Questions and Answers > Arizona State University, Tempe Campus - SOC 390 ASU: Homework #5: ANOVA Hand Calculations

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Hw #5 ​(Score: 9/10) Started: Aug 4 2020 Quiz Instructions Homework #5: ANOVA Hand Calculations Instructions:​ This assignment will cover materials from Module 6 and will include questions th... at require hand calculations. You do not need to submit/show your work for this assignment; however, I would still strongly recommend writing out your answers because 1) it will help you avoid silly mistakes, and 2) so that you can email me your work if you are getting stuck on a question (it will be much easier for me to help you if I can see what you are doing). You should complete this assignment individually.​ As mentioned, you will need to calculate the ANOVA by hand. Of course, you can check your final answer in SPSS (and I encourage you to do so), but some of the questions below will need to be calculate by hand so don’t just rely on SPSS. Finally, you can complete this assignment as many times as you would like before the due date.​ After you submit the assignment, you will receive immediate feedback on which questions you got right and which questions you got wrong so that you can go back and try again. If you get stuck, review the lecture and practice problems that correspond with one-way ANOVAs. If you have reviewed those materials and are still having trouble getting the correct answers, don’t guess – contact me (and send me your work showing me that you have tried) so that I can help you figure out where you made a mistake! Background Information The following is a made-up data set that contains scores for 15 children. The children are in three groups. Five of the children are in group 1, five of the children are in group 2, and five of the children are in group 3. Children in group 1 were shown a funny cartoon, children in group 2 were shown a boring cartoon, and children in group 3 were shown a sad cartoon. Data are ratings of children’s happiness. Happiness was rated on a scale of 1 (not at all happy) to 10 (extremely happy). Particip ant ID | Gro up | Happiness 3Each question below walks through the process for calculating and testing a hypothesis for a one-way between-subjects ANOVA by hand. In this assignment, we are going to use the steps and formula that are covered in the lecture and practice problem for this section. The steps and formula in the textbook are slightly different, but you would end up getting the same answer. We need a lot of information including each group’s mean, the total mean, the within-group deviations, between-group deviations, total deviations, and degrees of freedom. Let’s take it one step at a time and start with calculating means (this is no different than what we did way back in the beginning of the semester!). Question 1 ​0.25 pts What is the group mean for Group 1? (It is a whole number so need to round or include decimals for this question) Question 2 ​0.25 pts What is the group mean for Group 2? (Round your answer to two decimal places) Question 3 ​0.25 pts What is the group mean for Group 3? (Round your answer to two decimal places) Question 4 ​0.25 pts What is the total group mean? (Round your answer to two decimal places) x̄ Now that we have the group and total means, let’s calculate the between-group deviations and the squared between-group deviations. The formulas you will need are: (x̄g​ - x̄total​) and (x̄g​ - x̄total​)​2 Question 5 ​0.25 pts For ​Group 1​, what is the between group deviation? (Round your answer to two decimal places) Remember: (x̄g1​ - x̄total​) 2.47 Question 6 ​0.25 pts For ​Group 1​, what is the squared between group deviation? (Round your answer to two decimal places) Remember: (x̄g1​ - x̄total​)​2​, so you just have to square your answer from the previous questions! Question 7 ​0.25 pts For ​Group 2​, what is the between group deviation? (Round your answer to two decimal places) Remember: Question 8 ​0.25 pts For ​Group 2​, what is the squared between group deviation? (Round your answer to two decimal places) Remember: (x̄g2​ - x̄total​)​2​, so you just have to square your answer from the previous questions! Question 9 ​0.25 pts For ​Group 3​, what is the between group deviation? (Round your answer to two decimal places) Remember Question 10 ​0.25 pts For ​Group 3​, what is the squared between group deviation? (Round your answer to two decimal places) Remember: (x̄g3​ - x̄total​)​2​, so you just have to square your answer from the previous questions! 5.43 Question 11 ​0.5 pts Since we just calculated the between group deviations, let’s calculate the SS​between​ value, Ʃ(x̄g​ - x̄total​)​2​. If you remember from the practice problem/example in the lecture, we have to multiply the between-group squared deviation values we calculated above by the ​n​ of each group before summing (which is equivalent to calculating the value for each person). Once you have multiplied each of the three groups’ squared between group deviation by n, you will add those three new values together to get the answer. Use the table below as a guide. Value for (x̄g1​ - x̄total​)​2​ from above V x̄total​)​2​ from above Value f x̄total​)​2​ from above SS​between x̄total​)​2 ​ = ​ ______Note: You should only enter the value for SS​between​ below (the highlighted blank), not the individual values you computed to get that answer. Round your answer to two decimal places. 