Lab 2A - All About Distributions

Directions: Follow along with the slides, completing the questions in blue on your computer, and answering the questions in red 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 investigative 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's Personality Color data.

– Name your data colors when you load it.
Before analyzing a new dataset, 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 are involved in sports.

– How many variables are in the dataset?

– How many observations are in the dataset?

Estimating centers

Create a dotPlot of the scores for your predominant color.

– Pro-tip: If the dotPlot comes out looking wonky, include the nint and cex options.
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.

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.
Re-create a dotPlot of the scores for your predominant color and then run the code below filling in the blank with the name of your predominant color:
```
add_line(vline = mean(~____, data = colors))
```
Look at the spread of the scores from the mean score then complete the sentence below:

Data points in my plot will usually fall within units of 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)
```
How close was your estimate of the spread for your predominant color (from the previous slide) to the actual value?

Comparing introverts/extroverts

Do introverts and extroverts differ in their typical scores for your predominant color?

– Answer this investigative question using a dotPlot and numerical summaries.
Make a dotPlot of your predominant color again; but this time, facet the plot by the introvert/extrovert variable. Include the layout option to stack the plots as well as the nint and cex options.
Describe the shape of the distribution of scores for the extroverts. Do the same for the introverts.
Using similar syntax to how you facet plots, calculate either the mean or median to describe the center of your predominant color for introverts and extroverts.
Do introverts and extroverts differ in their typical scores for your predominant color?
Based on the MAD, which group (introverts or extroverts) has more variability for your predominant color’s scores?

On your own

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 investigative question and considers the shape, center and spread of the distributions of the graphs you create.