ANOVA Questions 1. Dr. Jones is investigating the effect of vitamins on reducing the sick days of children going to school. She randomly assigned 15 participants to one of three groups (Daily Multivitamin, Daily Multivitamin plus Additional Daily Dose of Vitamin C, Control [No Vitamins]). After taking the vitamins for an entire school year, the number of absences for each student through the year was recorded. The data for all three conditions is displayed below. Quiz Score Mj nj Daily Multi-Vitamin Multi-Vitamin + additional Vitamin C No Vitamins (Control) 2 3 9 10 6 6 5 10 8 4 7 6 7 5 18 13 14 15 10 14 5 a. What are the dependent and independent variables (include levels of the independent variable)? b. State the null and alternative hypothesis (symbols, not words). c. Calculate the grand mean d. Calculate the df-between, df-within, and the critical value for this test at = 0.05 e. Calculate the SS-between and the MS-between. f. Calculate the SS-within, df- within, and the MS- within. g. Calculate the obtained F. h. Make a statistical decision about the null. Will you reject or fail to reject the null based on your sample data? (Be sure to include appropriate test statistic and decision criteria). i. Provide a substantive conclusion about the results from your sample data. (Be sure to include the research context and descriptive statistics) j. What information is missing for the interpretation of an ANOVA if you only run an omnibus/overall ANOVA (without any post-hoc tests)? Why do we need to run post-hoc tests when we conduct a One-Way ANOVA? k. When we conduct a One-Way ANOVA, we first run an omnibus/overall test to see if a significant difference exists. If we obtain a significant F test statistic for the omnibus test, we move forward by conducting follow up post-hoc tests. Why are post-hoc tests done second as opposed to doing them first? l. Compute the effect size, r2. Describe what r 2 means in the context of this research question. 2. A researcher was interested in the ability to detect lying in three groups of people (U.S. Secret Service, California judges, and psychiatrists). Forty-five participants watched a video of people either lying or telling the truth about their feelings. Participants were categorized in one of three groups (U.S. Secret Service, California judges, or psychiatrists). The following scores represent the participant's number of correctly detected lies (out of a maximum of 10). Attached below is the SPSS output based on the research question. Given the output, please answer the following questions (using alpha of .05). a. What is the statistical result of the omnibus (overall) ANOVA? (Fail to reject or reject the null and why [include F and p value]?) b. Provide a substantive conclusion about the results from the above output. (Be sure to include the research context and descriptive statistics) c. What are the statistical results for the three post-hoc tests from the table below (using alpha of.05)? Report the significance and whether you will reject or fail to reject the null for each test. d. Provide a substantive conclusion about the post-hoc from the above table. (Be sure to include the research context and descriptive statistics) e. Interpret r 2 given the context of this study