(6) Chi-squared tests

Goodness of fit

Measures how well an observed frequency distribution fits to a known distribution

H₀ (null hypothesis)

There is no difference between the observed and theoretical distribution

H₁ (alternative hypothesis)

There is a difference between the observed and theoretical distribution

X² formula booklet (Measure of goodness of fit)

Calculate number of degrees of freedom

Number of cells - number of constraints

(after any combining)

When to combine cells

When any of the expected values are less than 5, then combine frequencies in the table until they are greater than 5

X² > critical value

Sufficient evidence to reject H₀

X² < critical value

Insufficient evidence to reject H₀

Degrees of freedom for discrete uniform dist

v = n - 1

Degrees of freedom for binomial/poisson/geometric dist

If p/λ is not estimated by calculation: v = n - 1

Otherwise v = n - 2

Expected frequency from contingency table

Number of degrees of freedom from contingency table

(h-1)(k-1)

h = rows

k = columns