Chi Square Tests

Why use Chi-square

Understanding nominal/ordinal data + frequency/proportion of response, depicts distribution of nominal variables

What does chi-square tests concern themselves with

Expected frequencies as compared to observed (actual) frequencies

What are the two tests of Chi-Square

Test of goodness of Fit , Test of Independence

test of goodness of fit

X2 determines if the distribution of observed frequencies differs from the theoretically expected frequencies

Test of independence

Determines if two variables are independent of each other, identifies the degree of association between the two variables

What are the assumptions made in a Chi-Square

Frequencies represent individual counts, categories = exhaustive + mutually exclusive, expected frequencies is at LEAST 5

What question does the Goodness of Fit test answer

How well does the actual distribution “fit” with the theoretical guess?

What information does the Goodness of fit test provide

Comparison of observed frequency counts with known or theoretical distribution and if the distribution will not significantly differ from the expected distribution

What can differences in a Goodness of Fit test be attributed to

Random fluctuations or chance occurrence

What does Goodness of Fit Uniform Distribution suggest

Equal distribution across all categories

Goodness of Fit Known Distribution Characteristics

Compares an observed distribution to a known one, illustrates how well the sample represents the population, involves residuals

What are residuals

Tell which category has the greatest discrepancy from expected value

What type of association does tests of independence determine

Association between two categorical variables (determine if the proportions of observations are independent of each other)

What type of table does a test of independence use

Contingency table

When do you use a MCNEMAR test

When independence of variables cannot be achieved

What are the 3 coefficients of association

Phi Coefficient, Cramer’s V, Contingency Coefficient

Phi coefficient

Association between nominal variables (2×2 table), value enervated between -1 and 1

Cramer’s V

Used when rows and columns are asymmetrical

Contingency coefficient

Association between nominal variables in a table larger than 2 × 2, but rows and columns have to equal