H_0:μ_1=μ_2=⋯=μ_k F=MSA/MSE F_(ν_1,ν_2 ) ν_1=a-1 , ν_2=N-a
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Null hypothesis of a one-way ANOVA is that the means are equal. Alternate hypothesis a one-way ANOVA is that at least one of the means are different.
ANOVA is an inferential statistic used to test if 3 or more population means are equal or to test the affects of interactions.
H_0:μ_(1∙)=μ_(2∙)=⋯=μ_(a∙) F=MSA/MSE F_(ν_1,ν_2 ) ν_1=a-1 , ν_2=(a-1)(b-1) H_0:μ_(∙1)=μ_(∙2)=⋯=μ_(∙b) F=MSB/MSE F_(ν_1,ν_2 ) ν_1=b-1 , ν_2=(a-1)(b-1)  
The F-test is designed to test if two population variances are equal. It compares the ratio of two variances. If the variances are equal, the ratio of the variances will be 1.The F-test provides the basis for ANOVA which can compare two or more groups.One-way (or one-factor) ANOVA: Tests the hypothesis that means from two or more samples are equal.Two-way (or two-factor) ANOVA: Simultaneously tests the hypothesis that the means of two variables from two or more groups are equal.
multiple means multiple, plus means plus.