This assignment is motivated by a desire to better understand the nature of phenotypic variation associated with bananas, and the sources of said variation.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Learning Objectives:

This assignment is motivated by a desire to better understand the nature of phenotypic variation associated with bananas, and the sources of said variation. From a learning objective perspective, this project will demonstrate your ability to i) manage data ii) perform a variety of different statistical tests iii) interpret the output of such tests iv) plot beautiful, meaningful figures/infographics v) present your findings to an interested audience. The required format for this assignment will be a narrated slide-deck, which is described in a later section of this document.

Project motivation / Research Questions

Bananas (Musca spp.) are a fruit consumed worldwide and the fourth most important food crop (after rice, wheat and maize) in the world (Prabha & Kumar 2015). Humans has been cultivating bananas for at least 8000 years (and possibly over 10,000 years)! Bananas are grown in over 150 countries each year with over 100 million metric tonnes of fruit being produced ear year. The most commonly internationally exported type of banana are those from the “Cavendish” cultivars belong to the AAA genome group, which includes the cultivars that have three sets of chromosome inherited from the wild (ancestral) species Musa acuminate. The bananas develop from flowers that grow on stems of this large, herbaceous (non-woody) plant. Bananas make up

~9% of the >6.5 billion dollars of fresh fruit imported in to Canada, (Agriculture and Agri-Food Canada, 2017), with ~ 15.70 kg of bananas consumed on average by each Canadian annually. Given their ubiquitous nature, bananas provide a great opportunity for us as biologists/statisticians to explore a number of different questions that are of great relevance from both biological and economic perspectives.

In this project, you use your own individualized banana dataset, and analyze it using the most appropriate statistical analysis techniques. The questions you will be trying to address are as follows:

1) How can we efficiently describe a banana’s phenotype? Does the phenotype of bananas depend on where (or) how they are bought?

2) Are there differences in the characteristics of groups of bananas that have come to Canada from different countries (or) by different companies? How much variation is there between/within these groups?

3) What is the relationship between a banana’s length and its width? Does it differ between those bananas on the inner row and the outer row?

4) Do the conditions under which bananas are stored affect how much it ripens over the course of a week?

How Will I Do this Assignment?

You should begin by visiting the course MyLS page to retrieve your personalized/individualized dataset (in csv format). The data therein contains a subset of the complete data collected by you and your classmates. The subset was created by me (using R of course) using a simple random

sampling technique to create a unique dataset for your personal use (i.e. everyone will have a slightly different set of data). To further individualize each of your assignments, the response and explanatory variables you will be analyzing will depend on when you were born & your student ID). Please consult the table below to determine which response variables you will be using.

Question 1: How can we efficiently describe a banana’s phenotype? Does the phenotype of bananas depend on where (or) how they were bought?

1. Using your individualized dataset, perform a Principle Component Analysis using the following variables: i) Outer curve length ii) Inner curve length, iii) Pedicel length, iv) Banana Circumference, v) Pedicel circumference, and vi) Number of sides.

2. Report in a table the loadings and % variance explained by the first 3 principle components. Depending on your birth month (see below), describe ONE of the principle components via your interpretation of its loadings

3. Using your re-scored Principle Component scores from your chosen component, as the response variables, determine statistically whether or there is a difference in the mean (or) median scores for bananas of the bananas bought in Kitchener-Waterloo or outside of K-W. Remember to first determine whether or not, for each of the two samples, whether the variables being compared have a normal distributions. Transform, in an appropriate fashion when the data is not be normally distributed, and determine whether the transformed data is/is not normally distributed. Also remember to first test whether the variances in the two samples are equal and choose the most appropriate parametric or non-parametric statistical test based on this information to make the comparison of means (or) medians.

4. Calculate the (appropriate) effect size statistic (& 95% CI) of this difference

5. Perform a two-sample power test to determine what the current power of your one- sample test is as well as determine the minimum sample size for a one sample test that would be necessary to detect a difference of this magnitude (with power = 0.8).

6. Using the graphing functions of R, create a simple box plot graph that summarizes the comparison being made in step 4 above. 

 

 

Question 3 (X variable - width)	“X” Variable
Birthday in January, February, March or April	Banana Diameter
Birthday in May, June, July or August	Pulp Diameter
Birthday in September, October, November or December	Banana Circumference

 

Question 3 (Y variable - length)	“Y” Variable
Next-to-last digit in your student ID number is odd	Outer Curve Length
Next-to-last digit in your student ID number is even	Inner Curve Length

 

Question 4: Do the conditions under which bananas are stored affect how much it ripens over the course of a week?

 1.  Perform a two-way ANOVA to determine if light treatment and/or spacing treatment have a significant effect on the in ripeness index (End index value – start index value).

 

2. Report & interpret the results of your ANOVA table.

3. Create a plot that best depicts in your opinion the most important results of your experiment, indicating the location of any statistically significant differences revealed by your statistical tests.

Attachments:

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