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# ANOVA-1 - Analysis of Variance Tests if there is a...

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Analysis of Variance Tests if there is a significant difference between several group means at once: multivariate Results are given as an F ratio or F value Acts the same as a t test but prevents needing to do multiple t tests, eg. If had groups A, B, C, D You would have to do t tests on: A & B, A & C, A & D, B & C, C & D which amounts to 6 t tests – this increases the risk of both Type I and II errors.

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How its done What ANOVA looks at is the way groups differ internally versus what the difference is between them. To take the above example: 1. ANOVA calculates the mean for each of the final grading groups (HD, D, Cr, P, N) on the tutorial exercise figure - the Group Means. 2. It calculates the mean for all the groups combined - the Overall Mean. 3. Then it calculates, within each group, the total deviation of each individual's score from the Group Mean - Within Group Variation. 4. Next, it calculates the deviation of each Group Mean from the Overall Mean - Between Group Variation. 5. Finally, ANOVA produces the F statistic which is the ratio Between Group Variation to the Within Group Variation. If the Between Group Variation is significantly greater than the Within Group Variation, then it is likely that there is a statistically significant difference between the groups. The statistical package will tell you if the F ratio is significant or not. All versions of ANOVA follow these basic principles but the sources of Variation get more complex as the number of groups and the interaction effects increase.
One Way or Simple ANOVA Done when there is one factor or one treatment variable and there are more than two groups within this factor. ANOVA deals with one factor or treatment variable (eg group membership) and more than two groups within this factor. An example is 3 groups of preschoolers all

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ANOVA-1 - Analysis of Variance Tests if there is a...

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