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Flashcards in Chi-Square Tests Deck (16)
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1
Q

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

A

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

2
Q

What is the statistic of chi-square?

A

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

3
Q

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

A

Close to zero

4
Q

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

A

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

5
Q

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

A

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

6
Q

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

A

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

7
Q

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

A

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

8
Q

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

A

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

9
Q

When are two variables considered independent?;

What does this mean?

A

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

10
Q

State the conceptual hypotheses

A

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)

11
Q

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

A

row total x column total / N

12
Q

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

A

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

Chi-square goodness of fit

13
Q

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

A

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)

14
Q

What are the assumptions of chi-square?

A

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)

15
Q

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

A

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

16
Q

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

A

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)