participant arousal ? HR base HR arousal-base

1 90.89 86.18 4.71

2 117.03 107.8 9.23

3 105.61 77.15 28.46

4 90.78 78.26 12.52

5 78 71.93 6.07

6 79.71 69.79 9.92

7 92.32 83.99 8.33

8 94.19 93.36 0.83

9 90 73.4 16.6

10 98.2 90.43 7.77

total: 10 104.44

mean: 10.444

standard error 2.414

The above table lists the heart rate (HR) values from participants following an arousing question, and when they are relaxing during a baseline period. Each participant gives a HR value for both conditions (arousal and baseline), and different participants are on different lines. Here I’ve only shown 10 participants; in the class data there are many more.

Question: Does answering an arousing question have an effect on heart rate?

In other words, are the HR values following an arousing question different than during a baseline period?

We can ask this question in a different way: If you subtract the baseline HR value from the arousal HR value for each participant, is the difference greater than 0? If it was the case that the HR values for arousal and relaxing were nearly equal, subtracting one from the other will give you values very near 0. However, if the HR values differ in these two conditions, subtracting one from the other should give values different from 0. In the last column of the table above you can see that if you subtract the two HR values, you get difference values above 0.

If you understand this, you understand the logic of a paired samples t-test. We use a “paired samples” form of the test because the same person is being tested twice – both when they are responding to the arousing question, and when they are in a baseline relaxation period. The paired samples t-test simply gives you a value (t) which reflects how great the difference is when one set of scores (e.g., relaxing) is subtracted from the other (e.g., lying). This difference, which is hypothesised to be 0 if the HR in both conditions is equal, is divided by a measure of how much variability is seen with these values (standard error).

A related samples t-test tells you whether the differences you observe between two conditions are unlikely to have occurred by chance. In our example the average difference between arousal and baseline is 10.444. The hypothesised difference if both conditions are equal is 0. The measure of variability, the standard error, is 2.414. The t-test is: t = (10.444 – 0)/(2.414). This gives a t value of 4.36.

If we look up this value on a table of T-values, we can figure out the probability of seeing this value. Typically, if there’s a 5% or less probability of obtaining this value, we say that the result is statistically significant. On the table, 5% is shown as .05.

What does this mean? It means that the differences between the HR for arousal and baseline are unlikely to have occurred by chance. To be precise, the probability of this difference being a chance result is just over .2%. The correct way to report this would be to say something like:

A paired samples t-test revealed that the heart rate associated with responding to an arousing question was significantly different from that associated with a preceding baseline period (t(9) = 4.36, p < 0.002). How do you do this in SPSS? 1) Open data spreadsheet 2) Select analyse, then compare means, then paired-samples t-test. 3) Highlight the two variables that you want to compare and move them to the paired-variables window. 4) Select the OK button. SPSS should produce an output that includes the means for each variable, and the Paired Samples Test. The t value is under the t heading; the degrees of freedom (the number of participants minus 1) are under the df heading, and the probability is under the Sig. (2-tailed) heading.