Twins and IQ

In the mid 20th century, a study was conducted that tracked down identical twins that were separated at birth: one child was raised in the home of their biological parents and the other in a foster home. In an attempt to answer the question of whether intelligence is result of nature or nurture, both children were given IQ tests.

This data is in a .csv file, which is a very general format for data and the format that your project data will be in. You can load our usual packages as well as the data with the following commands:

library(dplyr)
library(ggplot2)
twins <- read.csv("http://andrewpbray.github.io/data/twins.csv")

When you’re working on your project, you’ll be able to read it your data into your report by calling the same function, read.csv(), but using the path "../data/data.csv".

Back to the data at hand, since this data was read in from a .csv file, there is no help file associated with it, so I’ll just tell you that the IQ of the foster child is recorded in Foster and the IQ of the biologically-raised child in Biological. The socieoeconomic status of the biological family was also recorded in Social.

  1. Create a plot of the relationship between the IQs of the two children and describe the relationship in words (there is no clear independent variable here, so just put Biological on the x-axis).

  2. Fit a linear model to this data and have a look at the summary of the model. Which one of the following is false and why?
    • For each 10 point increase in the biological twin’s IQ, we expect the foster twin’s IQ to increase on average by roughly 9 points.
    • The linear model (the estimated mean function) is approximately \(\hat{y} = 9.2 + 0.9 \times x\).
    • Foster children with higher than average IQs (average of the foster children) will have biological twins with higher than average IQs as well (average of the biological children).

  3. Is it reasonable to draw conclusions from this model? Please assess the conditions for a valid model.

  4. This study was used to weigh in on the question of whether IQ is a result of nature (your genes) or nurture (your environment). If IQ was purely a result of nurture, what slope would you expect to see in your linear model? Phrase that hypothetical question in terms of a hypothesis test and interpret the p-value in the context of this problem.

  5. At the other end of the argument, the distribution of IQ might be entirely determined by genes. Use a 95% confidence interval on your slope to assess whether this claim is reasonable given your data set.

  6. Now consider how the association between IQs would change if social class were taken into account. Create a plot using the code below to illustrate the relationship between all three variables. Just by looking at the plot (and without fitting any models), does it appear that the relationship between the IQs is the same for high social class children as it is for low social class children?

qplot(x = Biological, y = Foster, color = Social, data = twins, geom = "point")

Endnote: The researcher that collected this data was named Cyril Burt, and his work was the subject of some controversy.