57.75 Question 12 ​1 pts Next, we are going to compute the within-group sum of squares value, SSwithin This next part requires a lot of calculations, but don’t worry, it’s nothing more than basic computations. The most tricky part is keeping everything organized. To calculate this, we need the individual scores for each participant, which are available in the data table, and the group means (not the total mean) for each of the three groups that you calculated earlier. I would strongly recommend writing this out in your notes. The first step is to subtract each individual value from it’s group mean (x - x̄g​). Hint: make sure you use the correct group mean (i.e., if you are using a participant from Group 1, make sure you are subtracting the Group 1 mean). You should have 15 new values now. The next step is to square each of these 15 new values (x - x̄g​)​2​. Nothing to this besides squaring each value (e.g., a value of -3 would go to -3​2​ = 9.00). Now, the final step is to add up all of these new values, which gives us our, SSwith Note: You should only enter the value for SS​within​ below, not the individual values you computed to get that answer. Round your answer to two decimal places. SS​w Question 13 ​1 pts Next, we are going to compute the total sum of squares deviation value, SStotal = Ʃ(x - x̄total​)​2​. This part also requires a lot of calculations, but don’t worry, it’s nothing more than basic computations. The most tricky part is keeping everything organized. To calculate this, we again need the individual scores for each participant, which are available in the data table, and the total mean that you calculated earlier (the mean for all 15 participants). I would strongly recommend writing this out in your notes. The first step is to subtract each individual value from the total mean (x - x̄total​). You should have 15 new values now. The next step is to square each of these 15 new values (x - x̄total​)​2​. Nothing to this besides squaring each value (e.g., a value of 2.47 would go to 2.47​2​ = 6.10). Now, the final step is to add up all of these new values, which gives us our SStotal = Ʃ(x - x̄total​)​2​ value. Note: You should only enter the value for SS​total​ below, not the individual values you computed to get that answer. Round your answer to two decimal places. Almost there! Now we need to compute the degrees of freedom within, degrees of freedom between, and degrees of freedom total. Formulas: Within degrees of freedom: ​N​-k Between degrees of freedom: k-1 Total degrees of freedom: ​N​-1 Where k = number of groups and ​N​ = sample size Question 14 ​0.5 pts What are the within-group degrees of freedom? (It is a whole number so need to round or include decimals for this question). df​with Question 15 ​0.5 pts What are the between-group degrees of freedom? (It is a whole number so need to round or include decimals for this question). df​between​ Question 16 ​0.5 pts What are the total degrees of freedom? (It is a whole number so need to round or include decimals for this question). We now have the pieces of information needed to compute the within-group mean squares (MS​within​) and the between-group mean squares (MS​between​). Formulas: MS​within​ = SS​within​ / df​within MS​between​ = SS​between​ / df​between Question 17​0.5 pts What is the within-group mean squares (MS​within​)? (Round your answer to two decimal places) (MS​within​) = Question 18 ​0.5 pts What is the between-group mean squares (MS​between​)? (Round your answer to two decimal places) (MS​between​) = Question 19 ​0.5 pts Finally, compute the observed ​F​ value. (Round your answer to two decimal places) Formula: F​obs​ = MS​between​ / MS​within Question 20 ​1 pts What is the critical value for this example? Use Table C.3 (or B.3 if you are using the second edition). You will need the degrees of freedom you calculated in the previous question (both df​between​ and df​within​). Assume that we set alpha = .05. Question 21 ​1 pts What is your decision regarding the null hypothesis that group means are equal? Group of answer choices: The observed F value does NOT exceed the critical F value so we fail to reject the null hypothesis that group means are equal. The observed F value exceeds the critical F value so we fail to reject the null hypothesis that group means are equal. The observed F value does NOT exceed the critical F value so we reject the null hypothesis that group means are equal. The observed F value exceeds the critical F value so we reject the null hypothesis that group means are equal. [Show More]

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