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Understanding One-Way ANOVA: Inference, F-Distribution, and Significance Testing

Learn how to interpret one-way ANOVA results using the F-distribution, degrees of freedom, and significance levels. Calculate F-values, understand ANOVA tables, and determine the influence of factors. Discover Excel output and interpret statistical significance.

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Understanding One-Way ANOVA: Inference, F-Distribution, and Significance Testing

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  1. 11/2112.1 Inference for one-way ANOVA

  2. Using Table E The F distribution is asymmetrical and has two distinct degrees of freedom. This was discovered by Fisher, hence the label “F.” Once again, what we do is calculate the value of F for our sample data and then look up the corresponding area under the curve in Table E.

  3. dfnum = I− 1 p F dfden=N−I Table E For df: 5,4

  4. Fcritical for a 5% is 3.49 F = 12.08 > 10.80 Thus p< 0.001

  5. The ANOVA table R2 = SSG/SST √MSE = sp Coefficient of determination Pooled standard deviation The sum of squares represents variation in the data: SST = SSG + SSE. The degrees of freedom likewise reflect the ANOVA model: DFT = DFG + DFE. Data (“Total”) = fit (“Groups”) + residual (“Error”)

  6. Excel output for the one-way ANOVA numerator denominator Here, the calculated F-value (12.08) is larger than Fcritical (3.49) for a 0.05. Thus, the test is significant at a 5%  Not all mean seedling lengths are the same; the number of nematodes is an influential factor.

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