1Cademy - Example of a One-Way ANOVA

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Example

Example of a One-Way ANOVA

To illustrate a one-way ANOVA, consider a health psychologist comparing the calorie estimates of three distinct groups: psychology majors, nutrition majors, and dieticians. The sample means are $187.50$ , $195.00$ , and $238.13$ , respectively. Using statistical software or an ANOVA table, the researcher finds the between-groups mean square ( $MS_B$ ) is $5,971.88$ , the within-groups mean square ( $MS_W$ ) is $602.23$ , and the resulting $F$ ratio is $9.92$ . With $2$ and $21$ degrees of freedom, the computed $F$ score ( $9.92$ ) exceeds the critical value of $3.467$ . Correspondingly, the $p$ -value is $.0009$ . Because this $p$ -value is less than the standard $.05$ alpha level, the researcher rejects the null hypothesis and concludes that the population mean calorie estimates for the three groups are significantly different.