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Lab 1G: What’s the FREQ?

Lab 1G - What's the FREQ?

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

Clean it up!

  • In Lab 1F, we saw how we could clean data to make it easier to use and analyze.

    – You cleaned a small set of variables from the American Time Use (ATU) survey.

    – The process of cleaning and then analyzing data is very common in Data Science.

  • In this lab, we'll learn how we can create frequency tables to detect relationships between categorical variables.

    – For the sake of consistency, rather than using the data that you cleaned, you will use the pre-loaded ATU data.

    – Use the data() function to load the atu_clean data file to use in this lab.

How do we summarize categorical variables?

  • When we're dealing with categorical variables, we can't just calculate an average to describe a typical value.

    – (Honestly, what's the average of categories orange, apple and banana, for instance?)

  • When trying to describe categorical variables with numbers, we calculate frequency tables

Frequency tables?

  • When it comes to categories, about all you can do is count or tally how often each category comes up in the data.

  • Fill in the blanks below to answer the following: How many more females than males are there in our ATU data?

    tally(~ ____, data = ____)

2-way Frequency Tables

  • Counting the categories of a single variable is nice, but often times we want to make comparisons.

  • For example, what if we wanted to answer the question:

    Does one gender seem to have a higher occurrence of physical challenges than the other? If so, which one and explain your reasoning?

  • We could use the following plot to try and answer this question:

    bargraph(~phys_challenge | gender, data = atu_clean)

  • The split bargraph helps us get an idea of the answer to the question, but we need to provide precise values.

  • Use a line of code, that’s similar to how we facet plots, to obtain a tally of the number of people with physical challenges and their genders.

Interpreting 2-way frequency tables

  • Recall that there were 1153 more women than men in our data set.

    – If there are more women, then we might expect women to have more physical challenges (compared to men).

  • Instead of using counts we use percentages.

  • Include: format = "percent" as an option to the code you used to make your 2-way frequency table. Then answer this question again:

    Does one gender seem to have a higher occurrence of physical challenges than the other? If so, which one and explain your reasoning?

    Did your answer change from before? Why?

  • It’s often helpful to display totals in our 2-way frequency tables.

    – To include them, include margins = TRUE as an option in the tally function.

Conditional Relative Frequencies

  • There is as difference between phys_challenge | gender and gender | phys_challenge.

    tally(~phys_challenge | gender, data = atu_clean, margin = TRUE)
    ##                 gender
    ## phys_challenge   Male Female
    ##   No difficulty  4140   5048
    ##   Has difficulty  530    775
    ##   Total          4670   5823
    tally(~gender | phys_challenge, data = atu_clean, margin = TRUE)
    ##         phys_challenge
    ## gender   No difficulty Has difficulty
    ##   Male            4140            530
    ##   Female          5048            775
    ##   Total           9188           1305
  • At first glance, the two-way frequency tables might look similar (especially when the margin option is excluded). Notice, however, that the totals are different.

  • The totals are telling us that R calculates conditional frequencies by column!

  • What does this mean?

    – In the first two-way frequency table the groups being compared are Male and Female on the distribution of physical challenges.

    – In the second two-way frequency table the groups being compared are the people with No difficulty and those that Has difficulty on the distribution of gender.

  • Add the option format = "percent" to the first tally function. How were the percents calculated? Interpret what they mean.

On your own

  • Describe what happens if you create a 2-way frequency table with a numerical variable and a categorical variable.

  • How are the types of statistical questions that 2-way frequency tables can answer different than 1-way frequency tables?

  • Which gender has a higher rate of part time employment?