Test whether observed frequency distributions fit expected patterns, or whether two categorical variables are independent. Reports ΟΒ², p-value, and CramΓ©r's V effect size.
ΟΒ² = Ξ£ [(Oα΅’ β Eα΅’)Β² / Eα΅’]
Degrees of freedom:
df = k β 1 (k = number of categories)
Enter observed counts in each cell. Each row represents one level of Variable 1; each column a level of Variable 2.
E(i,j) = (row_i total Γ col_j total) / grand total
ΟΒ² = Ξ£ [(O β E)Β² / E]
df = (rows β 1) Γ (cols β 1)
CramΓ©r's V (effect size):
V = β[ ΟΒ² / (N Γ min(rowsβ1, colsβ1)) ]