Stats: Independent sample t-tests

 

Last time we looked at how to do a one sample t-test analysis, today we look at the independent t-test. This examines whether the means of 2 separate samples are significantly different. An example might be a control group vs. an experimental group. The independent variable is condition (control, experimental), the dependent variable is the scores on a test. Our research question is – is the mean for the control group significantly different from the experimental group's mean? Our null hypothesis is that there will be no difference between the two groups. 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
condition	numeric	8	0	Condition	*(see below)	Ignore the rest
score	numeric	8	0	Score	None	Ignore the rest

 ·       For condition, Labels: 1= control; 2 = experimental

 Go back to Data View and enter the following: 

Condition	Score
1	5
1	6
1	8
1	2
1	4
2	11
2	15
2	9
2	7
2	12

 Go to Analyze/ Compare Means/ Independent samples t-test. Move your score variable into Test Variable. Move condition into Grouping Variable/ Define groups 1 and 2. Press ok.

 Your results should look like the following:

Group Statistics
	condition	N	Mean	Std. Deviation	Std. Error Mean
score	control	5	5.00	2.236	1.000
	experimental	5	10.80	3.033	1.356

 

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
score	Equal variances assumed	.433	.529	-3.442	8	.009	-5.800	1.685	-9.686	-1.914
	Equal variances not assumed			-3.442	7.356	.010	-5.800	1.685	-9.746	-1.854

 What does this mean? Your two samples are significantly different from each other (see highlighted areas). So let's write it up as you would in your paper: 

An independent sample t-test was conducted comparing the control group (M = 5; SD = 2.24) to the experimental group (M = 10.8; SD = 3.03). The result (t(8) =3.4, p= .009) indicates that there is a significant difference between the groups and the null hypothesis is rejected.

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

 

Condition	Score
1	5
1	6
1	8
1	2
1	4
2	6
2	4
2	7
2	5
2	6

 You run this one on your own. Here is how I write it up:

An independent sample t-test was conducted comparing the control group (M = 5; SD = 2.24) to the experimental group (M = 5.6; SD = 1.14). The result (t(8) =-.54, p= .608) indicates that there is not a significant difference between the groups 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 paired sample t-tests. 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

Stats: One sample t-tests

 
From Pamela:

One question I think would be helpful to explore is how to use SPSS for steps like t-tests. You know something basic. I know we all have had to take stats class but for me and perhaps others, it was a while ago and now we are at the point of having to do the number crunching and a reminder would be useful. 

Great idea Pamela! Over the next few posts, I will explain how to do some basic analyses. Today, since you asked, let's start with t-tests. There are 3 types of t-tests you need to consider, one sample, independent and paired sample. Today we will look at the one-sample t-test. 

One sample t-test. You use this when you are comparing a sample against a known number, an example might be the known population mean on an IQ test. Our research question is – is the sample significantly different from the population mean (μ =100) for the IQ test? Our null hypothesis is that there will be no difference between the sample mean and the population mean of 100. Let's do an example together. So open SPSS and enter the following data for your sample:

115

120

125

130

146 

Go to Analyze/ Compare Means/ One sample t-test. Move your variable into Test Variable. Make your Test Variable 100 (mean of the IQ test). Press ok. 

Your results should look like the following: 

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
VAR00001	5	127.2000	11.90378	5.32353

 

One-Sample Test
	Test Value = 100
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower	Upper
VAR00001	5.109	4	.007	27.20000	12.4195	41.9805

 

What does this mean? Your sample mean is significantly different from the IQ test's population mean of 100. So let's write it up as you would in your paper: 

A one-sample t-test was conducted comparing the sample (M = 127.2; SD = 11.9) to the population mean for the test (μ =100). The result (t(4) =5.109, p= .007) indicates that difference is significant and the null hypothesis is rejected. 

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

102

95

97

103

105

A one-sample t-test was conducted comparing the sample (M = 100.4; SD = 4.22) to the population mean for the test (μ =100). The result (t(4) =.212, p= .842) indicates that there is not a significant difference between the two means 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 independent t-tests. 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