Lab 2B - Oh the Summaries ...

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

Just the beginning

Means, medians,and MAD are just a few examples of numerical summaries.
In this lab, we will learn how to calculate and interpret additional summaries of distributions such as: minimums, maximums, ranges, quartiles and IQRs.

– We'll also learn how to write our first custom function!
Start by loading your Personality Color data again and name it colors.

Extreme values

Besides looking at typical values, sometimes we want to see extreme values, like the smallest and largest values.

– To find these values, we can use the min, max or range functions. These functions use a similar syntax as the mean function.
Find the min value and max value for your predominant color.
Apply the range function to your predominant color and describe the output.

– The range of a variable is the difference between a variable’s smallest and largest value.

– Notice, however, that our range function calculates the maximum and minimum values for a variable, but not the difference between them.

– Later in this lab you will create a custom Range function that will calculate the difference.

Quartiles (Q1 & Q3)

The median of our data is the value that splits our data in half.

– Half of our data is smaller than the median, half is larger.
Q1 and Q3 are similar.

– 25% of our data is smaller than Q1, 75% are larger.
Fill in the blanks to compute the value of Q1 for your predominant color.
```
quantile(~____, data = ____, p = 0.25)
```
Use a similar line of code to calculate Q3, which is the value that's larger than 75% of our data.

The Inter-Quartile-Range (IQR)

Make a dotPlot of your predominant color's scores. Make sure to include the nint option.
Visually (Don't worry about being super-precise):

– Cut the distribution into quarters so the number of data points is equal for each piece. (Each piece should contain 25% of the data.)
- Hint: You might consider using the add_line(vline = ) to add vertical lines at the quarter marks.
– Write down the numbers that split the data up into these 4 pieces.

– How long is the interval of the middle two pieces?

– This length is the IQR.

Calculating the IQR

The IQR is another way to describe spread.

– It describes how wide or narrow the middle 50% of our data are.
Just like we used the min and max to compute the range, we can also use the 1st and 3rd quartiles to compute the IQR.
Use the values of Q1 and Q3 you calculated previously and find the IQR by hand.

– Then use the iqr() function to calculate it for you.
Which personality color score has the widest spread according to the IQR? Which is narrowest?

Boxplots

By using the medians, quartiles, and min/max, we can construct a new single variable plot called the box and whisker plot, often shortened to just boxplot.
By showing someone a dotPlot, how would you teach them to make a boxplot? Write out your explanation in a series of steps for the person to use.

– Use the steps you write to create a sketch of a boxplot for your predominant color's scores in your journal.

– Then use the bwplot function to create a boxplot using R.

Our favorite summaries

In the past two labs, we've learned how to calculate numerous numerical summaries.

– Computing lots of different summaries can be tedious.
Fill in the blanks below to compute some of our favorite summaries for your predominant color all at once.
```
favstats(~____, data=colors)
```

Calculating a range value

We saw in the previous slide that the range function calculates the maximum and minimum values for a variable, but not the difference between them.
We could calculate this difference in two steps:

– Step 1: Use the range function to assign the max and min values of a variable the name values. This will store the output from the range function in the environment pane.
```
values <- range(~____, data=colors)
```
– Step 2: Use the diff function to calculate the difference of values. The input for the diff function needs to be a vector containig two numeric values.
```
diff(values)
```
Use these two steps to calculate the range of your predominant color.

Introducing custom functions

Calculating the range of many variables can be tedious if we have to keep performing the same two steps over and over.

– We can combine these two steps into one by writing our own custom function.
Custom functions can be used to combine a task that would normally take many steps to compute and simplify them into one.
The next slide shows an example of how we can create a custom function called mm_diff to calculate the absolute difference between the mean and median value of a variable in our data.

Example function

mm_diff <- function(variable, data) {
  mean_val <- mean(variable, data = data)
  med_val <- median(variable, data = data)
  abs(mean_val - med_val)
}

The function takes two generic arguments: variable and data
It then follows the steps between the curly braces { }

– Each of the generic arguments is used inside the mean and median functions.
Copy and paste the code above into an R script and run it.
The mm_diff function will appear in your Environment pane.

Using mm_diff()

After running the code used to create the function, we can use it just like we would any other numerical summary.

– In the console, fill in the blanks below to calculate the absolute difference between the mean and median values of your predominant color:
```
____(~____, data = ____)
```
Which of the four colors has the largest absolute difference between the mean and median values?

– By examining a dotPlot for this personality color, make an argument why either the mean or median would be the better description of the center of the data.

Our first function

Using the previous example as a guide, create a function called Range (Note the capial 'R') that calculates the range of a variable by filling in the blanks below:
```
____ <- function (____, ____) {
  values <- range(____, data = ____)
  diff(___)
}
```
Use the Range function to find the personality color with the largest difference between the max and min values.

On your own

Create a function called myIQR that uses the quantile function to compute the middle 30% of the data.