Chapter 12 part one One Way Analysis of Variance MICHELE R BARKHAUER Please put your name ON this document (as a header, or whatever works for you). Please also put your name ON the electronic file name of this document. Don't erase the question or the number of points it is worth, this makes it harder to grade and score. Make room to answer the questions fully and neatly. Please put all your answers in this document, one way or another (typing out, copying and pasting, inserting photos, etc.) This hw is worth 2% of your grade. Which isn't much, but it is key to being able to do the next two homeworks, which are worth more... Chapter 12 1 point unless noted. 19 points this section 1. When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests? When you find yourself having to compare more than a couple of treatment averages, trying to use multiple t-tests will cause your overall number of tests to go up in direct proportion to your groups size going up. The more t-tests you use the more likely it becomes you'll commit a type I error somewhere in your work. When you use an ANOVA instead of many different ttests, the F test will show if the means are actually significant or not (shows in a single test as opposed to many tests) and the probability of you committing a type one error goes way down, with the probability = to the alpha level and that won't change regardless of how many different groups you find yourself having to compare to each other. 2. What is stated by the null hypothesis (H0) for an ANOVA? The null for an ANOVA says that there's not a difference between ANY of the population means 3. What is stated by the alternative hypothesis (H1) for an ANOVA? . The ANOVA alternative hypothesis says that at least one if not several of the population means will differ from each other. (at least one mean will differ from another mean) 4. An analysis of variances produces dfbetween = 3 and dfwithin = 36. If each treatment has the same number of participants, then how many participants are in each treatment? (hint: to solve these types of problems, use your df formulas and work \"backward\" using simple algebra. So if df between is K-1, and DF between here is 3, then what is K? and so on.... Total=between+within so total = 3+36 = 39 Total sample size is 39+1=40 40/4=10 N=10 there are ten participants in each treatment 5. An analysis of variances produces dftotal = 42 and dfwithin = 38. For this analysis, how many treatment conditions are being compared? Total=within+between Between=total-within So 42-38 so the between = 4 6. An analysis of variance produces SStotal = 100 and SSwithin = 20. For this analysis, what is SSbetween? Between is total-within so between = 100-20 = 80 7. An analysis of variance produces SSbetween = 30, SSwithin = 60, and an F-ratio with df = 2, 15. For this analysis, what is the completed F-ratio? . 30/2=15 and 60/15=4 so F=15/4=3.75 8. An independent-measures research study compares four treatment conditions using a sample of n = 8 in each treatment. For this study, the four samples have SS1 = 20, SS2 = 40, and SS3 = 14, and SS4=22. What value would be obtained for MSwithin? Mswithin=sswithin/dfwithin 9. A researcher reports an F-ratio with df = 1, 24 for an independent-measures experiment. If all the treatments had the same number of participants, then how many individuals were in each treatment? dfBetween=1 and dfWithin=24 =25 so total sample is 26 then divide by 2 and you get 13 participants in each condition/treatment. 10. A researcher hypothesizes a difference in four autism treatments. She used ANOVA to compare 4 treatment conditions with separate samples of n=5 participants in each treatment. Some results are below. Complete the table. There are 10 total points in this problem. Fill in the table first to help answer the questions posed here. 1 point a. how many participants total? 1 point a. Was at least one treatment different from the others at an alpha of .01? Give the critical F at .01. 1 point b. Was one treatment significantly different from the others at an alpha of .05? Give the critical F at .05. 1 point c. If there was a significant finding, what step would the researcher take to see which group or groups were specifically different from the others? 1 point for each number that has a question mark next to it, 7 points in the table. Source SS Df MS Between 10 F=3.33 Treatments Within 48 Treatments Total