The Study - Gremlins! Gremlins first became famous for climbing inside airplane engines and causing malfunctions during WWII. Intrigued by this behavior (an really wanting to pet a mogwai), scientists set out to study the species to see if they could create less destructive gremlins. Now, everyone knows that if you get water on a mogwai, they multiply, and if you feed them after midnight, they turn into evil little creatures capable of great destruction. Scientists were curious which type of gremlin causes the most destruction, mogwai (who haven't turned evil, gremlin = 1), gremlins who were mogwai but were fed after midnight (gremlin = 2), or gremlins who are spawned by a gremlin getting splashed with water (gremlin = 3). The scientists developed a treatment designed to make the gremlins less destructive, wherein gremlins in the treatment group (treatment = 1) were given long warm hugs and treats while the control group gremlins (treatment = 0) received no hugs or treats. The scientists also measured how destructive the gremlins were (destruction), how aggressively they behaved (aggression), how many words they knew (vocabulary) and how mischievousness they were (mischievousness). Then, to see if they could create tamer gremlins, they conducted a series of three trials where scores indicate how much destruction the gremlin caused in each trial. Variables: gremlin - (1=mogwai, 2=food gremlin, 3=water gremlin) treatment - (0=control, 1=treatment) destruction - rating of how much destruction the gremlin caused aggression - rating of how aggressive the gremlin was vocabulary - how many words the gremlin knows mischievousness - rating of how mischievous the gremlin was trial1-3 - how much destruction the gremlin caused across three trials

Analysis 1: The researchers are interested in whether there is a difference in mischievousness across the different types of gremlin. However, they would first like to remove the effects of vocabulary, since vocabulary was thought to influence mischievousness. Run an analysis to determine whether the there is a difference in mischievousness between gremlin types (gremlin), after controlling for vocabulary. Question 1: What can be determined from the F value for the main effect of gremlin? a) The level of mischievousness differs by gremlin, F(2,96) = 6.625, p < .05. b) The level of mischievousness does not differ by gremlin, F(2,96) = 6.625, p > .05 c) The level of mischievousness differs by vocabulary, F(2,96) = 6.625, p < .05. d) There is an interaction between gremlin and mischievousness Question 2: Did you meet the assumption of homogeneity of regression slopes? a) Yes, because the effect of vocabulary is significant, F(1,94) = 230.279, p < .05 b) No, because the effect of gremlin is significant, F(1,94), 2.048, p < .05 c) Yes, because the interaction between vocabulary and gremlin is not significant, F(2,94) = .504, p > .05 d) No, because the interaction between vocabulary and gremlin is not significant, F(2,94) = .504, p > .05 Question 3: Which type of gremlin has the higher mean on mischievousness? a) Mogwai b) Food Gremlin c) Water Gremlin d) Cannot be determined from this analysis Analysis 2: Run an analysis to determine whether there is a linear relationship between the variables destruction and aggression. Question 4: What can be determined from this analysis? a) Destruction is unrelated to aggression b) More destruction is associated with higher levels of aggression c) More destruction is associated with lower levels of aggression d) There is a significant difference between destruction and aggression Question 5: The magnitude of the relationship between destruction and aggression is described by which number? a) .002 b) 100 c) .000 d) .311 Question 6: How would you describe the p value for this test? a) p < .05 b) p > .05Analysis 1: The researchers are interested in whether there is a difference in mischievousness across the different types of gremlin. However, they would first like to remove the effects of vocabulary, since vocabulary was thought to influence mischievousness. Run an analysis to determine whether the there is a difference in mischievousness between gremlin types (gremlin), after controlling for vocabulary. Question 1: What can be determined from the F value for the main effect of gremlin? a) The level of mischievousness differs by gremlin, F(2,96) = 6.625, p < .05. b) The level of mischievousness does not differ by gremlin, F(2,96) = 6.625, p > .05 c) The level of mischievousness differs by vocabulary, F(2,96) = 6.625, p < .05. d) There is an interaction between gremlin and mischievousness Question 2: Did you meet the assumption of homogeneity of regression slopes? a) Yes, because the effect of vocabulary is significant, F(1,94) = 230.279, p < .05 b) No, because the effect of gremlin is significant, F(1,94), 2.048, p < .05 c) Yes, because the interaction between vocabulary and gremlin is not significant, F(2,94) = .504, p > .05 d) No, because the interaction between vocabulary and gremlin is not significant, F(2,94) = .504, p > .05 Question 3: Which type of gremlin has the higher mean on mischievousness? a) Mogwai b) Food Gremlin c) Water Gremlin d) Cannot be determined from this analysis Analysis 2: Run an analysis to determine whether there is a linear relationship between the variables destruction and aggression. Question 4: What can be determined from this analysis? a) Destruction is unrelated to aggression b) More destruction is associated with higher levels of aggression c) More destruction is associated with lower levels of aggression d) There is a significant difference between destruction and aggression Question 5: The magnitude of the relationship between destruction and aggression is described by which number? a) .002 b) 100 c) .000 d) .311 Question 6: How would you describe the p value for this test? a) p < .05 b) p > .05

