DATASCI 6.4

What is a two-way table

A table that displays counts for combinations of two categorical variables, organized by rows and columns

What is the main goal of a chi-square test for independence?

To determine whether there is an association (dependence) between two categorical variables

State the null hypothesis for a chi-square test of independence

The two variables are independent (no relationship)

State the alternative hypothesis for a chi-square test of independence

The two variables are dependent (associated)

What does "dependent" (associated) mean?

The distribution of one variable changes depending on the category of the other variable

What assumption is made when calculating expected counts

That the two variables are independent

What do large contribution to X2 indicate?

Cells where observed counts differ greatly from expected counts, suggesting possible association

What type of test is the chi-square test (one -tailed or two-tailed)?

One-tailed (right-tailed only)

Why is the test right-tailed?

Because only large X2 values indicate strong evidence against independence

What does a small X2 value suggest?

Observed counts are close to expected which supports independence

What does a large X2 value suggest?

Observed counts differ from expected showing evidence of association

Why must expected counts be at least 5?

To ensure the chi-square approximation to the distribution is valid

How is the p-value calculated?

Using the upper tail of the chi-square distribution with the appropriate df

How do you interpret a rejection of H0 in context?

There is evidence of an association between the two variables

How do you interpret failing to reject H0?

There is not enough evidence to conclude an association exists

Why do we compare observed and expected counts?

To see whether the observed pattern could reasonably occur if the variables were independent

How is a two-way chi-square test different from a one-way test?

1-way tests fit to a distribution, 2-way tests association between two variables

What does the chi-square statistic summarize in a two-way table?

The overall deviation between observed and expected counts across all cells

If one cell has a very large deviation, what happens to X2?

It increases significantly, potentially leading to rejection of H0

Why do we multiply row and column totals when finding expected counts?

Because under independence, probabilities multiply, and counts follow from those probabilities.