Chapter 6: Analysing the Data |

## Example of paired sample t-testLet us consider a simple example of what is often termed "pre/post" data or "pretest Ð posttest" data. Suppose you wish to test the effect of Prozac on the well-being of depressed individuals, using a standardised "well-being scale" that sums Likert-type items to obtain a score that could range from 0 to 20. Higher scores indicate greater well-being (that is, Prozac is having a positive effect). While there are flaws in this design (e.g., lack of a control group) it will serve as an example of how to analyse such data. The value that we are interested in is the Figure 6.9 Data for the paired sample t test.
Notice that we have subtracted the first score away from the second to get a difference score or change score. Person #3's well-being score decreased by one point at the post-test. Person #5 increased their well-being score from 4 point to 10 points. The mean of the Pretest data is 3.33 and the mean of the Post test data is 7.0. The question is, "Is this a significant increase?" ## Output 6.5 Compare Means -> Paired Sample T test## Step 1: Stating the hypotheses:
The alternative is two-tailed and alpha = .05 ## Step 2: Check assumptionsThe assumptions underlying the repeated samples t-test are similar to the one-sample t-test but refer to the set of difference scores.
The measures are approximately interval scale numbers (self-report scores) and we assume that each person's score has not been influenced by other people's scores. The numbers look to have no major extremes or unusual distribution. ## Step 3: Calculate test statisticThe output is given in Output 6.5. Detailed comments on the output follow.
Notice the 95% Confidence Interval values are also given here. We do not place much emphasis on these in this unit. This information says that the true population mean lies between Ð6.357 and -.9763 with a 95% probability. Notice the hypothesised mean of zero does not fall within this range.
The answer! Here we can determine that the chance of this number occurring by chance alone (given the null hypothesis) is about .014 (or 1.4%). ## Step 4: Evaluate the resultThe result is significant t(9) = -3.143, p = .012. We reject the null hypothesis in favour of the alternative. Only once or twice out of every 100 times we repeated this experiment (and the null hypothesis was true) would we get a t-statistic of this size. We therefore conclude that it is more likely to have been due to some systematic, deliberate cause. If all other confounds are eliminated, this systematic cause must have been the Prozac drug. ## Step 5: Interpret the resultA significant increase in well-being occurred (t(9) = -3.14, p = .012, We have found strong evidence that Prozac enhances well-being in depressed individuals. However, the major lack of controls in this study would suggest we keep quiet about it until we can repeat the finding with more stringent safeguards against confounds! |

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