Assignment I for Biostats Course VHM 801 at AVC - Fall semester 2021

The assignment is worth 10% of the final course mark. Please be aware that by handing in the home assignment you implicitly acknowledge to have read and accepted the instructions for home assignments as described on the VHM 801 homepage.

This assignment is based on data provided with the PSLS textbook, originating from a study on ant morphology and genomics (Alvarado et al., 2015). The morphological features of interest were related to the size of the ants, and the present data include two variables related to size: scape length (scape) and head width (head), both measured in microns. The ants were sampled from mature ant carpenter colonies (Camponotus floridanus), which originated from queen ants collected in Florida, USA. The data provided here are measurements for 169 adult workers, and for each ant is also included a classification into two types of workers: major or minor workers (explored in more detail in the article, but it suffices for our purposes here to know about the distinction into these two types). The dataset is available in Minitab format and as a comma-separated file, for import into Stata and other statistical software.

The home assignment has four questions which should all be answered.

1. First, briefly describe the variable type of all the variables in the dataset, e.g. using one or several of the descriptors: nominal, ordinal, discrete, continuous. Next, select one of the two size variables (as you want), and carry out a descriptive analysis for this variable based on all 169 individuals. Choose the graphical representation and the statistics you find most useful to show the distribution. Comment on the distribution's different features, such as the center, spread and shape, as well as any 'potential outliers'. Finally, include in your descriptive analysis an assessment of whether it would seem reasonable to assume the values of this variable to be normally distributed. If you conclude that the variable is not normally distributed, describe how its distribution seems to differ from a normal distribution.

2. Continue your analysis from Question 1 by computing descriptive statistics and graphical displays to illustrate any differences in the distribution of your chosen size variable between the two types of ants. Repeat the steps of the analysis and description of the distribution from Question 1 for each ant type, including the assessment of normality. Summarize your findings from Questions 1-2 into a conclusion about the distribution(s). Note that you are not expected to compute any statistical tests to compare the distributions between the two types of ants.

3. Examine graphically the relationship between scape length and head width in adult carpenter ants, and describe your findings. Does this relationship appear to be the same for minor and major workers? Also here, you are not expected to compute any statistical tests to support your visual assessment.

4. With appropriate assumptions about the distribution of scape length within the two types of ants, carry out the following calculations:
   1. What is the probability that scape lengths of major workers are below 2100?
   2. What is the probability that scape lengths of minor workers are above 2100?
   3. Determine a value x, so that the probability of scape lengths of major workers being below x and the probability of scape lengths of minor workers being above x are the same? This value can be considered as a natural cut-point for whether an ant of unknown type should be considered as a minor or major worker (but there are also other ways of answering that question). (Hint: You may answer this last question either approximately by determining a value for x meeting the requirement, or analytically by solving a suitable equation. In any case, you need to describe your method; a correct answer without a description of the method will not be awarded a full score.)