Chi-Square Test for Goodness of Fit
In the ancient game of Rock, Paper, Scissors, each player simultaneously throws a sign and the winner is determined on the basis that rock destroys scissors, scissors cuts paper, and paper covers rock. One might well assume that the best strategy is to throw signs entirely at random and unpredictably, because if your opponents can guess which sign you’re more likely to throw, they will beat you the majority of the time. So is that what players actually do? Suppose we observe a group of 75 children playing RPS on the playground and we record the number of throws of each sign on an arbitrarily-selected trial. Those data are simulated in the data set, rps.csv. Before analyzing the data using a chi-square goodness of fit test, what do you think the expected frequencies of each sign should be?
(1) Download rps.csv and open it in Jamovi.
(2) Make sure the measure type and data type are correct.
(3) From the Frequencies menu select N Outcomes/Χ2 Goodness of fit.
(4) Move Sign into the Variable box. Jamovi automatically assumes that the expected proportion for each sign is .333, which you can see by opening the Expected Proportions menu.
(5) Check Expected counts.
(6) Save the Jamovi file as YourLastName_rps.omv and use it to answer the questions on the worksheet.
Chi-Square Test for Independence
Danielle Navarro tells the story of:
… watching an animated documentary examining the quaint customs of the natives of the planet Chapek 9. Apparently, in order to gain access to their capital city a visitor must prove that they’re a robot, not a human. In order to determine whether or not a visitor is human, the natives ask whether the visitor prefers puppies, flowers, or large, properly formatted data files. “Pretty clever,” I thought to myself “but what if humans and robots have the same preferences? That probably wouldn’t be a very good test then, would it?” As it happens, I got my hands on the testing data that the civil authorities of Chapek 9 used to check this. It turns out that what they did was very simple. They found a bunch of robots and a bunch of humans and asked them what they preferred. I saved their data in a file called chapek9.csv …. In total there are 180 entries in the data set, one for each person (counting both robots and humans as “people”) who was asked to make a choice.
So if there are reliable differences between how robots and humans answer this question, then the question may be useful for deciding who can enter the city. We can conduct a chi-square test of independence to evaluate the extent to which the categories of species and type of answer are independent.
(7) Download chapek9.csv and open it in Jamovi.
(8) Make sure the measure type and data type are correct for the two variables.
(9) From the Frequencies menu select Independent Samples/Χ2 test of association.
(10) Move species into the Rows box and choice into the Columns box.
(11) Open the Statistics tab and from the Tests menu select Χ2.
(12) From the Hypothesis menu select Group 1 ≠ Group 2.
(13) From the Nominal menu select Phi and Cramer’s V.
(14) Open the Cells tab and from the Counts menu select Observed counts and Expected counts.
(15) Save the Jamovi file as YourLastName_chapek9.omv and use it to answer the questions on the worksheet.
Instructions for submitting this assignment.
(1) Locate YourLastName_rps.omv, YourLastName_chapek9.omv, and Ch15 Homework.docx where you saved them on your computer.
(2) Click the title of this assignment (Ch15 Homework) to open the Upload Assignment page.
(3) In the ASSIGNMENT SUBMISSION section, attach YourLastName_rps.omv, YourLastName_chapek9.omv, and Ch15 Homework.docx. Click Submit.
(4) If you submit this assignment early enough, I might have time to provide feedback that you can use to improve it and possibly improve your grade. So soon after you submit it, return to this assignment to see if I’ve given you any feedback. Click the assignment title and on the Review Submission History page you’ll see the details of your prior submissions. To revise a prior submission, click Start New, download and revise, be sure to save it, and upload it as previously.
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