c) p = 0 d) p = .311 Analysis 3: Run an analysis to determine whether destruction differs by gremlin and by treatment. Question 7: What can be determined regarding the main effect of gremlin? a) Gremlin significantly predicts destruction b) Level of destruction differs depending on gremlin c) Level of destruction does not differ depending on gremlin d) There is a significant linear relationship between destruction and gremlin Question 8: What can be determined regarding the main effect of treatment? a) There is no difference in destruction depending on whether the gremlin was in the treatment or control group b) There is a significant difference in destruction depending on whether the gremlin was in the treatment or control group c) Level of destruction is higher among those who are water gremlins than food gremlins d) Gremlin is significantly related to treatment. Question 9: What can you say about the interaction between gremlin and treatment? a) The relationship between treatment and destruction differs depending on whether the gremlin is a mogwai, a food gremlin, or a water gremlin b) There is a significant difference in destruction between food gremlins and water gremlins, but not mogwai c) The relationship between gremlin and treatment differs by destruction d) The relationship between treatment and destruction does not differ between mogwai, food gremlins and water gremlins Analysis 4: Run an analysis to determine whether the destructiveness of the gremlin changes across the three trials (trial1 through trial3). Be sure to perform pairwise comparisons with a Bonferroni adjustment between the three levels of trial. Question 10: What does the Greenhouse-Geiser value for this analysis indicate? a) The Greenhouse-Geiser value is significant, p < .05 b) The assumption of sphericity has been met, as Greenhouse-Geiser = .997 c) The Greenhouse-Geiser value is not significant, p < .05 d) The assumption of sphericity has been violated, as Greenhouse-Geiser = .997 Question 11: What can be determined from the F-value for the effect of the within-subjects IV trial (trial1-3)? a) There is no change in destructiveness across the three trials b) There is a significant interaction between trial1 and trial3

c) There is evidence of significant change in destructiveness across trials d) There was more destruction in trial1 than at trial3 Question 12: What do the Pairwise Comparisons tell you about differences in positions mastered across the three trials (trial1 through trial3)? a) Destructiveness in trial1 was significantly less than at trial3. b) There was a significant difference between trial1 and trial2, but not between trial1 and trial3 c) There was a significant difference between trial2 and trial3, but not between trial1 and trial2. d) There were significant differences between all three trials. Analysis 5: Run an analysis to determine whether the number of positions mastered differed depending on whether the gremlin was in the treatment group or the control group (treatment), whether the destructiveness changed across the three trials, and whether the rate of change in desctuctiveness differed depending on whether the gremlin was in the treatment or the control group (treatment). Question 13: What does the F value for the effect of treatment tell you? a) There is a significant difference in destruction between treatment and control groups b) There is a significant interaction between treatment and trial c) Destructiveness did not differ depending on whether the gremlin was in the treatment or control group d) There is a significant difference in destructiveness across the 3 trials Question 14: Which group was more destructive on average; treatment or control group gremlins? a) Treatment group gremlins were more destructive over all b) Control group gremlins were more destructive over all c) There was no difference between treatment and control groups in destructiveness d) Cannot be determined from this analysis Question 15: What does the F value for the main effect of trial tell you? a) Destructiveness differed between treatment and control groups b) Destructiveness changed significantly across the three trials c) Destructiveness did not change significantly across the three trials d) There is an interaction between trial and treatment Question 16: How would you interpret the interaction between treatment and trial? a) There is a significant difference between treatment by trial b) Control group gremlins experienced an increase in destructiveness across the three trials, while treatment group gremlins did not c) Treatment group gremlins did not appear to become more destructive, while control group gremlins became more destructive across the three trials d) There is no interaction between treatment and trial

Analysis 6: Run an analysis predicting mischievousness from vocabulary. Question 17: How much variance in mischievousness can be accounted for by vocabulary? a) .821% b) .673% c) 82.1% d) 67.3% Question 18: How can the b coefficient for the intercept value be interpreted in this analysis? a) For every one unit increase in mischievousness, the expected vocabulary increases by 2.4 b) The intercept value of 2.4 is the effect of vocabulary on mischievousness. c) For those who have 0 mischievousness, you can expect a change of 2.4 for every one unit increase in vocabulary d) Those who have a 0 on vocabulary can be expected to have a score of 2.4 on mischievousness. Question 19: How can the b coefficient for the effect of vocabulary be interpreted in this analysis? a) For every one unit increase on mischievousness, the expected vocabulary increases by .306 b) For every one unit increase in vocabulary, the expected score on mischievousness increases by .306 c) For every one unit increase in mischievousness, the expected vocabulary decreases by .306 d) For every one unit increase in vocabulary, the expected score on mischievousness decreases by .306 Question 20: What does the t value for the b coefficient for the effect of vocabulary test? a) It tests whether there is a significant difference between the two groups b) It tests whether the intercept is significantly different from 0 c) It tests whether the slope (effect of vocabulary) is significantly different from 0 d) It tests whether the p value is significantly different from 0