Statistics and Statistical Programming (Winter 2017)/Problem Set: Week 5

Programming Challenges

PC0. I've provided the full dataset from which I drew each of your samples in a TSV file in the directory week_05 in class assignment git repository. These are tab delimited, not comma delimited. This is also a common format. Go ahead and load it into R. Take the mean of the variable x in that dataset. That is the true population mean — the thing we were creating estimates of in week 2 and week 3.

PC1. Go back to the dataset I distributed for the week 3 problem set. You've already computed the mean for this in week 2. You should compute the 95% confidence interval for the variable x in two ways:

• (a) By hand using the normal formula for standard error $({\frac {\sigma }{\sqrt {n}}})$.
• (b) Using a built-in R function. These number should be the same or very close. Can you explain why they might not be exactly the same?
• (c) Compare the mean for sample, and your confidence interval, to the true population mean. Is the true mean in or out?

PC2. Compare the distribution from your sample of x to the true population. Draw a histogram and compute other descriptive and summary statistics. What do you notice? Be ready to talk for a minute or two about the differences. Why is your mean different?

PC3. Compute the mean of y from the true population and then create the mean and confidence interval from the y in your sample. Is it in or out?

Questions on Gelman and Stern Paper

Q5: First, walk us through the result visualized in Figure 1. Explain and interpret the result for us. Now go back to the blockquote on page 329 and, by referencing the figure, explain why Gelman and Stern think that this is a good example to illustrate their point about the difference between statistically significant versus non-significant.

Q6: Move on to the study about EMF. Walk us through Figure 2. First explain the basic result and then explain why Gelman and Stern thinks that Figure 2b is better than 2a.

Q7: In the paper's abstract Gelman and Stern describe their approach as different from three other problems: that statistical significance, that dichotomization of significant/not-significant encourages dismissing observed differences, and that thresholds are arbitrary. Summarize why these are important issues in your own words (and ideally, with examples) and explain how Gelman's key critique is different.