Chi-Squared Tests

Question 1

How do you calculate the expected value for a cell?

Answer 1

(Row Total x Column Total) / Sample Size

Question 2

How do you calculate the chi-squared values for each cell?

Answer 2

(f_o - f_e) ² / f_e

Question 3

What is the test statistic for chi-squared testing?

Answer 3

The sum of the chi-squared values

Question 4

What is the formula for the number of degrees of freedom?

Answer 4

(m - 1)(n - 1) where ‘m’ is rows and ‘n’ is columns

Question 5

What is the critical value?

Answer 5

Using the formula booklet table, find the value given for the number of degrees of freedom and given significance level

Question 6

What is the conclusion if the test statistic > critical value?

Answer 6

Reject H₀ and suggests there is association

Question 7

What is the conclusion if the test statistic < critical value?

Answer 7

Reject H₁ and suggests there is no association

Question 8

What does a greater chi-squared values signify?

Answer 8

A greater chi-squared signifies a larger disparity between observed and expected values

Question 9

Why can causation not be assumed if there is some association?

Answer 9

Causation cannot be assumed as a third variable may be involved

Question 10

What does an expected frequency less than 5 suggest?

Answer 10

If they are less than 5, they are likely to be inaccurate because small samples create more random fluctuations

Question 11

What is the solution to an expected frequency less than 5?

Answer 11

You combine categories suitably to give expected values greater than 5

Question 12

What must you remember once you have combined categories?

Answer 12

You must re-evaluate the observed values as the categories for them have been combined too

Question 13

What does chi-squared distribution assume about the data?
What does this mean for expected values less than 5?

Answer 13

Chi-squared distribution assumes that the observed frequencies are approximately normally distributed about the expected frequencies
If f_e < 5, distribution of f_o is asymmetrical so needs to be combined

Question 14

What does a goodness of fit test, test?

Answer 14

Goodness of fit test tests whether a given set of data fits a particular distribution

Question 15

What variables have an impact on the procedure of the goodness of fit test?
What is the impact?

Answer 15

When the expected values are estimated for poisson and probability for binomial, you subtract one from the number of degrees of freedom

Question 16

What is the recurrence relation for Poisson Distribution?

Answer 16

P(X = r + 1) = P(X = r) x (y / r + 1)

Question 17

When do you combine categories?

Answer 17

When expected frequency is less than 5

Question 18

How do you calculate the sum of chi-squared values for Poisson distribution?

Answer 18

Expected frequencies can be calculated using the poisson recurrence relation and the sample size
Chi-Squared values are calculated as usual

Question 19

How do you calculate the sum of chi-squared values for binomial distribution?

Answer 19

Expected frequencies calculated by multiplying sample size and probability from binomial distribution
Probability can be calculated through binomial expectation
Chi-squared values are calculated as usual