Lab 2A - All About Distributions

Lab 2A - All About Distributions

Directions: Follow along with the slides and answer the questions in bold 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.