# Chapter 13 Ethics in Statistics and Data Science

## 13.5 Fisher controversy

This assignment will be due Wednesday September 2. You will turn in the assignment on Canvas. If you do part of the assignment by hand on paper, use TinyScanner, CamScanner, Adobe Scan, or another similar free smartphone app to create a pdf file of your work before submitting.

This assignment will be due Wednesday October 14. You will turn in the assignment on Canvas. If you do part of the assignment by hand on paper, use CamScanner, Adobe Scan, or another similar free smartphone app to create a pdf file of your work before submitting.

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Do the following problems from Chapter Four of the STAT2 textbook: 17, 18, 20, 21. (These are from Sections 4.6 and 4.7 on Randomization Tests and Bootstrapping; note that the three methods of bootstrapping talked about in the text are the percentile/quantile method, the standard error method, and the bootstrap-$$t$$ method, referred to as Methods 1, 2, and 3, respectively)

You may wish to use the DescTools package for this problem. The median absolute deviation or $$MAD$$ statistic is an alternative to the variance for measuring the amount of spread in a sample. $MAD = Median(|x_i-Median(x)|)$ For technical reasons, it is often multiplied by the constant 1.4826.

The following code will compute the $$MAD$$ statistic for the pH of brain tissue, found in the BrainpH data set in the Stat2Data package.

require(tidyverse)
require(mosaic)
require(Stat2Data)
require(DescTools)
data(BrainpH)
median(BrainpH$pH) ## [1] 6.885 mad(BrainpH$pH,constant=1) # don't multiply by 1.4826
## [1] 0.19
mad(BrainpH\$pH) 
## [1] 0.281694

Since I doubt you have ever been taught a formula for the 95% confidence interval of the median absolute deviation, use bootstrapping to find the 95% CI, use the percentile/quantile, standard error, and $$BCa$$ methods (the latter is not in the textbook). Use $$B=1000$$ bootstrap samples.

You can use code as demonstrated in class, or you can investigate the MAD, BootCI, and MADCI functions in the DescTools package. The MADCI function uses a formula from the following recent paper by Arachchige & Prendergast. If you look at the paper, you see computing the CI for the MAD is quite involved and certainly not something that would be taught in an introductory statistics course.

Arachchige, Chandima N. P. G., and Prendergast, Luke A. (2019) Confidence intervals for median absolute deviations, https://arxiv.org/abs/1910.00229

Do the following problems from Chapter Five of the STAT2 textbook, on one-way ANOVA: 1-8, 16, 18, 20, 23, 24, 27, 28, 37, 39.

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