Institute of Natural and Mathematical Sciences (Statistics)

MASSEY UNIVERSITY College of Sciences Institute of Natural and Mathematical Sciences (Statistics) Introductory Statistics 161.120

Assignment 1: An Experiment on Paper Airplanes Due date for electronic submission Sunday 24th September 2017 Assessment value: 10%

Note: • This assignment involves data collection and will take several days to plan and complete. Don’t leave it until the last minute!

• Your report should be computer produced and uploaded to Stream in pdf format.

• You are expected to use Minitab (or Minitab Express) for your analyses with the output incorporated into your report.

The objective of this experiment is to explore and model the effect of a single categorical variable on the flight of a paper airplane

The measurements need to include one (1) continuous numerical variable (the response) and one (1) categorical variable (an explanatory factor or “treatment” under your control) which must have at least 4 different levels.

You will need at least 20 measurements at each level of your categorical variable (but it is not essential to have an equal number of replicates in each level of your categorical variable.)

Choose a research question to investigate. You can use one of the following questions OR you can create your own question based on another numerical response measurement and/or another categorical factor that can be varied.

1. Does the flight time of a paper airplane differ depending on the design of the airplane?

2. Does the flight time of a paper airplane differ depending on the weight of the airplane? (e.g. Using number of paper clips added [0 ,1 ,2 and 3] OR different weights of paper)

3. Does the flight time of a paper airplane different for paper airplanes of different sizes? (e.g. constructed from A4, A5, A6 and A7 paper)

Or questions 1A,2A,3A replace the words “flight time of” above by “distance travelled by”.

If you want to investigate a different research question, please contact your lecturer to discuss its suitability.

You should design and conduct the experiment using ‘good’ experimental design so you need to carefully consider the three main principles of experimental design: control, replication and randomisation. These will be discussed in lectures in week 5, but a helpful summary of the principles is given on the first page of www.lar.msstate.edu/pdf/Basics%20of%20Experimental%20Design.pdf

Why would we need to do this? Think about whether anything might change over the course of throwing 80-100 paper airplanes and how we might control for these changes, to ensure that any differences we see are as much as possible due to the treatment we use and as little as possible due to uncontrolled variation and error. You will be marked (see below) not just on collecting the data but on how you have used these ideas of replication, randomisation and control. Here are a few websites that may be useful when designing your planes: http://www.paperairplanes.co.uk/planes.html - a variety of simple planes made from A4 paper with instructions. http://www.zurqui.co.cr/crinfocus/paper/airplane.html - detailed instructions on how to make an elaborate paper plane. http://bestpaperairplanes.com/ - a variety of simple planes with instructions.

Bear in mind the following guidelines:

• You will require the help of at least one friend to collect your data.

• If your friend is also doing this paper, the collected data must be unique for each student (i.e. you may not share the data). You can plan and carry out the data collection together, but you will need to repeat the data collection process, so you have different data to each other.

• Subsequent analysis of the data and report writing (including description of methods used) must be done independently.

• You may need to carry out a small pilot experiment to check whether your methodology will work.

Keep a record of your data. It will be needed for Assignment 2.

Prepare a report of no more than 6 pages, using the following headings and addressing the points stated under each heading.

We have provided a Report Template on Stream that must be used when you write your report.

This assignment is marked out of 40 marks. Mark allocation is noted next to each section heading. Note that 4 of these marks will be given for presentation.

Part A: Introduction [7 marks]

• Overview: briefly state the research question you investigated. [ 1 mark ]

• Introduction: Describe the response (numeric) variable and how you measured it, including the units you used, and how accurately you measured. [ 2 marks ] Describe details on what the levels of your categorical variable (“treatment”) are. [ 2 marks ]

• Setting: Indicate where and when you carried out the experiment. Why did you choose this setting? If you collected the data with a classmate, give this person’s name and ID number. [ 2 mark ]

Part B: Experimental Design [13 marks]

Describe how you set up your experiment, what you did and why you made the decisions you did. Enough information should be given so that someone else could repeat your experiment.

• List possible sources of variation other than that caused by the “treatment”. [3 marks]

• Discuss how you controlled for these sources of variation, i.e. how you tried to ensure that the experimental units were as similar as possible except for the treatment. In particular:

o Describe your use of replication. E.g. if you used 20 throws for a particular level, were the throws truely replicates (independent and identical, how you controlled for extraneous factors)? Did you use more than one airplane for each level, if so why and when did you swap: by plan, or because one got bent, etc. [ 4 marks ]

o Describe your use of randomisation. (Hint: why would it not be good to do all the throws for one level first, followed by all the throws for the next level, etc.?) How did you mix up the order of throws so as to be fair to all the levels? If you used randomisation, how did you generate the random order? Attach a listing of the order in which you carried out the throws, as an appendix to your report. [ 3 marks ]

• Comment on any practical difficulties you encountered, and changes you would make to your experimental design if you were going to repeat this task. [2 marks ]

Attach a copy of your data to your report as an appendix. Keep an electronic copy of the data for use in Assignment 2. [ 1 marks ]

Part C: Data analysis [14 marks] Use Minitab (or Minitab Express) and incorporate the output into your report.

1. Data entry and simple descriptive analysis [10 marks] • Draw side-by-side dot plots and boxplots of your numerical variable to compare the levels of the categorical variable. (note side-by-side means all levels on the same graph, not separate graphs). [3 marks for the plots + this will be taken as evidence of data entry 3 marks]

• For each level of your categorical variable, produce numerical summaries of the numerical variable. Include the sample size, mean, standard deviation and the five number summary. [2 marks]

• Summarize the important features of your data, as shown by your graphs and numerical summaries. [2 marks]

2. Confidence intervals [4 marks] (These should be covered in week 7) • For each level of your categorical variable, produce a 95% confidence interval for the mean of your numeric variable.

• Interpret the confidence intervals in the context of your research question, by completing the following sentence for each level of your categorical variable:

We are 95% confident that the …

Part D: Discussion and Conclusion [3 marks]

Discuss what your experiment and analysis tells you about your research question.

Presentation [3 marks] Your report length should be no more than six pages including graphics but excluding the data and a list showing the order of throws.

1 mark for staying within the 6 page limit (excluding raw data and throw order) 1 mark for readability/flow, and spelling/grammar 1 mark for overall effective presentation (NOT for prettiness!)