The following examples show how to decide to reject or fail to reject the null hypothesis in both a one-way ANOVA and two-way ANOVA. To decide if we should reject or fail to reject each null hypothesis, we must refer to the p-values in the output of the two-way ANOVA table. There is no interaction effect between the two variables.All group means are equal at each level of the second variable.All group means are equal at each level of the first variable.0.05) then we can reject the null hypothesis and conclude that not all group means are equal.Ī two-way ANOVA is used to determine whether or not there is a statistically significant difference between the means of three or more independent groups that have been split on two variables (sometimes called “factors”).Ī two-way ANOVA tests three null hypotheses at the same time: If the p-value is less than some significance level (e.g. To decide if we should reject or fail to reject the null hypothesis, we must refer to the p-value in the output of the ANOVA table. H A: At least one group mean is different from the rest.A one-way ANOVA is used to determine if there is a statistically significant difference between the mean of three or more independent groups.Ī one-way ANOVA uses the following null and alternative hypotheses:
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