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?

Sum of Squares

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

The goal is to create the table SourceSSdfMSFp Between(g)roups – 1SS between /dfMS between /MS within Withinn – gSS within /dfblank Totaln – 1blank 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

F distribution

F table – differs by alpha

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.

Theoretical example Point numberGroup 1Group These are BA per acre estimates from point sampling Walnut Woods total points divided in half to create 2 groups. Group 2 basically equals points Did the higher numbered points have fewer stems?

Point Locations

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

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.

Result Anova: Single Factor SUMMARY GroupsCountSumAverageVariance Column Column ANOVA Source of VariationSSdfMSFP-valueF crit Between Groups Within Groups Total

F table – differs by alpha

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

Questions?