All About Distributions

Lab 2A

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

In the beginning ...

  • 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.

How to talk about data

  • 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.

Let's begin!

  • 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 birth gender and whether they participated in playing sports.
    • How many variables are in the data set?
    • How many observations are in the data set?

Estimating centers

  • 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

  • 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.

Comparing birth_genders

  • Make a dotPlot of your predominant color again; but this time, facet the plot based on gender.
  • Use a line of code, using similar syntax to how you facet plots, to calculate a value that describes the center of each birth gender.
    • Do males and females 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 one birth gender score over the other for your predominant color?

Estimating Spread

  • 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 birth gender, if either, seem to have values that are more spread out from the center?

Mean Absolute Deviation

  • 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 birth gender has more variability for your predominant color's scores?
    • Does this match the answer you gave for the last question in the previous slide?

On your own

  • Do boys and girls 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.