• Lec20 Different Types of Sampling:
  • You are a statistician and you meet someone who claims to be able to tell by tasting whether the tea or the milk was added first to a cup.
  • Say you have 8 cups, tea, and milk handy.
• Lec21 Randomized Experiments:
  • How would you design an experiment to test whether a) they can really tell which came first or b) they are just guessing?

Today…

• Lec22: You run the experiements and get results. What now?

This experiment is known as The Lady Tasting Tea, occurred in the early 1900's and the statistician was Ronald Fisher:

• Reports indicate the taster got all 8 cups right.

Recall the two competing hypotheses:

1. She truly has the ability to tell which came first: milk or tea.
2. She is just guessing.

Let's suppose 2 is true…

… i.e. suppose she is guessing.

1. What is the probability she guesses one cup right?
2. What's more likely? That she get 4 correct or get 7 correct?
3. What is the probability she guesses all eight right?
4. Big One: How unlikely is this result? This is the ultimate statement: BS or not?

1. See if using the resample() and do() commands you can
   • simulate many, many, many cases of someone guessing at random for the eight cups, then
   • count the number of correct guesses
2. How would you compare
   • the observed number of correct guesses (in this case 8)
   • to the typical number of correct guesses assuming she is guessing at random?

Create a new R Script (File -> New File -> R Script) and copy the following starter code:

library(ggplot2)
library(dplyr)
library(mosaic)

# Single cup
guess_cup <- c(1, 0)

• We define guess_cup <- c(1, 0) where
  • 1 denotes correctly guessed
  • 0 denotes incorrectly guessed
• So to count the number correct you only need to sum() values of 0 and 1.