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 and write down 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 are smaller than Q1, 75% are larger.
  • 75% of our data are smaller than Q3, 25% 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 and write down 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 for your predominant color 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 a previous slide that the range function calculates the maximum and minimum values for a variable, but not the difference between them.
• We could calulate 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 and write down 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 capital ‘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.