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.
- Identify values for r, c, and n and then use the formulae provide in lecture and the reading to compute all degrees-of-freedom.
- 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.
- 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).
- No functions, beyond using `distrib()` to calculate p-values, will be useful for these calculations.