Exercise

# Dr. Max Funn: Identifying Spurious Results with Bad Proxy Variables

Dr. Max Funn from the previous question then runs a second experiment: this time measuring the effect of *work hours* on happiness, once again using income as a proxy variable. The respondents in his treatment group agree to work an additional 10 hours at their primary jobs per week for one year. This time he finds a statistically significant effect: increasing work hours appears to increase happiness (measured as income). But the relationship between work hours and happiness might be suspect.

In this question, we shall see how a more experienced economist replicates the study. In addition to duplicating the newest experiment by Dr. Funn, this economist also directly measures the effect of work hours on happiness to test whether the original proxy variable was appropriate.

Using the dataframe,`econometrics`

, determine whether income is a good proxy variable for happiness in this experiment by doing the following:

Instructions

**100 XP**

- 1) Examine the structure of the economist's data.
- 2) Demonstrate that the proxy variable for happiness,
`Income`

, is correlated with the outcome of interest,`Happiness`

. Use the cor() function. - 3) Run a t-test to determine the average treatment affect of the experiment (
`Treatment`

) on`Income`

. - 4) Run a t-test to determine the average treatment affect of the experiment (
`Treatment`

) on`Happiness`

.