Need help with my Statistics question – I’m studying for my class.
“What would you have done in terms of a study to demonstrate confidently whether or not the Lady could indeed distinguish if the milk or tea had been added first to the cup of tea.” Note that the Lady need only get four cups correct in terms of whether tea or milk was added first because that automatically ensures the other four cups are correctly identified. It can be shown using combinatorics math that there are 70 ways she could randomly pick 4 cups out of 8 and there is only one way in which she could get all 4 correct. According to historical accounts she indeed got all 4 cups correct. The chances of her getting all 4 correct is 1 in 70; again, there is only one way to get all four correct. “Are you convinced”? “Would you be convinced if she had gotten 3 correct”? (using what is called the hypergeometic probability distribution one can show the chances of 3 out of 4 correct are 16/70). As a historical note, Fisher would only believe she had true ability to distinguish if she got all 4 cups correct. Do you think this a reasonable criterion? Again, carefully read Senn’s article and you will see that some controversy exists even today as to the exact probability, however such depth of detail is well beyond the scope of this course.