Question 1-3

The Day3Quest1_3.csv data file contains measurements on the growth (change in height), over a one-year period, in the flower spike length of Australian grass trees in four different locations in Western Australia: Yanchep, Mundaring, Mandurah, and Pickering Brook. All the plants in each location are approximately the same age. The measurements are recorded in cm. The indexing of the values in the data file is such that: L1 = Yanchep, L2 = Mundaring, L3 = Mandurah, and 4 = Pickering Brook. There is also an additional column that identifies when the area was burnt: Spring or Autumn. So, although there are several data columns, you have a factor variable for "Location" (four levels), a factor variable for time of "Burn" (two levels), and the actual data measurements.

For this research project you have three supervisors. Supervisor one is from the School of Agriculture and Environment; supervisor two is from the School of Biological Sciences; and supervisor three is from the School of Molecular Sciences.

Supervisor one provides the following instructions. Check for unequal group variance using the Bartlett test, with the groups defined by a Burn Location interaction factor. If the assumption of equal group variance is valid, then assuming equal group variance is the approach with the greatest power to detect differences, if differences exist. If the assumption is not valid, assuming equal group variance results in hypothesis testing that is incorrect. The supervisor therefore tells you to use a heteroskedasticity robust covariance matrix when conducting the Anova test, if, and only if required. Conduct the analysis as directed and select the appropriate answers for Question 1.

Supervisor two provides the following instructions. Check for unequal group variance by directly modelling the group variance defined by the Burn Location interaction factor variable and comparing the result for this model to a model that assumes equal group variance. Based on the result of comparing the two models conduct an Anova test using the appropriate model. Conduct the analysis as directed and select the appropriate answers for Question 2.

Supervisor three does not like the Bartlett test and prefers the non-parametric Fligner-Killeen test. (This test was used in exercises earlier in the course and when using R the test is implemented with fligner.test(.)). Supervisor three therefore provides the following instructions. Check for unequal group variance using the Fligner-Killeen test, with the groups defined by the Burn Location interaction factor variable. If you fail the test, then conduct the Anova test using a heteroskedasticity robust covariance matrix, otherwise use the standard covariance matrix for the Anova. Conduct the analysis as directed and select the appropriate answers for Question 3.

The one thing that all three supervisors agree on is that the Anova test should be conducted using the Type-II sum of squares formula and so for the Anova test they all recommend using the Anova() function rather than the anova() function.

solve using R