Title: Assignment: Mini Project 1
Course: PSYC 301 Statistical Methods in Psychol

For this project you will essentially do the work done for the OA2, but at a more formal level also using some techniques learned in OA3. You will write a very short report that will answer a set of questions indicated below that are intended to explore the hypothesis statement below. You will write your response to the questions in a Word document that you submit for this assignment. Write the report as if you are responding to a committee who asked you to find statistical answers to these questions.

You will be looking at the data I acquired for analyzing the decision making of referees in soccer matches in Major League Soccer. You will be looking at the data to determine if there is evidence to support these two hypotheses:

1) Red cards become more likely in the closing minutes of a soccer match.

2) Yellow cards do not become more likely in the closing minutes.

We have to define a few things:

A Red card is given for very serious violations of standards and rules in the game and result in an immediate removal from the game and suspension for the next league game. Yellow cards are a warning that more bad behavior will result in a red card.

Closing Minutes is defined as the last 20 minutes of a match. Soccer matches are 90 minutes long and the clock counts upward from zero to 45 for the first half and from 45 to 90 for the second half. Because soccer matches can run longer than the 'clock time' you can see cards given past the 45th minute of the first half and the 90th minute of the end of the match. But, those are comparatively rare.

Data File: MP1Cards is a jamovi file. Click to download.

The data file consists of nearly 20,000 yellow and red cards issued against MLS players from 1996 through the 2018. It has the following columns with the following definitions:

    - Color is indicating the color of the card issued by the referee to sanction the player with levels of Yellow and Red (see above).
    - Minute is the time in the game in which the card was given.
    - Year is the league season in which the game occurred. (only relevance is for describing the data used)

There are numerous ways to examine this data to attempt to find evidence consistent with the above hypothesis. Below is one, but you are free to use other methods, but correctness in whatever method you choose will be taken into account in grading.

1. Open the data file in jamovi
2. There are about 1000 cards for which no Year is indicated, we should filter them out. Hint, this should be done using the technique from OA3. Furthermore to filter out 'missing' data you can type a single quote twice with no space between ('') not a double quote ("). The single quote typed twice in succession means 'nothing there'. You are filtering out cases based on the variable Year not having data.
3. As before, we will be using the Descriptives options from the Explorations button. Put Minute into the Variables box.
4. For Statistics, click on Mode, Median, Mean, N, Std. deviation, and under plots select Histogram. De-select everything else. Note the value for Mode, Median, and Mean.
5. Read in your textbook about skewness in section 4.3.
6. Answer this question as the first thing in your report: What kind of skewness, if any, does this histogram display?
7. Put Color in the Split by box.
8. Interpret: You now have means, medians, and modes for when the yellow cards were given and when the red cards were given. You'll see the standard deviations are very similar, so that is not an issue. You also have comparable histograms for when each kind of card was given. Using all that information, interpret the data summaries in terms of the hypothesis given above. Which of your various sources of information are supportive of the hypothesis? Which are not supportive of the hypothesis? And, in the end, are you persuaded by the data that they hypothesis is supported or not supported?  Note: relative sample size (N) for each group is meaningless for any of these interpretations.
9. Write all of that up in a Word document that also includes the 'split by' plot pasted into it in an appropriate place. You should include a table that shows the statistics used in your discussion, including N, each line being a statistic, each column being a card color.
10. Submit the Word document.

This will be graded based on completeness, accuracy, and quality of describing the findings directly and clearly.