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Statistics

ANOVA, or Analysis of Variance, is a statistical method used to test if the means of different groups are significantly different. It compares sample means by analyzing variances within and between groups. Key components include the total sum of squares (SSTotal), within-group sum of squares (SSWithin), and between-group sum of squares (SSBetween). By applying the F-test statistic, researchers can infer significance at a given alpha level, typically 5%. This method helps determine if changes in a measured parameter, such as baseline area per acre in Walnut Woods, exist between distinct groups.

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Statistics

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  1. Statistics ANOVA

  2. What is ANOVA?

  3. Analysis of Variance • Test if a measured parameter is different between groups • Literally comparing the sample means by analyzing the variances

  4. Differing Variances – same mean

  5. Remember Variance? = _____ n – 1 • The mean of the squared deviations

  6. Sum of Squares = _____ n – 1

  7. Partitioning the Variance • SSTotal = SSbetween + SSwithin • SSWithin = mean of squared deviations within each group summed • SSbetween = SStotal – SSwithin

  8. The goal is to create the table SS = Sum of Squares df = degrees of freedom MS = Mean Squares (like variance since you divide by the portion of the sample size) F = the F test statistic, need to choose a alpha level i.e. 5% p = probability

  9. F distribution

  10. F table – differs by alpha

  11. For Instance • If we had split the class into 2 groups and had each group cruise the entire walnut woods tract the same way. We could compare the values obtained by group 1 to those from group 2.

  12. Theoretical example These are BA per acre estimates from point sampling Walnut Woods 2013. 14 total points divided in half to create 2 groups. Group 2 basically equals points 8-14. Did the higher numbered points have fewer stems?

  13. Point Locations 1 4 2 5 7 9 11 3 6 8 10 12 13 15 14

  14. Hypothesis • Walnut woods has the same BA/acre in the west half and the east half • Use F statistic to infer significance

  15. Single factor ANOVA in Excel • 1. On the Data tab, click Data Analysis. • 2. Select Anova: Single Factor and click OK. • 3. Click in the Input Range box and select the range B2:C8. • 4. Click in the Output Range box and select an empty cell such as A10. • 5. Click OK.

  16. Result

  17. F table – differs by alpha

  18. Result • Since F > F crit we reject the null hypothesis that the 2 samples have the same BA/acre.

  19. Questions?

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