Note Your answers to the questions below should follow the expectations for homework found here. Due date is on the Dates page.

ANOVA Table

Cattails

A study was conducted to determine if the mean density of non-native cattail plants differed between two years, two habitats (“near” and “far” from a road), or the interaction between year and habitat. The researchers collected information at 25 sampling sites within each year and habitat combination. The summarized density of cattails in each year and habitat are shown below.

Response  Year  Habitat       n       Mean     Median      StDev
Density   2015    far        25      75.45      75.15      14.76
                  near       25      74.46      74.48      13.25
          2016    far        25      83.98      79.97      13.59
                  near       25      80.70      79.15      14.20

Use these result to complete the ANOVA table below. This question can be hand-written, but clearly show your work for all calculations.

Source df SS MS F p-value
Among          
   Year          
   Habitat          
   Year:Habitat          
Within       xxx xxx
Total   20227.3 xxx xxx xxx

   

Hints:
  1. Identify values for r, c, and n and then use the formulae provide in lecture and the reading to compute all degrees-of-freedom.
  2. Construct a 2x2 table (Year as rows, Habitat as columns) of treatment means and then append the level means and grand mean in the margins. Note that level (and grand) means are simply the mean of treatments means when the sample sizes in the treatments are equal, as they are in this example.
  3. Use the definitions of r, c, and n, and your table of means to compute SSamong, SSrow, and SScolumn according to formulae provided in class and in the reading. Compute the remaining SS with simple addition and subtraction (from principles of how SS partition).
  4. No functions, beyond using `distrib()` to calculate p-values, will be useful for these calculations.