smirnova	Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
score	baseline	.134	10	.200*	.953	10	.705
posttreatment	.235	10	.124	.912	10	.292
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction

• The mean for the baseline scores is 3.0300 (SD = 1.664) while that of the post-treatment scores is 0.9834 (SD = 0.3109).

Mean scores

Paired Samples Statistics
	Mean	N	Std. Deviation	Std. Error Mean
Pair 1	baseline	3.0300	10	1.66403	.52621
posttreatment	2.0400	10	.98342	.31098

• Based on the Paired dependent T-test analysis, the t-value is given as 2.865 as shown in the T-test results below.

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 – posttreatment	.99000	1.09286	.34559	.20822	1.77178	2.865	9	.019

• The t-value (2.865) is statistically significant as shown in the above table at 9 degrees of freedom. Ideally, the P-value is given as 0.019 which is less than alpha 0.05 – and this indicates that the null hypothesis that “there is no significant reduction in the emotional distress from baseline to post-treatment is rejected.
•  Considering the above Paired samples test, there is a 0.019 chance or 1.9% likelihood (identified by the P-value) to obtain a t-value that is at least extreme, assuming that the null-hypothesis in this case is true.
• Considering the mean scores for the baseline and post-treatment, and the overall significant of the mean score difference, it can be concluded that there was an improvement of the affective distress scores. Actually, the mean difference for the scores was 0.99 which was positive indicating that the overall change after the rehabilitation programme, the emotional distress was suppressed – there was a positive change. Also, this can be seen with the fact that the mean scores for distress in the post-treatment group were lower than that of baseline scores.

Difference mean

Descriptive Statistics
	N	Minimum	Maximum	Mean	Std. Deviation
difference	10	-1.00	2.20	.9900	1.09286
Valid N (listwise)	10

Baseline vs, post-treatment mean scores

Paired Samples Statistics
	Mean	N	Std. Deviation	Std. Error Mean
Pair 1	baseline	3.0300	10	1.66403	.52621
posttreatment	2.0400	10	.98342	.31098

• Patients who participated an emotional distress rehab (n = 10) showed significantly lower levels of distress scores on the post-treatment (M = 3.030, SD = 1.664) compared to the baseline scores (M = 2.04, SD = 0.9834), t₉ = 2.865, P < 0.05.
• The above results indicate that the emotional distress rehab program is effective in reducing the emotional distress by lowering the distress scores for patients suffering from injuries – and this can be integrated in clinical practice, hence helping people gain functional dependence, control anger and stress and move towards a more positive direction in their lives. 
• One of the main weaknesses of this study was a small sample (n = 10) making it challenging to generalize the findings to the larger population. The number of people having this condition (emotional distress) may be infinite indicating that a larger sample, perhaps 1000 people would offer more credible results. Such a small sample size may have biasedness in presenting the scores as it may be drawn using a non-probabilistic approach from ne race, gender, socio-economic class or even ethnicity.