Lecture 26- HT Chisq

Question 1

Fill in the expected contingency table based on the example on slide 493 and go through the method for hypothesis testing using Chi-Squared test…

Answer 1

Answers in sides

Question 2

What is a Chi-squared test used to determine?

Answer 2

-The χ2-Test is used with two-way contingency tables to compare the
data we observed with what we would have expected to see under the null hypothesis of no association between the two variables.

-May be used in contingency tables that are larger than 2 × 2

-It uses the same hypothesis testing framework as the other hypothesis
tests we’ve seen.

Question 3

How do you work out an expected cell count?

Answer 3

Times the associated row total by the column total and divide by n (the total number of trials/ patients)

Question 4

How do you work out degrees of freedom?

Answer 4

ν = (number of rows - 1) × (number of columns - 1)

This determines the shape of the chi distribution we are using.

Question 5

What is the chi distribution showing and what does a large test statistic therefore mean?

Answer 5

• Distribution shows what would expect to see if H naught was true
• Therefore the larger the value (test statistic) the more we would reject H naught (cause far in tail)

Question 6

What do we use to quantify how big a value needs to be before the null is rejected?

Answer 6

-Calculate a P-value using: pchisq(9.70,1,lower.tail = FALSE) in r.
(test statistic and degrees of freedom will obviously vary depending on situation).

-As per usual the significance level for P is at 0.05 or 5% so at values less than this there is no association between the variables we reject the null (which says they are the same) and support the alternative hypothesis.

Question 7

Carry out a hypothesis test using the alternative (correlation) method for the example on slide 507…

Answer 7

Answers in slide

Question 8

How is maximum power achieved in this method?

Answer 8

If there is equal numbers in each ‘exposure’ group. This is often not possible to achieve in observational studies

Question 9

When is the chi squared method unreliable?

Answer 9

If counts are small, in particular if any of the expected cell counts are less than 5.

Question 10

Do we round expected cell counts?

Answer 10

No