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Statistics

Statistics. ANOVA. What is ANOVA?. Analysis of Variance. Test if a measured parameter is different between groups Literally comparing the sample means by analyzing the variances. Differing Variances – same mean. Remember Variance?. = _____ n – 1 The mean of the squared deviations.

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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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