Contingency Analysis

Question 1

What is relative risk

Answer 1

compares the probability of an outcome in two groups. Common in cohort studies (prospective)

Question 2

How do you calculate relative risk

Answer 2

RR = P(event|unexposed) / P(event|exposed)
​
Or in terms of a 2×2 table:

               Event (Yes)	 Event (No)	Total Exposed	         a                    b                a + b Unexposed	 c                     d               c + d 

RR = a/(a+b) / c/(c+d)

Question 3

What do the different values of RR mean

Answer 3

RR = 1 → no difference in risk

RR > 1 → increased risk in exposed group

RR < 1 → decreased risk in exposed group

Question 4

What is an odds ratio

Answer 4

compares the odds of an event occurring in one group to another
common in case - control studies

Question 5

Whats the formula for an OR from a 2x2 table

Answer 5

OR = a x d / b x c

Question 6

What do the different values of OR mean

Answer 6

OR = 1 → no association

OR > 1 → higher odds in exposed group

OR < 1 → lower odds in exposed group

Question 7

How do you calculate a confidence interval for OR

Answer 7

1. Calculate the log OR:
   log(OR)
2. Calculate the standard error of log(OR):
   𝑆𝐸 log (𝑂𝑅) = √(1/a) + (1/b) + (1/c) + (1/d)
3. Construct the CI on the log scale:
   log(OR) ± z∗ x SE log(OR)
   ​
4. Exponentiate the endpoints to get the CI for OR:
   (𝑒 lower, 𝑒 upper)

Question 8

When do you use the Chi-Squared contingency test

Answer 8

To test whether two categorical variables are independent (no association)

Question 9

How do you calculate a Chi-Squared contingency test

Answer 9

1. Set up a 2×2 or r×c table of observed counts
2. Calculate expected counts:
   𝐸𝑖𝑗 = rowtotal x columntotal / grandtotal
3. Use test statistic:

𝜒² = ∑ ( 𝑂𝑖𝑗 - 𝐸𝑖𝑗)² / 𝐸𝑖𝑗

4. Degrees of freedom:
   df=(r−1)(c−1)
5. Compare to critical value or get p-value from χ² table.

Question 10

When should you use the Chi-Squared contingency test

Answer 10

only if all expected counts ≥ 5

Question 11

When do you use Fisher’s exact test

Answer 11

used instead of chi-squared when sample sizes are small (especially expected count < 5 in any cell

Question 12

How do you carrying out Fisher’s exact test

Answer 12

1. Use a 2×2 contingency table
2. Calculate the exact probability of observing the data (or more extreme data) under the null hypothesis of no association

3.Done using software or online calculator (exact formula involves factorials)