Research Design, Research Ethics, and Evidence of Causation

Learning Objectives

• Compare categories with graphs and numbers.
• Interpret boxplots, crosstabs, and comparisons of means.
• Apply the rule of direction to interpret relationships.

Comparing Categories

We’re interested in how one variable differs across categories of another.

• Example: Do people who vote differ from those who don’t in terms of education?
• We’ll look at:
  • Boxplots
  • Crosstabs
  • Means

Boxplots

Great for comparing a quantitative variable across categories.

Boxplots: Example Interpretation

• Which class has the highest median highway MPG?

• Which has the widest IQR?

• Are there outliers?

Crosstabs

Compare two categorical variables.

 
   Cell Contents
|-------------------------|
|                       N |
| Chi-square contribution |
|           N / Row Total |
|-------------------------|

 
Total Observations in Table:  234 

 
             | suv_df$is_suv 
  suv_df$drv |   Not SUV |       SUV | Row Total | 
-------------|-----------|-----------|-----------|
           4 |        52 |        51 |       103 | 
             |     7.425 |    20.598 |           | 
             |     0.505 |     0.495 |     0.440 | 
-------------|-----------|-----------|-----------|
           f |       106 |         0 |       106 | 
             |    10.124 |    28.085 |           | 
             |     1.000 |     0.000 |     0.453 | 
-------------|-----------|-----------|-----------|
           r |        14 |        11 |        25 | 
             |     1.042 |     2.891 |           | 
             |     0.560 |     0.440 |     0.107 | 
-------------|-----------|-----------|-----------|
Column Total |       172 |        62 |       234 | 
-------------|-----------|-----------|-----------|

 

Crosstab: Example Interpretation

• Among front-wheel drive vehicles, what % are SUVs?

• Among rear-wheel drive vehicles?

• Is SUV-ness associated with drive type?

Comparing Means

Compare the mean of a quantitative DV across categories of a categorical IV.

# A tibble: 7 × 2
  class      mean_hwy
  <chr>         <dbl>
1 compact        28.3
2 subcompact     28.1
3 midsize        27.3
4 2seater        24.8
5 minivan        22.4
6 suv            18.1
7 pickup         16.9

Mean Comparison: Interpretation

• Which class has the highest average MPG?

• Is the difference between compact and midsize vehicles large?

• Any surprises?

The Rule of Direction

To describe relationships: Start with the category of the IV that is “more of something.”

• Example: “People with more education are more likely to vote.”

This applies across boxplots, crosstabs, and means.

Summary

• Use boxplots to visualize distribution across groups.

• Use crosstabs for two categorical variables.

• Use means to summarize quantitative outcomes by group.

• Rule of direction helps make clear comparisons.