# Causation and lurking variables/Self-check assessment

Use the following quiz questions to check your understanding of simple linear regression. Note that as soon as you have indicated your response, the question is scored and feedback is provided. As feedback is provided for each option, you may find it useful to try all of the responses (both correct and incorrect) to read the feedback, as a way to better understand the concept.

Lurking variables
• A fictional research study examined the relationship between the amount of time spent in front of a screen (computer, tv, tablet, smart phone) and cardiovascular endurance. The study reported a -0.71 correlation between screen time and cardiovascular endurance. Which of the following statements is the best interpretation of the results?
• There is a strong, negative, linear relationship between screen time and cardiovascular endurance.
• That's not quite right. Although there is a strong negative correlation, without examining a scatterplot we cannot conclude that the relationship is linear. Try again.
• Decreasing one's time watching tv, on the computer, or using a tablet or smart phone increases a person's cardiovascular endurance.
• That's not quite right. Although there is a strong, negative correlation between screen time and cardiovascular endurance, correlation does not equate with causation. Notice how this statement implies causation when it suggests that a person can gain cardiovascular endurance by changing their screen time. Try again.
• The relationship may well be a common response, resulting from the amount of physical activity a person engages in.
• That's correct. Physical activity may be serving as a lurking variable, influencing both screen time and cardiovascular endurance.
• The correlation is larger than would be expected due to the confounding effects of extraneous variables.
• That's not quite right. Although there may in fact be confounding variables which were not part of the study, the issue is not with the observed correlation. Consider what a correlation suggests about the relationship between two variables. Try again.
• A study in 2011 reported that the number of board certified teachers on a high school campus has a positive correlation with achievement, in the range of 0.20 to 0.26 across various subject areas. Upon reading the results a school superintendent implements a policy to recruit and hire board certified teachers in preference over other teachers. Is the new policy justified based on the research outcome? Which of the following statements best reflects correct reasoning?
• The new school policy to prefer board certified teachers is not justified by the research results because it is possible that there is a lurking variable, such as teacher ambition, which causes a teacher to obtain board certification and to provide a better learning experience for students.
• That's correct. It is possible that there is a lurking variable, such as teacher ambition, which influences both obtaining board certification and student achievement.
• The new school policy to prefer board certified teachers is not justified due to the low correlations with achievement outcomes.
• That's not quite right. Although the correlations are indeed low, if they reflect a causative relationship, changes in the explanatory variable would have a noticeable impact on the response. Consider, rather, what a correlation suggests about the relationship between two variables. Try again.
• The new school policy to prefer board certified teachers is justified based on the outcome that having board certified teachers causes an increase in achievement scores.
• That's not quite right. Remember that correlation does not equate with causation. Consider what a correlation suggests about the relationship between two variables. Try again.
• The new school policy to prefer board certified teachers is justified because it is based on the results of a research study.
• That's not quite right. Just indicating that research study results support a certain action is insufficient as the basis for a new policy. The research results must be correctly interpreted and applied to the specific situation. Try again.
• In the 1970's, the University of California, Berkeley was sued for bias against women who had applied for admission to graduate schools there. The admission figures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance (44% vs. 35%). But when the admit rates for individual university departments (English, math, etc.) were examined, for 4 out of 6 departments women had a larger admit rate than men, and there was no department where men had a substantially larger admit rate than women.[1] Which of the following statements is true. (check all that apply)
• It is mathematically impossible for the direction of the association to switch from favoring men to generally favoring women when examined at the department level. There must have been a mistake in the data collection.
• That's not quite right. It is possible for an association in one direction to exist when examined for several groups, but which reverses direction when the data are combined to form a single group. Try again.
• This is an example of Simpson's paradox.
• That's correct. This is an example of Simpson's paradox because there is an association for a single group which reverses direction when examined for several groups.
• This is an example of a direct causation model.
• That's not quite right. Remember it is only appropriate to consider an association to be causal when the researchers are able to vary the level of the explanatory variable while controlling for other variables. This study did not control for other variables. Try again.
• University department may be serving as a lurking variable in the analysis.
• That's correct. When an association for a single group reverses direction when examined for several groups, the variable used to create the several groups is a lurking variable, which in this case is university department.

Explaining associations

Indicate the most likely explanation for each of the following associations: direct causation, common response, or confounding. Note that more than one lurking variable may be included in the model.

• Researchers divided the approximately 11,000 third-graders enrolled in the national Early Childhood Longitudinal Study into two categories: those with no or minimal recess (less than 15 minutes a day) and those with more than 15 minutes a day. Also included in the ECLS study data was a rating of classroom behavior, as assessed by the children's teachers using a questionnaire. Researchers found that children who enjoyed daily recess behaved better, than children who did not have recess on a daily basis. confounding
• The number of firemen at a fire has a high correlation with the extent of damage from the fire. common response
• In a study of the school-level factors which influence student achievement, the percent of children receiving free lunch at a school was shown to have a strong negative correlation with school-level mean math and reading achievement scores. common response
• In a study of whether drinking sugary beverages contributes to childhood obesity, at the end of 18 months children who were randomly assigned to receive a daily sugar-based drink gained two pounds more than children who were randomly assigned to receive a daily sugar-free drink. direct causation
• A study of how crash risk is related to texting while driving, which entailed outfitting the cabs of long-haul trucks with video cameras over 18 months, found that when the drivers texted, their collision risk was 23 times greater than when not texting. confounding
• In an investigation of whether social distress causes feelings of physical pain, researchers induced feelings of social rejection in subjects, measuring the strength of rejection and also the blood flow to the portion of the brain activited by physical pain. Feelings of social distress were strongly correlated (r=0.88) with blood flow to the pain region of the brain. direct causation

## Notes

1. Adapted from the Wikipedia article describing the gender bias case.