Q Psychology Statistics Dr. Robin Akawi Spring 2022 STATS PACK 2: WEEK 8 Finding Ways to Take the “Anxiety” out of “Math Anxiety”! Note: Keep in mind the “page lengths” that are longer just mean there are more tutorial info or tables/charts to refer to, or room to work out the calculations. Example: “Power” says 4 pages, but there are only 8 short answers to give. Hope that helps. ? Worksheets included: Concepts Page Length Week 5 Effect Size 1 Power 4 Type I and Type II Errors 4 Week 6 Independent Samples t-Test 2 Dependent Samples t-Test 3 Word Problem Template for Exam 1 Prep 2 Week 7 Exam 1 – You have the whole week to finalize your study guide and 4 hours to complete the exam, as long as it is done by 11:59pm of the due date. Week 8 One-Way ANOVA for Independent and Repeated Measures Samples 5 Week 9 Factorial (Two-Way) ANOVA for Independent/Dependent/Mixed Samples 5 One-Way ANOVA Activity “Independent Samples” A statistics instructor who wants to reduce student stress by ensuring they feel confident in their learning of the material. She tries three strategies… Students were randomly assigned to either do “No Homework” or just tell them they “Must Complete” it or need to “Complete Until Correct” (or as correct as possible). Each group includes 6 students. She then examines each group’s test scores for number of errors and analyzes the data with ? = .05 (one- tailed since it is an F distribution, not a t or Z distribution). Compare previous bell curves to the one tailed distribution on this worksheet. 1. What is the independent variable, how many levels are there, and what scale of measurement is it (nominal, ordinal, interval or ratio)? See lecture video in Resource Page for breakdown. 2. What is the dependent variable, and what scale of measurement is it (nominal, ordinal, interval or ratio)? See lecture video in Resource Page for breakdown. 3. What is the null hypothesis statement? Null: 4. What is the alternative/research/experimental hypothesis statement? Alternative: 5. Based on how the scenario is worded, will you be using an independent groups analysis or a dependent/correlated/repeated-measures groups analysis? Look for key words that make it evident, like “randomly assigned” or participants were in “this group OR the other group” vs “participants were measured on _____ AND then again two weeks later”. Highlight your choice: INDEPENDENT DEPENDENT/CORRELATED/REPEATED-MEASURES 6. Here are your data. Please complete the calculations (first line done to get you started): No Homework Must Complete Must Be Correct XNH X-MNH = Deviation Deviation 2 XMC X-MMC = Deviation Deviation 2 XMBC X-MMBC = Deviation Deviation 2 22 22–25.5= -3.5 -3.52 =12.25 23 19 28 21 14 27 24 16 28 26 17 24 19 15 24 22 18 ?X = 153 MX = 25.5 ?Diff = 0 SSD = ? = 135 MX = 22.5 ?Diff = 0 SSD = ? = 99 MX = 16.5 ?Diff = 0 SSD = Grand Mean = GM = 21.5 7. Workspace for remaining One-Way ANOVA Calculations. Use the needed values from the table above (item #6) for the formulas below to determine the results of your One-Way ANOVA, starting with the degrees of freedom between groups and within groups. = ________ = _____________________________ 8. Now for determining the variance between groups. We’ve seen S2 for variance before, and MS is the same (stands for Means Squared). This set of formulas is to determine the top of the fraction for your F Ratio (statistic). Mean -Grand Mean Diff Diff2 25.5 NH -21.5 22.5 MC -21.5 16.5 MBC -21.5 SSD= ?SSD ?NGroups – 1 (the n is # of participants per group… i.e. “6” in our case) 9. Now for determining the variance within and within groups. We’ve seen S2 for variance before, and MS is the same (stands for Means Squared). This set of formulas is to determine the bottom of the fraction for your F Ratio (statistic) and is also called within groups error. (Note for the formula above: Each group’s S2 = SS/n-1 = SS/df ) 10. Now to take your answers from #8 and #9 to determine your F Ratio. = 11. To see if our F Ratio is significant, we need to compare it to the value that “starts” the critical region. An F Ratio with a higher value than the critical region value is considered statistically significant. What is our critical F value? ______ Note: Top row in yellow is dfBetween First column in yellow is dfWithin Find the value that aligns with both df values 12. Run the analyses in Vassarstats to help fill out the Source Table below: Source SS df MS F p Between 252.0 Within (error) 78.5 Total 330.5 17 Based on the source table above, are your results statistically significant? Explain how you determined your answer. 13. Chart your results (critical region value and F Ratio value). Based on the results you charted, are your results statistically significant? What does it suggest about your hypothesis? 14. Paste or type or draw the “Tukey HSD Test” from Vassarstats below. These are the “Post Hoc” analyses. What are the significant pairings, meaning what would you tell your fellow students if they wanted to know how to make less errors on their coursework? Be sure to talk about all three pairings somehow in how you describe the results. Remember M1 is “No Homework”, M2 is “Must Complete” and M3 is “Must Be Correct”. One-Way ANOVA Activity “Dependent Samples… What, again? No really, this is different!” 15. Using the same scenario as the Independent samples One Way ANOVA that you finished above, recalculate it now as a “Repeated Measures” (Dependent Samples) One Way ANOVA. For this, just plug in the answers needed to complete the table below (they are the same ? and M for each group from the Independent calculations), then run the data through Vassarstats to see what values change when testing the same people over and over rather than three totally separate groups of people. Thus, log it into Vassarstats the same way but click the “Correlated” option instead if “Independent”. ? The Scenario: A statistics instructor who wants to reduce student stress by ensuring they feel confident in their learning of the material tries three strategies… Students were asked for one week to “do No Homework”. The next week they were told this time they “Must Complete” it. The final week they had to “Complete Until Correct” (or as correct as possible). Each week they were given a test on what the learned. Number of errors were measured each time and the data were analyzed with ? = .05 (one- tailed since it is an F distribution, not a t or Z distribution). Here are your data: No Homework Must Complete Must Be Correct XNH XMC XMBC 22 23 19 28 21 14 27 24 16 28 26 17 24 19 15 24 22 18 ? = M = ? = M = ? = M = GM = 21.5 16. Source Table based on “Independent samples”: Source SS df MS F p Between 252.0 Within (error) 78.5 Total 330.5 17 Source Table based on “Correlated (Repeated Measures) samples”. Highlight what changed. Source SS df MS F p Between 252.0 2 Within (error) Ss/Bl Total 330.5 17 17. Critical thinking question… answers can vary. Why do you think the changes happened? ? 18. Paste or type or draw the “Tukey HSD Test” from Vassarstats below. These are the “Post Hoc” analyses. Other than the critical values (the values for HSD .05 and HSD .01), you’ll notice we got the same results. Note though, sometimes when looking at the Tukey post-hoc tests they can be different. For example, we can see a significance for one pairing when doing independent, then see two significant pairings when changing it to repeated measures. So always look for that. ? 19. You explained what you saw in the results for #14. Here you will need to report it like you would in a publication. Look in the Resources Page for the documents on write ups for publication. Use those as a model for yours. 20. As an introduction to what comes in the next week next, Factorial ANOVA, share your thoughts on what other factors can influence number of errors students make on exams “other than” the homework scenarios we just looked at. Name as many factors as you’d like, but note a minimum of two factors. Psychology Statistics