# STA 6166 Assignment 3

A Plant Inbreeding Study

The quantitative analysis of genetic information is currently an important topic. But agricultural scientists have been quantifying the results of interbreeding experiments for a long time. Below is an example of a typical trial.

A plant breeder wishes to understand the effect of inbreeding on plant weight of red clover. Let F0 be the parent plant material. Six (6) individual plants from this parent population were chosen and plant weight, in grams, at the height of the growing season was recorded. Three other interbred lines were also studied. The FA population consisted of individuals who were the result of breeding just one pair of plants selected at random from the F0 population. The FB group consisted of individuals who were the result of breeding just one pair of plants selected at random from the FA population. The FC group consisted of individuals who were the result of breeding just one pair of plants selected at random from the FB group. In this way, F0, FA, FB and FC represent populations in increasing order of inbreeding (four inbred lines). For each population, six (6) individuals were selected and plant weight, in grams, at the height of the growing season was recorded:

 F0 FA FB FC 297.0 220.0 185.6 200.7 271.2 186.6 200.3 160.8 218.3 173.7 232.9 167.7 270.6 269.2 149.2 192.0 299.1 185.5 207.9 163.2 289.7 190.5 159.9 146.2

Your task is to exhaustively analyze this data using the one-way analysis of variance (AOV) techniques of Unit 3. In the process, you should give complete answers to the following questions:

1. Are there statistical differences in average plant weight among the four red clover inbred lines?
2. Is the assumption of equal population variances supported for this data? If not what did you do?
3. Do the residuals from the one-way AOV model fit suggest normality? If not what did you do?
4. Assuming you conclude that average plant weight is not the same for all four inbred lines, determine which lines are different from which other lines. Choose one of the many multiple comparison procedures to use. Indicate why you chose that method.

Instructions:

• Here is the data as a plain text file.
• You will notice that no guidance was given as to when to declare statistical significance i.e. what value of alpha to use. You are all big boys and girls now, so you will have to make your own decision! In any specific inference, be sure to inform the reader what value you are using, with brief reason.
• Typeset your results as a report, using the same format, template, and general instructions as for Assignment 2

NOTE: This example is totally synthetic. Any similarity to real cases or situations is completely incidental.