Fisher F-Test
used on: continuous data
assumptions: independent, normally ditributed groups
used for: checking homoscedasticity (homogeneity of variances of two populations)
null: \(H_0: \sigma_1^2 = \sigma_2^2\);
statistic:
\(F_0 = \frac{S^2_1}{S^2_2} \sim F_{n_1-1,n_2-1}\) distribution where \(S_1^2\) is the bigger of the two
Two-Way ANOVA
used on: continuous data
assumptions independent, normally distributed groups with constant variance
used for: comparing population means for combinations of two factors
null: maybe one of three:
(1)the population means of the first factor are equal (more like one-way ANOVA for the row factor)
(2)the population means of the second factor are equal (more like one-way ANOVA for the column factor)
(3)there is no interaction between the two factors
statistic:for each hypotheses given above, there is an F-test which is the mean square for each main effect and the interaction effect divided by the within variance
Chi-square Test
used on: categorical data
used for: checking if distributions of categorical variables are independent of each other
assumptions: no single population parameter, so invloves non-parametric statistic
null: all pairs of groups are independent;
statistic:
\(X^2_0 = \sum^k_{i=1} \frac{(x_i-m_i)^2}{m_i} \sim \chi^2_{k-1}\) distribution where \(k\) is the number of categories, \(x_i, \ m_i\) are the frequency and expectation of \(i\)th class respectively
Proportions Test
used on:ordinal data
assumptions:no single population parameter, so invloves non-parametric statistic
used for: comparing two populations proportions
null: \(H_0: p_1 = p_2\)
statistic:may either be odds ratio, relative risk or even chi-square statistcs