Stats: Paired T-tests

Last time we looked at how to do an independent t-test analysis, today we look at the paired sample t-test. This examines whether the means of one sample tested at 2 different times are significantly different. An example might be a pre-study survey and post-study survey. The independent variable is time (pre or post), the dependent variable is the scores on a test. Our research question is – is the mean for the pre-study survey significantly different from the post-study survey's mean? Our null hypothesis is that there will be no difference between the two times. Let's do an example together. So open SPSS and enter the following data for your samples:

Under Variable view (see tab at bottom of page), It should look like: 

Name	Type	Width	Decimals	Label	Values	Ignore the rest
prescore	numeric	8	0	Prestudy score	None	Ignore the rest
postscore	numeric	8	0	Poststudy score	None	Ignore the rest

 Go back to Data View and enter the following: 

prescore	postscore
5	9
8	11
4	5
7	10
2	6
6	9
9	15
1	6
3	8
8	13

 Go to Analyze/ Compare Means/ paired samples t-test. Move both of your score variables into Paired Variables. Press ok. 

Your results should look like the following:

Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	prestudy score	5.30	10	2.751	.870
	poststudy score	9.20	10	3.190	1.009

 

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	prestudy score - poststudy score	-3.900	1.449	.458	-4.937	-2.863	-8.510	9	.000

What does this mean? Your two test times are significantly different from each other. So let's write it up as you would in your paper: 

A paired sample t-test was conducted comparing the pretest survey (M = 5.3; SD = 2.75) to the posttest survey (M = 9.2; SD = 3.19). The result (t(9) = -8.51, p= .0001) indicates that there is a significant difference between the test times and the null hypothesis is rejected. 

What happens if the results were NOT significantly different, as in this example: 

prescore	postscore
8	9
12	11
4	5
10	10
5	6
10	9
14	15
5	6
8	8
12	13

 

A paired sample t-test was conducted comparing the pretest survey (M = 8.8; SD = 3.39) to the experimental group (M = 9.2; SD = 3.19). The result (t(9) = -1.5, p= .168) indicates that there is not a significant difference between the test times and the null hypothesis is retained. 

A great resource for SPSS is

Pallant, J. (2013). The SPSS Survival Manual, 5^th edition. Open University Press. 

Next time, we will look at correlations. Do you have an issue or a question that you would like me to discuss in a future post? Send me an email with your ideas. leann.stadtlander@waldenu.edu