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## 1. p-values

Download the ASA’s Statement on p-values, (see Wasserstein and Lazar 2016 reference below).

Skip the “Context, Process and Purpose” section and **read** the section “ASA Statement on Statistical Significance and P-values” starting on page 3.

Answer the following questions:

We usually think about a small p-value providing evidence against the null hypothesis. What else does the article imply a small p-value may cast doubt on?

What is the primary argument for not basing scientific conclusions or policy decision solely on whether the p-value is below some threshold?

What is

*p-hacking*?Can a p-value measure the size of an effect? What can measure the size of an effect?

Skim through the references in the “A brief p-Values and Statistical Significance Reference List”, and shortlist three article titles that interest you. (

*You may be required to read one of these in a future homework*)

## 2. Data analysis

The Behavioral Risk Factor Surveillance System (BRFSS) is a nationwide health-related survey of U.S. residents. For this question you can get a sample of responses from the 2003 survey by downloading an R data file from the class website:

```
library(tidyverse)
download.file("http://st551.cwick.co.nz/data/brfss.rds",
"brfss.rds", mode = "wb")
```

Then load it into the variable `brfss`

with:

```
brfss <- read_rds("brfss.rds")
brfss
```

The variables `weight_kg`

and `wtdesire_kg`

correspond to the responses to the questions:

- About how much do you weigh without shoes?
- How much would you like to weigh?

respectively converted to kilograms.

You can create a variable to represent the amount of weight a respondent would like to lose with:

`brfss <- mutate(brfss, desired_loss = weight_kg - wtdesire_kg)`

Find summary statistics (mean, standard deviation and number of observations) for

`desired_loss`

for both males and females in the sample.Produce histograms of

`desired_loss`

for both males and females.Do US resident females, on average, want to lose weight (i.e. is the mean desired loss greater than zero)?

**Conduct the appropriate analyses and write a statistical summary of your findings**Do US resident males, on average, want to lose weight (i.e. is the mean desired loss greater than zero)?

**Conduct the appropriate analyses and write a statistical summary of your findings**

## 3. Performance of t-test

Explore the Type I error rate of the t-test for a two-sided level \(\alpha = 0.05\) test, for samples of size \(n = 5, 10, 25, 50\), for **one** of the following population distributions:

- Uniform(0, 1)
- Chi-squared(1)
- Beta(.5, .5)
- Exponential(1)

Use at least 10,000 simulations for each scenario.

Provide a table of the estimated Type I error rate by sample size.

Write a short (3-5 sentence) summary of how the t-test performs: is it close enough to exact that you would be comfortable using it even when the underlying distribution is as far from normal as these distributions?

## References

Wasserstein, Ronald L, and Nicole A Lazar. 2016. “The ASA’s Statement on P-Values: Context, Process, and Purpose” 70 (2): 129–33. doi:10.1080/00031305.2016.1154108.