Section 26 One-way ANOVA: Steps


26.1 Model

SBP = overall mean + sampling variability

\[ \large y_{j} = \mu + \epsilon_{j} \]


SBP = overall mean + Group effect + sampling variability

\[ \large y_{ij} = \mu + \tau_{i} + \epsilon_{ij} \]


\(\large i\) = treatment index; i: 1 to g

\(\large j\) = observation index within treatment; j: 1 to n

\(\large y_{ij}\) = j -th observation (replicate) in the i -th treatment

\(\large \mu\) = overall mean effect

\(\large \tau_{i}\) = effect of treatment group i

\(\large \epsilon_{ij} \sim NID(0, \sigma^2)\)


26.2 Assumptions

  • Values within each group are independent and normally distributed

  • Variances of the all groups are equal


26.3 Hypothesis

\[ \large H_O: \tau_1 = \tau_2 = ...= \tau_g \]

\[ \large H_A: \tau_i \ne 0 \space for \space at \space least \space one \space \tau_i\]