zyBooks- Chapter 1

1.1 Example: Paired designs Learning goals Identify a study design as having paired or independent groups. Identify a study design as paired using repeated measures or paired using matching. Does listening to music with lyrics interfere with studying? Many students like to study while listening to music. What does research say about how well students can focus while listening to music with lyrics? Researchers plan to design an experiment with 27 students with two treatments: listening to music with lyrics and listening to music without lyrics. The researchers will then compare students' performance on a memorization game: Students will study a list of 25 common ±ve-letter words for 90 seconds and then write down as many of the words as they can remember. PARTICIPATION ACTIVITY 1.1.1: Possible experimental design. Randomly assigned to groups 27 students With Lyrics Without Lyrics ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 6/5/24, 9:24 PM zyBooks https://learn.zybooks.com/zybook/MTH_218_58079156/chapter/1/print 1/78

PARTICIPATION ACTIVITY 1.1.2: Music study design. 1) The experimental units are _____. the students the lyrics the music 2) The explanatory variable is _____, which is a _____ variable. the number of words memorized; quantitative whether the student listened to music with lyrics; categorical Animation content: Static ±gure: A possible study design to measure the effect of listening to music with lyrics on memorization. Step 1: Suppose 14 students are randomly assigned to listen to music with lyrics and 13 students are randomly assigned to listen to music with no lyrics. Step 2: Each of the 27 individuals provides exactly one response value, which is the number of words memorized. Data Student Music Type # Words 1 With lyrics 5 ... ... ... 14 With lyrics 10 15 No lyrics 5 ... ... ... 27 No lyrics 10 Animation captions: 1. Suppose 14 students are randomly assigned to listen to music with lyrics and 13 students are randomly assigned to listen to music with no lyrics. 2. Each of the 27 individuals provides exactly one response value, which is the number of words memorized. ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 6/5/24, 9:24 PM zyBooks https://learn.zybooks.com/zybook/MTH_218_58079156/chapter/1/print 2/78

3) The response variable is _____, which is a _____ variable. whether the student listened to music with lyrics; categorical the number of words memorized; quantitative 4) For the music study, what is the purpose of the random assignment? To generalize the results from these 27 students to a larger population of students. To create similar treatment groups. To generate a null distribution. Another study design The above study design can be referred to as an independent groups design. In an independent groups design , the data recorded for one group are unrelated to the data recorded in the other group(s). The goal of random assignment is to create groups that are similar on all possible confounding variables. However, sometimes the created groups could be unequal on one or more variables just by chance. Ex: Substantial variation in individual memorization skill may still lead to groups that are not completely equally distributed with respect to that variable even if an independent groups design is used. To guard against such unevenness, other study designs are possible. PARTICIPATION ACTIVITY 1.1.3: Paired study design. With Lyrics With Lyrics Without Lyrics Without Lyrics Memorization Independent groups design Paired study design ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 6/5/24, 9:24 PM zyBooks https://learn.zybooks.com/zybook/MTH_218_58079156/chapter/1/print 3/78

Randomly assigned first treatment With Lyrics Without Lyrics Animation content: Static ±gure: A paired study design is explored to minimize the chance of unequal groups on the observed difference in effect. Step 1: In an independent groups design for the music study, more of the people with better memorization skills could end up in the without lyrics group by random chance. Step 2: To account for the variability in scores due to prior differences in memorization skills between people, a paired study design instead asks each student in the study to play the memorization game twice, once with lyrics and once without. Step 3: Randomization is used to decide which treatment the students participate in ±rst. Step 4: The resulting dataset has two measurements of the number of words remembered for each person. Paired study design data Student First Music Type # Words Second Music Type # Words 1 With lyrics 5 No lyrics 6 ... ... ... ... ... 14 With lyrics 10 No lyrics 7 15 No lyrics 5 With lyrics 8 ... ... ... ... ... 27 No lyrics 10 With lyrics 11 Animation captions: 1. In an independent groups design for the music study, more of the people with better memorization skills could end up in the without lyrics group by random chance. 2. To account for the variability in scores due to prior differences in memorization skills between people, a paired study design instead asks each student in the study to play the memorization game twice, once with lyrics and once without. 3. Randomization is used to decide which treatment the students participate in ±rst. ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 6/5/24, 9:24 PM zyBooks https://learn.zybooks.com/zybook/MTH_218_58079156/chapter/1/print 4/78

PARTICIPATION ACTIVITY 1.1.4: Paired design in the music study. 1) In a paired study design, randomness is present in _____. deciding which treatment is given to each experimental unit deciding which experimental units are paired deciding the orders of the treatments 2) Using a paired study design, any difference in words memorized by a particular student will be mainly due to _____. randomness the explanatory variable confounding variables 3) In using the paired study design, the Lyrics and Without Lyrics groups are ___ to be balanced on general memorization skill. likely guaranteed not likely Other paired designs A paired design using repeated measurements is a study in which each experimental unit is measured twice under different conditions where the order of the conditions is randomly assigned. Randomizing the order of the treatments is important to guard against any changes over time. Ex: Both familiarity with the memorization game and fatigue can change over time and could affect the number of words memorized. But changes over time are accounted for in the music study by randomizing the order of the treatments. Having each subject experience both treatments is not always an option, and other paired designs are possible. A paired design using matching creates pairs by matching up two very similar experimental units and then randomly assigning one to each treatment. 4. The resulting dataset has two measurements of the number of words remembered for each person. ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 ©zyBooks 06/05/24 21:24 2090300 Melinie Weaver MTH_218_58079156 6/5/24, 9:24 PM zyBooks https://learn.zybooks.com/zybook/MTH_218_58079156/chapter/1/print 5/78