Hockenbury Discovering Psychology 5th txtbk

A-12 APPENDIX A Statistics: Understanding Datainferential statisticsMathematical methods used to determinehow likely it is that a study’s outcome isdue to chance and whether the outcomecan be legitimately generalized to a largerpopulation.t-testTest used to establish whether the means oftwo groups are statistically different fromeach other.Inferential StatisticsLet’s say that the mean number of physical symptoms (like pain) experienced bythe participants in each of the three groups was about the same at the beginningof the health-promotion study. A year later, the number of symptoms had decreasedin the two intervention groups but had remained stable in the controlgroup. This may or may not be a meaningful result. We would expect the averagenumber of symptoms to be somewhat different for each of the three groupsbecause each group consisted of different people. And we would expect somefluctuation in level over time, due simply to chance. But are the differences innumber of symptoms between the intervention groups and the control grouplarge enough not to be due to chance alone? If other researchers conducted thesame study with different participants, would they be likely to get the same generalpattern of results? To answer such questions, we turn to inferential statistics.Inferential statistics guide us in determining what inferences, or conclusions,can legitimately be drawn from a set of research findings.Depending on the data, different inferential statistics can be used to answer questionssuch as the ones raised in the preceding paragraph. For example, t-tests areused to compare the means of two groups. Researchers could use a t-test, for instance,to compare average energy level at the end of the study in the traditional andalternative groups. Another t-test could compare the average energy level at the beginningand end of the study within the alternative group. If we wanted to comparethe means of more than two groups, another technique, analysis of variance (oftenabbreviated as ANOVA), could be used. Each inferential statistic helps usdetermine how likely a particular finding is to have occurred as a matter of nothingmore than chance or random variation. If the inferential statistic indicates that theodds of a particular finding occurring are considerably greater than mere chance, wecan conclude that our results are statistically significant. In other words, we canconclude with a high degree of confidence that the manipulation of the independentvariable, rather than simply chance, is the reason for the results.To see how this works, let’s go back to the normal curve for a moment. Rememberthat we know exactly what percentage of a normal curve falls between any twoz scores. If we choose one person at random out of a normal distribution, what isthe chance that this person’s z score is above 2? If you look at Figure A.9 (it’s thesame as Figure A.5), you will see that 2.28 percent of the curve lies above a z score(or standard deviation unit) of 2. Therefore, the chance, or probability, that theperson we choose will have a z score above 2 is .0228 (or 2.28 chances out of100). That’s a pretty small chance. If you study the normal curve, you will see thatthe majority of cases (95.44 percent of the cases, to be exact) fall between 2 and2 SDs, so in choosing a person at random, that person is not likely to fall above az score of 2.Figure A.9 The Standard Normal Curve