Statisitical Experimental Design Question

All questions can be done in theory. You do not need to build paper helicopters.

Context:
A researcher would like to investigate how long a paper “helicopter” can stay in the air, where the helicopter is dropped from a height of 2 meters. Here is how she makes the paper helicopters (see the figure below for an example) to be used for the experiment.

Some potential treatment factors are:
1) Paper type (light, medium, and heavy);
2) Rotor length (7.5cm or 8.5cm);
3) Leg length (7.5cm or 12 cm);
4) Leg width (3.2cm or 5cm).

Questions:
(a) Suppose the researcher would like to compare the response between different paper types while keeping other factors fixed.
What are the experimental units?

What are the measurement units?

Which experiment design she can apply?


(b) Suppose the researcher would like to conduct an experiment using 15 paper helicopters, explain how she can perform the randomization and replication procedures here.

(c) Think of a situation that the researcher would need to consider a RCBD.

(d) If the researcher wants to study what effects that the leg length and width have on the flying time of heavy paper helicopters, which design is most appropriate for this situation? If the researcher wanted to have 5 replicates for each treatment combination, how many heavy paper helicopters does she need?

Word Problem Statistics
Fannypack Fannypack
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Answer

A)
The experimental units are simply the paper helicopters (with the same dimensions). The treatments are the types of paper used on these helicopters.

The measurement unit is seconds (or any other time measurement); the time it takes for the helicopter to descend. (Measurement of the response variable, that is)

A simple randomized design is used, such as the order in which the descents are made are randomly chosen among the three types.

B)
Assuming she still wants to investigate the effects of paper type, then she should have 5 paper helicopters of each paper type (with same dimensions)
To randomize, she could assign each of the 15 paper helicopter with a number, and then perform the experiment in a randomized order of numbers 1 to 15.
There is replication for each paper type (5 for each type) and these are all used in the experiment, according to the randomized order.

C)
A randomized controlled block design would be if she were to measure the effect of changing a dimension, across paper types.
Suppose she wanted to see the effect in changing the rotor length.
She could block the experiment by paper type.
Within light paper type, she would (for example) have 3 planes with 7.5 cm rotor length, and 3 planes with 8.5 cm rotor length.
Within medium paper type, she would have 3 planes with 7.5cm rotor length, and 3 planes with 8.5cm rotor length.
Same with heavy paper type.

It's controlling for paper type: it's isolating the effect of paper type, only to focus on the effect of rotor length.
Randomization similar to suggestion in part B.
This would not be limited to rotor length, but also the other dimensions.

D)
A factorial design is appropriate. There are 4 treatment combinations: (in order of length, width)
(7.5, 3.2) (7.5, 5) (12, 3.2) (12, 5)
So 5 replicates of each, would mean 5 x 4 = 20 planes.

Matchmaticians Alumnus Matchmaticians Alumnus
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  • Fannypack Fannypack
    0

    Thank you. It was mainly C and D I was stuck on. I did get a different answer for a though as the definition of measurement unit is defined as a group of units that must have the same treatment. Initially what you put was what I had as well and then my teacher defined it this way. I tried looking for better descriptions and couldn't. Since the only factor that changed was paper weight I put all of the other factors as measurement units. I gave you credit regardless.

The answer is accepted.
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