One categorical variable

ONE CATEGORICAL VARIABLE

What does the Pearson chi-square goodness-of-fit test evaluate?  (chisq.test() or goodnessOfFitTest())

It tests whether observed frequencies match a specified probability distribution.

• H₀: observed data are consistent with the specified distribution

• H₁: observed data are not consistent with the distribution

Typical use-case: are all levels of a categorical variable equally likely?

What are the null and alternative hypotheses?

• H₀: all class probabilities are equal

• H₁: not all class probabilities are equal

What is the chi-square test statistic, and how are degrees of freedom calculated?

O = observed frequency

E = expected frequency

• Larger X² values correspond to a lower probability of H₀ being true

• Degrees of freedom: k − 1

  • where k is the number of categories (levels of the categorical variable)

*exact rejection region depends on degrees of freedom

What is Cohen’s W, and how is it interpreted (3)? - Effect size

Cohen’s W measures the size of the deviation from the expected distribution:

• 0.10 = small effect

• 0.30 = medium effect

• 0.50 = large effect

*Larger values correspond to a larger deviation from the specified probability distribution under H0

What are the 2 assumptions of the chi-square goodness-of-fit test?

• Expected frequencies are all at least 5 in each category

  • in case of violation: use the exact goodness of fit test

• Observations are independent