Week 6 day 2

Question 1

What is the difference between a chi-squared Goodness of Fit Test and a chi-square test for independence?

Question 2

What are residuals?

Answer 2

They are the difference of what was expected.
The difference between observed and expected values.

Question 3

Does a test statistic need to be a single number?

Answer 3

yes.

Question 4

As X-square values increase, are we more likely to reject the null?

Answer 4

Yes.

Question 5

How are the degrees of freedom calculated for chi-square tests for independence?

Answer 5

df = (R-1)(C-1)

R - number of rows.
C - number of columns.

Question 6

How to calculate the p-value for a chi-square in R?

Answer 6

1-pchisq(95th quantile x-square value,df=…)

95th quantile X-square: qchisq(0.95,df=…)

Question 7

Do people ever use Pearson residuals and ‘standard’ or ‘adjusted’ residuals?

Answer 7

Yes.

Question 8

What effect size is used often with chi-square testing?

Answer 8

Cramer’s V.

Question 9

What does effect size tell us?

Answer 9

Tell how big an observed difference is, regardless of p-value.

Question 10

Why don’t we just use chi-square stat for an effect size measure?

Question 11

What function do we use to calculate Cramer’s V?

Answer 11

CramerV() from DescTools package.

Question 12

In the chisqr() function, if we do not specify the p= argument, what does it assume it is?

Answer 12

It assumes that the expected frequency is an equal distribution across all variables.

Question 13

What are the assumptions for a chi-square test?

Answer 13

1. “Large” expected frequencies.
2. Independence of the data.

Question 14

How do we determine whether our assumptions for our test are met “enough”?

Question 15

What is the FIscher Exact Test, and when do we use it?

Answer 15

The Fischer Exact Test is used when there are low expected frequencies (generally less than 5) per cell.

Question 16

Does R warn us if our expected frequencies are too low for the assumptions required for a chi-square test?

Answer 16

Yes.

Question 17

What does the Fischer Exact Test tell us?
Does it give us a test stat?
Does it give us a p-value? If so, what does the p-value represent?

Answer 17

The Fischer exact test does not give a test stat, it only gives a p-value. The p-value tells us whether the distribution of data is the same as what would be expected or not.

Question 18

Why is the chi-square distribution the shape that it is?

Question 19

When a X-squared stat that is significant, how do we determine WHERE the significant difference within the data is?

Answer 19

Using adjusted residuals.

If the adjusted residuals are + or - 1.96 then the significant difference has come from these cells.

Question 20

What are the two assumptions that are required for a chi-squared analysis?

Answer 20

1. “Large” expected frequencies.
2. Independence of data.

Question 21

What tests can we do if either of the two underlying assumptions for chi-squared analysis are violated?

Answer 21

1. 2.

Question 22

What is the Fischer test and when do we use it?

Answer 22

The Fischer Exact test is used for when the expected frequencies are less than 5 (generally) and we want to measure whether a statisically significant relationship exists between two categorical variables, such as whether Flopsy and Shadow have the same distribution of colours in their wardrobes, or whether if women are more likely to vote for Greens than men.

Question 23

What is the McNemar test and when do we use this?

Answer 23

The McNemar chi-squared test is used when our data is not independent. This could be when we are measuring someone’s response pre- and post- a treatment as measured by a non-continuos scale.