All About Distributions

Lab 2A

Directions: Follow along with the slides and answer the questions in red font in your journal.

• Most of the labs thus far have covered how to visualize, summarize, and manipulate data.
  • We used visualizations to explore how your class spends their time.
  • We also learned how to clean data to prepare it for analyzing.
• Starting with this lab, we'll learn to use R to answer statistical questions that can be answered by calculating the mean, median and MAD.

• When we make plots of our data, we usually want to know:
  • Where is the bulk of the data?
  • Where is the data more sparse, or thin?
  • What values are typical?
  • How much does the data vary?
• To answer these questions, we want to look at the distribution of our data.
  • We describe distributions by talking about where the center of the data are, how spread out the data are, and what sort of shape the data has.

• Export, upload and import your class' Personality Color data.
  • Name your data colors when you load it.
• Before analyzing a new data set, it's often helpful to get familiar with it. So:
  • Write down the names of the 4 variables that contain the point-totals, or scores, for each personality color.
  • Write down the names of the variables that tell us an observation's introvert/extrovert designation and whether they participated in playing sports.
  • How many variables are in the data set?
  • How many observations are in the data set?

• Create a dotPlot of the scores for your predominant color.
  • Pro-tip: If the dotPlot comes out looking wonky, try changing the value of the character expansion argument, cex.
  • The default value is 1. Try a few values between 0 and 1 and a few more values larger than 1.
• Based on your dotPlot:
  • Which values came up the most frequently? About how many people in your class had a score similar to yours?
  • What, would you say, was a typical score for a person in your class for your predominant color? How does your own score for this color compare?

• Means and medians are usually good ways to describe the typical value of our data.
• Fill in the blank to calculate the mean value of your predominant color score:

mean(~____, data = colors)

• Use a similar line of code to calculate the median value of your predominant color.
  • Are the mean and median roughly the same? If not, use the dotPlot you made in the last slide to describe why.

• Make a dotPlot of your predominant color again; but this time, facet the plot based on the introvert/extrovert variable.
• Use a line of code, using similar syntax to how you facet plots, to calculate a value that describes the center of your predominant color for introverts and extroverts.
  • Do introverts or extroverts differ in their typical scores for your predominant color? Answer this statistical question using your dotPlot.
• Assign the mean values a name. Then place the name into the diff() function to calculate the difference. How much more/less did introverts/extroverts score over the other for your predominant color?

• Now that we know how to describe our data's typical value we might also like to describe how closely the rest of the data are to this typical value.
  • We often refer to this as the variability of the data.
  • Variability is seen in a histogram or dotPlot as the horizontal spread.
• Look at the spread of the dotPlot you made for your predominant color then fill in the blank:

Data points in my plot will usually fall within ____ units of the center.

• Which group (introverts and extroverts), if either, seem to have values that are more spread out from the center?

• The mean absolute deviation finds how far away, on average, the data are from the mean.
  • We often write mean absolute deviation as MAD.
• Calculate the MAD of your predominant color by filling in the blanks:

MAD(~_____, data = colors)

• Based on the MAD, which group (introverts or extroverts) has more variability for your predominant color's scores?
  • Does this match the answer you gave for the last question in the previous slide?

• Do introverts and extroverts in your class differ in their color scores?
  • Perform an analysis that produces numerical summaries and graphs.
  • Then, write a few sentence interpretations that addresses this statistical question and considers the shape, center and spread of the distributions of the graphs you create.