Name______________________________ Date____________ PSYC 3101 HW Assignment 13 (Bonus) For the data presented below run the appropriate inferential test, and then state what conclusions the researcher may make. Are they based on simple main effects or post hoc tests (hint: run post hoc t-tests if there is an interaction effect)? A researcher interested in the effects of high speed media influences on perception of speed and memory has designed an experiment where participants are first exposed to one of two video games, then shown a video of a car collision, and then provided with a questionnaire. The questionnaires were identical except for one question asking how fast the cars were going when they ______ (hit or smashed) each other? Participants only received one version of the critical question. The speed estimates were then recorded. Subject # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Gender 2 2 2 2 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 1 = Male 2= Female Age 37 20 23 60 25 22 24 24 22 23 36 24 22 24 22 26 22 26 27 22 Race 1 1 1 1 2 1 2 4 2 1 4 1 1 1 1 2 2 1 1 2 1= White 2= Black 3= Asain 4= Other Game 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 Question 1 1 2 2 2 1 1 1 2 2 1 2 2 1 1 2 1 2 2 1 1 = Blur 2= Tetris 1 = Hit 2= Smash Speed 20 23 35 30 35 30 21 32 40 38 19 40 25 30 26 36 21 41 30 31 Chi-Square (set up the null and research hypothesis for each problem below and determine if the observations suggest a significant result). 1) Nicki made a tetrahedral (four-sided) die using cardstock, and then tested it to see whether it was fair. She observed the following results: Score 1 2 3 4 Frequency 12 15 19 22 Is the die fair? 2) Joe has a standard six sided die. He is concerned that the die is biased. After rolling it several times, he observes the following: Score 1 2 3 4 5 6 Frequency 17 20 29 20 18 16 Is the die biased? 3) Entrances to, and exits from, a large department store face each of the cardinal directions. The number of customers entering or leaving each door is monitored. Door North South East West Customers 327 402 351 380 Does it appear each door is used with equal odds? Independent T-test The Researcher wants to determine if there is a significant difference between the speeds that the car crashed and when it smashed. The Hypotheses statements are: H0: There is no significance difference between the speed that the car Hits and when it smashes Ha: There is a significance difference between the speed that the car Hits and when it smashes The output is as below. Group Statistics Question Speed N Mean Std. Deviation Std. Error Mean Hit 10 25.30 5.078 1.606 Smash 10 35.00 5.228 1.653 Independent Samples Test Levene's Test t-test for Equality of Means for Equality of Variances F Sig. t df Sig. (2- Mean Std. Error 95% Confidence tailed) Difference Difference Interval of the Difference Lower Upper Equal variances Speed .195 .664 -4.209 18 .001 -9.700 2.305 -14.542 -4.858 -4.209 17.985 .001 -9.700 2.305 -14.543 -4.857 assumed Equal variances not assumed The mean Hit Speed is 25.30 while mean smash speed is 35.00. The two tailed P-value for the test is 0.001. We thus reject the null hypothesis and conclude that there is a significance difference between the speed that the car hits and when it smashes. In other words, the higher the likelihood that when the car hits, it smashes. Chi-square Question 1 This is a chi-square goodness of fit question Hypotheses statements H0: Die is fair Ha: Die is not fair Score Observed N Expected N Residual 1 12 17.0 -5.0 2 15 17.0 -2.0 3 19 17.0 2.0 4 22 17.0 5.0 Total 68 Test Statistics Score Chi-Square 3.412a df Asymp. Sig. 3 .332 a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 17.0. From the SPSS output above, the P-value for the test is 0.332 which is much larger than the preset threshold of 0.05. We fail to reject the null hypothesis and conclude that the die is fair at 5% significance level. Question 2 Hypotheses statements H0: Die is unbiased Ha: Die is biased Score Observed N Expected N Residual 1 17 20.0 -3.0 2 20 20.0 .0 3 29 20.0 9.0 4 20 20.0 .0 5 18 20.0 -2.0 6 16 20.0 -4.0 Total 120 Test Statistics Score Chi-Square df Asymp. Sig. 5.500a 5 .358 a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 20.0. The P-value for the test is 0.358 which is greater than 0.05. We thus fail to reject the null hypothesis and conclude that the die is unbiased at 5% significance level. Question 3 Hypotheses statements H0: Door used with equal odds Ha: Door used with unequal odds Door Observed N Expected N Residual North 327 365.0 -38.0 South 402 365.0 37.0 East 351 365.0 -14.0 West 380 365.0 15.0 Total 1460 Test Statistics Door Chi-Square df Asymp. Sig. 8.860a 3 .031 a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 365.0. The P-value for the test is 0.031 which is less than 0.05. We reject the null hypothesis and conclude that the doors are used in unequal odds at 5% significance level. Independent T-test The Researcher wants to determine if there is a significant difference between the speeds that the car crashed and when it smashed. The Hypotheses statements are: H0: There is no significance difference between the speed that the car Hits and when it smashes Ha: There is a significance difference between the speed that the car Hits and when it smashes The output is as below. Group Statistics Question Speed N Mean Std. Deviation Std. Error Mean Hit 10 25.30 5.078 1.606 Smash 10 35.00 5.228 1.653 Independent Samples Test Levene's Test t-test for Equality of Means for Equality of Variances F Sig. t df Sig. (2- Mean Std. Error 95% Confidence tailed) Difference Difference Interval of the Difference Lower Upper Equal variances Speed .195 .664 -4.209 18 .001 -9.700 2.305 -14.542 -4.858 -4.209 17.985 .001 -9.700 2.305 -14.543 -4.857 assumed Equal variances not assumed The mean Hit Speed is 25.30 while mean smash speed is 35.00. The two tailed P-value for the test is 0.001. We thus reject the null hypothesis and conclude that there is a significance difference between the speed that the car hits and when it smashes. In other words, the higher the likelihood that when the car hits, it smashes. Chi-square Question 1 This is a chi-square goodness of fit question Hypotheses statements H0: Die is fair Ha: Die is not fair Score Observed N Expected N Residual 1 12 17.0 -5.0 2 15 17.0 -2.0 3 19 17.0 2.0 4 22 17.0 5.0 Total 68 Test Statistics Score Chi-Square 3.412a df Asymp. Sig. 3 .332 a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 17.0. From the SPSS output above, the P-value for the test is 0.332 which is much larger than the preset threshold of 0.05. We fail to reject the null hypothesis and conclude that the die is fair at 5% significance level. Question 2 Hypotheses statements H0: Die is unbiased Ha: Die is biased Score Observed N Expected N Residual 1 17 20.0 -3.0 2 20 20.0 .0 3 29 20.0 9.0 4 20 20.0 .0 5 18 20.0 -2.0 6 16 20.0 -4.0 Total 120 Test Statistics Score Chi-Square df Asymp. Sig. 5.500a 5 .358 a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 20.0. The P-value for the test is 0.358 which is greater than 0.05. We thus fail to reject the null hypothesis and conclude that the die is unbiased at 5% significance level. Question 3 Hypotheses statements H0: Door used with equal odds Ha: Door used with unequal odds Door Observed N Expected N Residual North 327 365.0 -38.0 South 402 365.0 37.0 East 351 365.0 -14.0 West 380 365.0 15.0 Total 1460 Test Statistics Door Chi-Square df Asymp. Sig. 8.860a 3 .031 a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 365.0. The P-value for the test is 0.031 which is less than 0.05. We reject the null hypothesis and conclude that the doors are used in unequal odds at 5% significance level