Data set: Music
Three students in an introductory statistics class read an article suggesting that listening to certain types of music helps doctors perform chest compressions for cardiopulmonary resuscitation (CPR). It is suggested that optimal CPR performance is 100 beats per minute. Most doctors start out at the right pace but tend to slow down over time. Gore and Lloyd found that doctors performed much better when listening to the song Stayin’ Alive, by the Bee Gees, which has a rhythm of 103 beats per minute. 7 These students developed a research question asking if music also influences performance in other areas. They designed an experiment testing whether music tempo or length of test (1 minute or 3 minutes) influenced students’ ability to type fast and accurately. Would subjects listening to Sta-yin’ Alive type at a different speed than subjects listening to Yesterday by the Beatles? Forty undergraduate students consented to be in the study. Each subject took four tests from the website typingtest. com in random order based on two coin flips: 1 min/Yesterday, 1 min/ Stayin’ Alive, 3 min/ Yesterday, and 3 min/Stayin’ Alive. The questions the researcher wanted to test were the effect of Song, Length, and Song* Length on words per minute (WPM).
a. Specify whether each factor (Subject, Song, and Length) is fixed or random and whether each factor is crossed or nested.
b. Calculate an appropriate ANOVA for this study using WPM as the response. State your conclusions, taking into account random sampling and random allocation. Provide appropriate plots.
c. Check the model assumptions. Create a plot to check if the data appear to be skewed or have outliers. Is there reason to doubt the equal variance assumption? Are the error terms approximately normally distributed?
d. Draw a Hasse diagram corresponding to this study.
e. These introductory students initially conducted a completely randomized design with only the Song, Length, and Song* Length terms in the ANOVA model (block designs are not covered in the introductory class). They were disappointed to not see any significant results in their study. If the blocks are ignored in this study, the conclusions will be incorrect. Write a short paragraph explaining to these students why a block design (including Subjects as blocks) should be used instead of a completely randomized design. Include a main effects plot with Subject, Song, and Length (or other appropriate graphs) in your explanation.
f. The student researchers were concerned that the order of the tests or the actual text used could influence the results. They were primarily concerned that subjects might struggle on the first test, so they decided to have each of the 40 subjects start with a 1- minute practice test. Results were not recorded for this practice test. Five distinct texts were also used for each of the tests. The order in which the five texts were given was the same for all subjects. For example, Trial 1 used the same text for all subjects.
Create a plot to see if there are any patterns in the residuals that can be explained by trial number in the study.
If no pattern exists by trial number, we can have confidence that order or type of text did not bias our results. If a pattern exists by trial number, it should be noted that order or text may bias our ANOVA and conclusions. As in any study, it is dangerous to add new hypothesis tests after we have searched for patterns in our data. In addition, if a pattern existed, the design of this study would make it impossible to distinguish whether order or text was biasing the results. If the effect of order or text was important, a new study should be designed that properly accounts for these factors.