Stats: Chapter 11

When data are frequency counts for different categories, the appropriate statistic is:

Chi-Square

Chi-Square is considered a nonparametric test because:

it does not analyze population parameters such as means and standard deviations

The specific nonparametric test covered in this course is:

Chi-Square

What type of data require a Chi-Square analysis?

Nominal data

The Chi-Square Goodness of Fit test analyzes:

frequency counts within a single variable

The Chi-Square Test of Independence analyzes:

frequency counts across two variables

Goodness of Fit uses how many variables?

One nominal variable

Chi-Square Independence uses how many variables?

Two nominal variables

The null hypothesis for Goodness of Fit states:

observed frequencies are similar to expected frequencies

The alternative hypothesis for Goodness of Fit states:

observed frequencies differ from expected frequencies

The null hypothesis for Chi-Square Independence states:

the two variables are not associated

The alternative hypothesis for Chi-Square Independence states:

the two variables are associated

Expected frequencies represent:

the frequencies expected if the null hypothesis is true

If an expected frequency is less than 5:

Chi-Square assumptions are violated

A Chi-Square should not be performed when expected frequencies are less than:

5

Chi-Square analyzes:

frequency counts

Chi-Square does not analyze:

means

Chi-Square does not test for:

causation

A significant Chi-Square result indicates:

the variables are likely associated

A non-significant Chi-Square result indicates:

the variables are not likely associated

The numerator of the Chi-Square formula measures:

the difference between observed and expected frequencies

If the null hypothesis is true, the difference between observed and expected frequencies should be close to:

0

The denominator of the Chi-Square formula helps determine:

whether the difference is large relative to the expected frequency

How many observed and expected pairs are calculated in Chi-Square?

One pair for every category or cell

For Goodness of Fit, expected frequencies are calculated by:

N divided by the number of categories

For Goodness of Fit with N = 90 and 3 categories, the expected frequency is:

30

For Goodness of Fit with N = 120 and 4 categories, the expected frequency is:

30

For Chi-Square Independence, expected frequencies are calculated using:

(Row Total × Column Total) ÷ Grand Total

Goodness of Fit expected frequencies are:

usually equal across categories

Independence expected frequencies are:

calculated separately for each cell

If the obtained Chi-Square has a small p-value, there is:

compelling evidence against the null hypothesis

If p < .05, the Chi-Square result is:

statistically significant

If p > .05, the Chi-Square result is:

not statistically significant

A significant Chi-Square result should be interpreted as:

an association between variables

A significant Chi-Square result should NOT be interpreted as:

a cause-and-effect relationship

Chi-Square is the nonparametric equivalent of:

correlation

The appropriate effect size when both variables have two levels is:

Phi coefficient

The appropriate effect size when at least one variable has more than two levels is:

Cramer's Phi

Which test would be used for favorite color preferences?

Chi-Square Goodness of Fit

Which test would be used for Gender × Favorite Color?

Chi-Square Test of Independence

Which test would be used for Political Party × Gender?

Chi-Square Test of Independence

Which test would be used for Dog, Cat, Bird preferences?

Chi-Square Goodness of Fit

A Goodness of Fit test uses:

one nominal variable

A Chi-Square Independence test uses:

two nominal variables

The most common interpretation of a significant Chi-Square result is:

the variables are associated