Data-Centric Statistical Inference Using R and Tidyverse/

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Case Study: Is Yawning Contagious?

Case Study: Is Yawning Contagious?

Take a look at a case study of whether yawning is contagious or not.

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Let’s apply our knowledge of confidence intervals to answer the question: “Is yawning contagious?” If we see someone else yawn, are we more likely to yawn?

Mythbusters study data

Fifty adult participants who thought they were being considered for an appearance on a US show called Mythbusters were interviewed by a show recruiter. In the interview, the recruiter either yawned or didn’t yawn. Participants then sat by themselves in a large van and were asked to wait. While in the van, the Mythbusters team watched the participants using a hidden camera to see if they yawned. The data frame containing the results of their experiment is available in the mythbusters_yawn data frame included in the moderndive package:

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mythbusters_yawn

The variables are:

  • subj: This is the participant ID with values 1 through 50.

  • group: This is a binary treatment variable indicating whether the participant was exposed to yawning. The "seed" indicates that the participant was exposed to yawning, while "control" indicates the participant wasn’t.

  • yawn: This is a binary response variable indicating whether the participant ultimately yawned.

Recall that we learned about treatment and response variables in the Correlation Is Not Necessarily Causation lesson in our discussion on confounding variables. Let’s use some data wrangling to obtain counts of the four possible outcomes:

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mythbusters_yawn %>% 
    group_by(group, yawn) %>% 
    summarize(count = n())

Let’s first focus on the “control” group participants who weren’t exposed to yawning. Twelve such participants didn’t yawn, while four such participants did. So out of the 16 people who weren’t exposed to yawning, 4/16 = 0.25 = 25% did yawn.

Let’s now focus on the "seed" group participants who were exposed to yawning, where 24 such participants didn’t yawn, while 10 such participants did yawn.

So out of the 34 people who were exposed to yawning, 10/34 = 0.294 = 29.4% did yawn. Comparing these two percentages, the participants who were exposed to yawning yawned 29.4% - 25% = 4.4% more often than those who weren’t yawning.

Sampling scenario

Let’s review the terminology and notation related to sampling we studied previously. Our study population was the bowl of𝑁𝑁 = 2,400 balls. Our population parameter of interest was the population proportion of these balls that were red, denoted mathematically by pp. In order to estimate pp, we extracted a sample of 50 balls using the shovel and computed the relevant point estimate. This point estimate was the sample proportion that were red, denoted mathematically by p^\hat{p} ...