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