Chi-Square Tests

Question 1

What does a chi-square goodness of fit test analyse?

Answer 1

Tests whether the observed frequencies of a single categorical variable correspond to the frequencies expected if the null hypothesis is true

Question 2

What is the statistic of chi-square?

Answer 2

Chi-square = the sum of (O - E) squared / E (where O = observed frequencies & E = expected frequencies)

Question 3

If the null is true, what value should the obtained chi-square equal?

Answer 3

Close to zero

Question 4

Explain the process of a chi-square goodness of fit test

Answer 4

State null & alternative hypotheses; calculate expected frequencies; calculate chi-square; compare with critical chi-square; reach a decision; interpret result

Question 5

What is the alpha value of chi-square?;
What does the df depend on?;
What else do we include when reporting results?

Answer 5

.05 (two-tailed test);
Number of cells, not number of participants (df = k-1);
Sample size

Question 6

Can chi-square values be negative?;
What happens if we increase the sample size?;
When will chi-square be small?

Answer 6

No, only positive;
We can increase obtained chi-square, but critical chi-square remains the same;
If differences between O & E are small

Question 7

How do we determine expected frequencies if the null is true?

Answer 7

They can be uniformly distributed (equiprobable distribution); distributed in accord with theory; distributed in accord with previous observed frequencies; normally distributed

Question 8

When do we use a chi-square test of independence (or contingency chi-square)?

Answer 8

To determine whether two categorical variables are related or independent (tests whether classification on row variable is independent of classification on column variable)

Question 9

When are two variables considered independent?;

What does this mean?

Answer 9

When the frequency distribution for one variable has the same shape for all levels of the second variable;
Chi-square is not significant

Question 10

State the conceptual hypotheses

Answer 10

Null: there is no relationship between the two variables (independent of each other); Alternative: there is a relationship between the two variables (frequency distribution on one is contingent on levels of the other)

Question 11

What is the formula for determining the expected frequencies for each cell?

Answer 11

row total x column total / N

Question 12

What degrees of freedom do we use for a chi-square test of independence?;
Otherwise, the process is the same as….

Answer 12

(r - 1) (c - 1); where r = row & c = column;

Chi-square goodness of fit

Question 13

How does the sign test relate to the Wilcoxon’s MP ranked-sign test?;
What is the formula for expected frequencies?

Answer 13

It’s also used for repeated measures & deals with signs of the difference scores, ignoring any zeros; but values are are also ignored (signs only) & observed frequencies are compared to expected frequencies (using chi-square);
E = N / 2 (null expects equal numbers of positive & negative)

Question 14

What are the assumptions of chi-square?

Answer 14

Independence of observations (subjects must fall into only 1 category so can’t use on repeated measures designs); all expected frequencies should be at least 5 (the greater the df, the more lenient this is); inclusion of non-occurrences (calculations must be based on all subjects in sample)

Question 15

How is the chi-square test like the z-test, t-test & ANOVA?

Answer 15

Chi-square goodness of fit examines one group like the z or t-test; Chi-square test of independence examines two independent groups like independent groups t-test & also assess 3 or more independent groups like a one-way independent groups ANOVA

Question 16

What is Cramer’s phi?;
How can it be interpreted?;
What’s the formula?

Answer 16

A follow-up test to a chi-square test for independence; provides a measure of association between 2 variables;
Like Pearson’s r (scale from 0-1);
Square root of: chi-square divided by N (k-1)