An eating disorders clinic would like to assess the efficacy oftheir 10-week mindfulness training program with clients who haveBinge Eating Disorder (BED). The clinic researchers first measuredthe number of binges in the previous week for 16 clients throughself-report. One month after the mindfulness training sessions wereconducted, the clients were again asked to report the number ofbinges in the last week. The data are listed in the table below.The clinic researchers have set the significance level at ? = .05.# of Binges per week Subject Before Training After Training
| # of Binges per week |
Subject | Before Training | After Training |
1 | 4 | 2 |
2 | 2 | 1 |
3 | 4 | 4 |
4 | 1 | 1 |
5 | 5 | 2 |
6 | 4 | 1 |
7 | 3 | 2 |
8 | 2 | 3 |
9 | 5 | 2 |
10 | 7 | 5 |
11 | 6 | 4 |
12 | 3 | 1 |
13 | 3 | 2 |
14 | 2 | 2 |
15 | 2 | 1 |
16 | 3 | 1 |
Part I. (25 points total) a) Identify the outcome (dependent)variable and the independent variable (that differentiates the twopopulations being compared). What are the “samples” in thispaired-samples t test? (Or, what are the “means” in thisdependent-means t test?) (1 point) b) The clinic researcherspredict the number of binges per week will decrease after themindfulness training. In other words, the researchers believe themindfulness training will be helpful in reducing binge eating. Whatwould be the null and alternative hypotheses in both words andsymbol notations? c) Calculate the difference scores by subtractingthe “before” scores from the “after” scores. (In other words, setup the columns to calculate after minus before.) Create a tablebelow for “difference score.” d) Calculate the mean from the sampleof the difference scores. e) Estimate the standard deviation of thecomparison population (that represents the null hypothesis). f)Calculate the standard error (standard deviation of the samplingdistribution). g) Calculate the t statistic for the sample. h)Because the hypotheses are directional, a one-tailed test can beperformed. Determine the critical t value based on the degrees offreedom and the preset alpha level. Compare the t statistic withthe critical t value. Is the calculated t statistic more extreme orless extreme than the critical t value? Then make a decision aboutthe hypothesis test, stating explicitly “reject” or “fail toreject” accordingly. i) Interpret the result in 1-2 sentences (youmay restate the hypothesis accepted or explain it in your ownwords). ( a) Calculate the raw and standardized effect size of thishypothesis test. The clinic researchers could also set up thehypothesis to see if there are any differences (increases ordecreases) in binge eating behavior after mindfulness training. a)What would be the null and alternative hypotheses for thisalternative analysis? Compose them in symbol notations only. b)Since a non-directional hypothesis is examined with a two-tailedtest, determine the critical t values for the two-tailed test usingthe same alpha level and degree of freedom. c) Compare the tstatistic with the critical t values. Is the calculated t statisticmore extreme or less extreme than the critical t value? What is thedecision of the hypothesis test now? d) Was the two-tailed testresult (Part II) different from the one-tailed test result (fromPart I)? Why or why not?
