Results

Paired Samples T-Test

We have 12 arachnophobes who were exposed to a picture of a spider (picture) and on a separate occasion a real live tarantula (real).

The table below tells us whether the difference between the means of the two conditions was significant;y different from zero. The table tells us the mean difference between scores. The table also reports the standard error of the differences between participants’ scores in each condition. The test statistic, t, is calculated by dividing the mean of differences by the standard error of differences (t = −7/2.8311 = −2.47). The size of t is compared against known values (under the null hypothesis) based on the degrees of freedom. When the same participants have been used, the degrees of freedom are the sample size minus 1 (df = N − 1 = 11). JASP uses the degrees of freedom to calculate the exact probability that a value of t at least as big as the one obtained could occur if the null hypothesis were true (i.e., there was no difference between these means).

The two-tailed probability for the spider data is very low (p = 0.031) and significant because 0.031 is smaller than the widely-used criterion of 0.05. The fact that the t-value is a negative number tells us that the first condition (the picture condition) had a smaller mean than the second (the real condition) and so the real spider led to greater anxiety than the picture. Therefore, we can conclude that exposure to a real spider caused significantly more reported anxiety in arachnophobes than exposure to a picture, t(11) = −2.473, p = .031.

This output also contains a 95% confidence interval for the mean difference. Assuming that this sample’s confidence interval is one of the 95 out of 100 that contains the population value, we can say that the true mean difference lies between −13.231 and −0.769. The importance of this interval is that it does not contain zero (i.e., both limits are negative) because this tells us that the true value of the mean difference is unlikely to be zero.

The effect size (corrected for the correlation between the obervations) is given in the output as d = -0.68. Therefore, as well as being statistically significant, this effect is large and probably a substantive finding.

The resulting error bar plot is above. The error bars slightly overlap, which is a reminder that we cannot use overlap of confidence intervals to conclude whether we there is a significant group difference, and it's much more accurate to instead look at the confidence interval for the difference scores when we are working with a within-subjects design.