Chi-Squared test

Question 1

What is meant by predicting categorical outcome variables?

Answer 1

in which category an entity falls

Question 2

What is used to measure categorical values numerically?

Answer 2

Frequencies

Question 3

What is the Chi-squared test used for?

Answer 3

defining whether there is a relationship between two categorical variables

Question 4

What does the Chi-Squared test compare to assess this?

Answer 4

It is comparing the observed frequencies with the expected frequencies.

Question 5

What formula does the chi-squared test use?

Answer 5

𝑋2 = ∑ (𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑠𝑐𝑜𝑟𝑒 − 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑠𝑐𝑜𝑟𝑒)^2 /𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑠𝑐𝑜𝑟𝑒

Question 6

How do you calculate the expected score?

Answer 6

row total * column total /n

Question 7

How do you calculate the degrees of freedom for the chi square?

Answer 7

(r-1) (c-1)

Question 8

In order to use the chi squared distribution with the chi-squared test, what is required?

Answer 8

In order to use the chi-squared distribution with the chi-squared statistic, there is a need for the expected value in each cell to be greater than 5.

Question 9

If the expected value is not greater than 5, what can be done?

Answer 9

Fisher’s exact test can be used.

Question 10

What is an alternative to the chi-squared statistic?

Answer 10

Likelihood ratio statistic

Question 11

What does the Likelihood ratio statistic utilise?

Answer 11

Comparing the probability of obtaining the same data under the null hypothesis

Question 12

What distribution does the Likelihood ratio use?

Answer 12

Chisq distribution

Question 13

What error does the Chi-sq distribution tend to make (when) and how can this be corrected?

Answer 13

The chi-square statistic tends to make a type-I error if the table is 2 x 2. This can be corrected for by using Yates’ correction

Question 14

What assumptions does the chi-sq test carry? (3)

Answer 14

One assumption the chi-square test uses is the assumption of independence of cases. Each person, item or entity must contribute to only one cell of the contingency table. Another assumption is that in 2x2 tables, no expected value should be below 5. In larger tables, not more than 20% of the expected values should be below 5 and all expected values should be greater than 1.

Question 15

What is the result of not meeting this expected values assumption?

Answer 15

leads to a reduction in test power.

Question 16

What is meant by the residual?

Answer 16

The residual is the error between the expected frequency and the observed frequency.

Question 17

How is the standardised residual calculated?

Answer 17

observed-expected / sqrt(expected)

Question 18

How do individual standardised residuals have a direst relationship with the test statistic?

Answer 18

the chi-square statistic is composed of the sum of the standardized residuals.

Question 19

What is used to give an effect size in chi sq

Answer 19

Cramer’s V can give an effect size

Question 20

In odds tables, what is usually used as the effect size?

Answer 20

odds-ratio (times A occurred/ times A did not occur)

Question 21

What is the actual odds ratio?

Answer 21

odds of event A divided by the odds of event B

Question 22

When is the phi test accurate?

Answer 22

2 x 2 contingency tables ( for measuring associations from 0-1)

Question 23

What should be used for phi test outside 2x2?

Answer 23

Contingency coefficient

Question 24

What shortcomings does the contingency coefficient and what attempts to mend this?

Answer 24

between 0-1 but seldom reaches upper limit and so Cramer V corrects for this

Question 25

If expected values are below 5 what are the recommended options if you have more than 2 variables? (4)

Answer 25

(1) collapse the data across the variables (preferably least likely to have an effect
(2) collapse levels of one of the variables
(3) collect more data
(4) accept the loss of power