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CHAPTER 6: Independent Groups Designs 209null hypothesis assumes no effect of the independent variable). The p valuefor the F-test that was computed for the effect of the video-game version wasless than the .05 level of significance; thus, the overall effect of the video-gamevariable was statistically significant. To interpret this outcome, we would needto refer to the descriptive statistics for this experiment in Table 6.1. There wesee that the mean aggressive cognition for the three video-game conditionswas different. For example, aggressive cognition was highest with the rewardvideo game (.210) and lowest with the nonviolent video game (.157). The statisticallysignificant outcome of the F-test allows us to make the claim that thevideo-game version did produce a difference in aggressive cognition.Researchers want to make more specific claims about the effects of independentvariables on behavior than that the independent variable did have aneffect. F-tests of the overall differences among the means tell us that somethinghappened in the experiment, but they don’t tell us much about what did happen.One way to gain this more specific information about the effects of independentvariables is to use confidence intervals.Key ConceptUsing Confidence Intervals to Examine Mean Differences The confidence intervalsfor each of the three groups in the video-game experiment are shown inTable 6.1 on page 204. A confidence interval is associated with a probability(usually .95) that the interval contains the true population mean. The widthof the interval tells us how precise our estimate is (the narrower the better).Confidence intervals can also be used to compare differences between two populationmeans. We can use the .95 confidence intervals presented in Table 6.1to ask specific questions about the effects of the video-game version on aggressivecognition. We accomplish this by examining whether the confidence intervalsfor the different video-game groups overlap. When the confidence intervalsdo not overlap, we can be confident that the population means for the two groups differ.For example, notice that the confidence interval for the reward group is .186 to.234. This indicates there is a .95 probability that the interval .186 to .234 containsthe population mean for aggressive cognition in the reward condition(remember the sample mean of .210 only estimates the population mean). Theconfidence interval for the nonviolent group is .133 to .181. This confidence intervaldoes not overlap at all with the confidence interval for the reward group(i.e., the upper limit of .181 for the nonviolent group is less than the lower limitof .186 for the reward group). With this evidence we can make the claim thataggressive cognition in the reward condition was greater than aggressive cognitionin the nonviolent video-game condition.When we compare the confidence intervals for the reward group (.186–.234)and the punishment group (.151–.199), however, we come to a different conclusion.The confidence intervals for these groups do overlap. Even thoughthe sample means of .210 and .175 differ, we cannot conclude that the populationmeans differ because of the overlap of the confidence intervals. Wecan offer the following rule of thumb for interpreting this result: If intervalsoverlap slightly, then we must acknowledge our uncertainty about the true meandifference and postpone judgment; if the intervals overlap such that the mean of onegroup lies within the interval of another group, we may conclude that the population