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PSTAT 122
Project Description

Please choose from one of the following options:

1) Randomized Complete Block Design (RCBD) or Generalized Randomized Block Design (GRBD)

In this option, you will design and implement an experimental study with one primary factor of interest and one blocking variable. Here are two possible suggestions:

i) Paper Airplanes RCBD

In this option, similar to Lab 2, you will investigate the impact of a paperclip on how far the paper airplane flies. However, here your factor of interest will contain more than just 2 levels; they will be:

Your paper airplanes should all be of the same design. The outcome of interest is how far the airplane flies when you throw it.

Create an online survey via any platform of your choosing such as Google Forms that you will distribute to fellow UCSB undergraduate students. Your survey will primarily consist of ONE statement on a potentiallycontroversial topic (i.e.  political, something about campus, etc), and your factor of interest will be the specific wording of the statement. Your outcome of interest will be a score from 0 to 10 indicating the respondent’s degree of agreement with the statement.

Your blocking variable will be the class standing of the student. You may choose to keep it only to traditional Freshmen/Sophomores/Juniors/Seniors, or you may make it more flexible. Either way, the only other question in your survey will be the class standing of the student.

How you distribute your survey is up to you; for example, you may email it to individuals or to a group email list, or you may post it on your social media account, or a combination of these two; if you are distributing different links for each version of the statement, you will need to have a way to do this randomly. Your report should discuss the implications of how you distributed your survey in terms of whether you have truly obtained a random sample or not, and how this might impact your results.

Unlike in the RCBD, you will potentially have many replicates within each block. You just need to make sure that you have each treatment group represented at least once in each block, but potentially many more times depending on your sample size calculations.

You may also design your own RCBD or GRBD experiment. It must have one factor of interest with at least 3 levels, and one blocking variable with at least 3 blocks. You may also choose one of the above options but modify it in any way to your liking as long as it is still a RCBD or GRBD with the required number of levels and blocks. If you choose to design your own RCBD or GRBD or make modifications to the above suggestions, you must submit a brief description of your plan to Canvas by Monday Nov 11 so that we can ensure that it is a proper design and that it will be feasible in the time that you have before the deadline.

2) Full Factorial Design

In this option, you will design and implement a study with at least two primary factors of interest. Here are

That is, you could potentially have 2 or 3 paper clips on the airplane in any given replicate, unlike in the RCBD in which you will always have at most 1 paper clip on the airplane.

The outcome of interest is again how far the airplane flies when you throw it. Your experiment should have multiple replicates, with the number of replicates determined by a sample size calculation which may utilize your results from Lab 2 as a pilot study.

Obtain a sample of multiple cans or bottles of any brand of soda (to be more economical, you might want to try to find a large pack of the smallest individual size possible). The number of cans/bottles that you obtain may be guided by your sample size calculations. The question at hand here is whether two factors of interest have any impact on the enjoyment (taste or otherwise) of drinking the soda.

The factors of interest are:

• Method of pouring:

– Down the side of the glass

– Straight onto the center of a glass

– Leave it in the can/bottle

• Method of consumption:

– Via a straw

– Straight from the container

• 2 factors with at least one of the factors having at least 3 levels
• 3 or more factors, in which case each factor may have only 2 levels (but more is also just fine)

You may also choose one of the above options but modify it in any way to your liking as long as it is still factorial design with the required number of factors and levels. If you choose to design your own factorial experiment, you must submit a brief description of your plan to Canvas by Monday Nov 11 so that we can ensure that it is a proper design and that it will be feasible in the time that you have before the deadline.

In this option, you will design and implement a simulation study in which you will investigate the implications of modeling assumptions not being met. Specifically, your simulation study should investigate scenarios in which the data are simulated according to each of the following factors:

Your overall task is to compare the performance of standard ANOVA to the permutation test, under all of the combinations of factors that you choose. Specifically, on page 72 of our textbook, it states that while ANOVA is relatively robust to violations in the equal variances assumption, it is much more sensitive to it in unbalanced designs. The goal of this simulation study is to investigate and characterize that, and determine if and when the permutation test does better. Performance should be defined as the probability of making a Type I Error and statistical power, as appropriate.

You may keep the number of groups constant and you may use any overall distribution of your choosing throughout all of your simulations (e.g. normal, gamma, etc); otherwise, each of the above factors must have at least 3 levels (more might be necessary to make your point). You should choose your factor levels such that they clearly demonstrate an overall  message; this may require some exploration beyond what you wouldactually present in your final report.

While you can run initial experiments at lower repetitions/iterations as you investigate, in your final report your permutation test should be run with at least 10,000 repetitions, and your Type I Error probabilities and power should be estimated with at least 1,000 iterations. You can expect it to take an extremely long time to run all of your required simulations at this level (perhaps multiple days running overnight); you will want to plan ahead! It will be best if your simulations are written in a script file, which then saves your ，output to an RData file, and then your Rmd file reads in the RData file; it will be overly cumbersome to write simulations of this magnitude in an Rmd file. If you do not know what all of this means, this project option is probably not a wise choice.

A grading rubric and a skeleton project example that highlights the expectations of your report will be made available by Friday Nov 15.