9. Contingency Analysis

Question 1

contingency analysis

Answer 1

tests the independence of 2 categorical variables

Question 2

With independence, relationship between Pr[X AND Y ] and Pr[X] and Pr[Y]

Answer 2

Pr[X AND ] = Pr[X] * Pr[Y]

Question 3

Process of Contingency analysis

Answer 3

1. Determine EXPECTED probability of each combined category
   (ex. Pr[X AND Y] Pr[X AND y] etc) by calculating Pr[X], Pr[Y]. Pr[x], Pr[y], and multiplying those probabilities to give probability of both.
2. multiply proportions by total number of individuals to give expected count
3. Calculate the chi squared value, (Observed - exp)^2/exp for each category
4. Calculate degrees of freedom df = (# columns - 1) * (# rows - 1)
5. determine critical value, and compare chi squared to that value

Question 4

How to calculate degrees of freedom for contingency analysis test

Answer 4

df = (# columns - 1) * (# rows - 1)

Question 5

Assumptions of contingency test

Answer 5

same assumptions of chi squared

No expectations less than 1, and no more than 20% less than 5

Question 6

Fisher’s exact test

Answer 6

used in a 2 X 2 contingency analysis, makes no assumptions about size of expectations

hard to do by hand, but can do through R

Question 7

Odds

Answer 7

The probability of success divided by the probability of failure

when p = probability of success

O = p / (1 - p)

Question 8

Odds ratio

Answer 8

the odds of success in one group divided by odds in another

OR = (odds in treatment group) / (odds in control group)