13.4 4 Summarizing, Describing, and Comparing Data Distributions CA-337 Class Activity 15x Why Does Variability Matter When We Compare Groups? CCsS cCSS SMP4, 7.SP3, 7.SP4 Some researchers are doing an ex domly assign patients to two groups: a treatment group and a control group. They then determine periment to see if a treatment is effective for an illness. They ran- how long it takes each patient to recover from the illness In this activity you will consider two hypothetical scenarios for the experiment and think about why we should take measures of center and of variability into account when comparing the treat- ment and control groups. Sceaarkali Treatment 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 3 1 Days to recovery Control 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Days to recovery Scenario 2: Treatment 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 23 29 30 31 32 33 34 35 Days to recovery Control 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Days to recovery Compare the two hypothetical scenarios. How are they similar? How are they different? 1. 2 If you have not done so already, discuss the following questions. a. How much better does the treatment group do than the control group? Can you d tify that? b. Does the treatment seem to have more of an effect in one scenario than in the other How so? If you have not done so already, compute the means and MADs for all four data sets (the treatment and control groups for both scenarios). For each scenario, how does the difference in means between treatment and control groups compare with the MAD? How is that related to the difference in the effect of the treatment in the two scenarios? 3. 13.4 4 Summarizing, Describing, and Comparing Data Distributions CA-337 Class Activity 15x Why Does Variability Matter When We Compare Groups? CCsS cCSS SMP4, 7.SP3, 7.SP4 Some researchers are doing an ex domly assign patients to two groups: a treatment group and a control group. They then determine periment to see if a treatment is effective for an illness. They ran- how long it takes each patient to recover from the illness In this activity you will consider two hypothetical scenarios for the experiment and think about why we should take measures of center and of variability into account when comparing the treat- ment and control groups. Sceaarkali Treatment 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 3 1 Days to recovery Control 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Days to recovery Scenario 2: Treatment 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 23 29 30 31 32 33 34 35 Days to recovery Control 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Days to recovery Compare the two hypothetical scenarios. How are they similar? How are they different? 1. 2 If you have not done so already, discuss the following questions. a. How much better does the treatment group do than the control group? Can you d tify that? b. Does the treatment seem to have more of an effect in one scenario than in the other How so? If you have not done so already, compute the means and MADs for all four data sets (the treatment and control groups for both scenarios). For each scenario, how does the difference in means between treatment and control groups compare with the MAD? How is that related to the difference in the effect of the treatment in the two scenarios? 3