HW 05: Describing Relationships

Exploring Associations between two variables

Purpose

To fully explore the relationship between two variables both summary statistics and visualizations are important.

Instructions

Right click and download this template, then put it into your Homework folder.

For this assignment you will describe the relationship between these four specific combinations of data types:

  • Categorical response and categorical explanatory variable. (C ~ C)
  • Quantitative response and categorical explanatory variable. (Q ~ C)
  • Any combination of the above with a binary variable (B ~ C, C ~ B, or Q ~ B)
  • Quantitative response and quantitative explanatory variable. (Q ~ Q)

Before you start,

Determine what variables you want to graph based on your research topic.

  • You will need a mixture of categorical and quantitative variables for this assignment.
  • You should use variables that are relevant to your research topic.
  • If you have not yet identified both a quantitative (Q), a binary (B), and a categorical (C) variable that you are interested in, now is the time to go back to the codebook and figure this out.

If you do not already have a binary variable in your clean data you can either a) go back and edit your dm file to include a binary variable, or b) dichotomize one of your categorical variables into two levels. (Make a new variable, don’t overwrite your categorical variable).

For each bivariate relationship under consideration you will do the following:

  1. Name and explain the two variables under consideration.

  2. Create the appropriate graphic for bivariate relationship under consideration. For these plots binary variables are treated as categorical variables with only 2 levels.

    • C ~ C: Side by side barplot
    • Q ~ C: Paneled histogram with density overlaid, or a grouped boxplot with overlaid violin plot.
    • Q ~ Q: Scatterplot. Add both lowess and linear trend lines.

  3. Calculate appropriate grouped summary statistics

    • For continuous outcomes you’ll want to describe measures including the sample size, mean, median, range and variance for each level of the categorical variable.
    • For categorical outcomes you’ll want to calculate %’s of your outcome measurement across levels of your covariate. Create an appropriate table using tbl_summary
      • i.e. proportion of males who are smokers compared to proportion of females who are smokers
      • or proportion of smokers who are male, compared to proportion of non-smokers who are male.

  4. Explain the relationship or trends you see in the data in a summary paragraph. Put this paragraph below the graphic.

    • Use summary statistics in your text explanation.
    • Use specific features of the graphic in your text explanation.
      • i.e. are there outliers only in one group?
      • Do the data seem clumped or clustered in one region of the scatterplot?
      • Is there a linear or non-linear pattern?
      • Does one combination of categorical levels (C~C) seem to hold most the data?
      • Are there any outlying data points? Don’t list off each one, just state if there is and where approximately it’s at.

Submission instructions

  • Upload your PDF to Canvas by the due date.

Example

library(tidyverse); library(ggdist)
library(sjPlot); library(gtsummary)

pen <- palmerpenguins::penguins

C ~ C Association

This example explores the association between the species of the penguin and the year it was measured. I specifically want to compare the percent of each species type across years

pen %>% select(year, species) %>%
  tbl_summary(by = "year")
Characteristic 2007
N = 1101		 2008
N = 1141		 2009
N = 1201
species


    Adelie 50 (45%) 50 (44%) 52 (43%)
    Chinstrap 26 (24%) 18 (16%) 24 (20%)
    Gentoo 34 (31%) 46 (40%) 44 (37%)
1 n (%) 
plot_xtab(x=pen$year, grp=pen$species, show.total=FALSE, margin='row')

The amount of Adelie penguins sampled each year is pretty consistent, 45.5% (n=50) in 2007, 43.9% (n=50) in 2008, and 43.3% (n=52) in 2009. 2008 saw the highest proportion of Gentoo penguins sampled (40.4%, n=46) and correspondingly lowest proportion of Chinstrap (15.8%, n=18).

Q ~ C Association

This example explores the association between the depth of a penguins bill and the species of the penguin. The quantitative response variable is bill depth in mm (bill_depth_mm) and the categorical explanatory variable is species (species).

ggplot(pen, aes(x=bill_depth_mm, y=species, fill=species)) + 
      stat_slab(alpha=.5, justification = 0) + 
      geom_boxplot(width = .2,  outlier.shape = NA) + 
      geom_jitter(alpha = 0.5, height = 0.05) +
      stat_summary(fun="mean", geom="point", col="red", size=4, pch=17) + 
      theme_bw() + 
      labs(x="Bill depth (mm)", y = "Species") + 
      theme(legend.position = "none")

Calculate summary statistics - option 1: dplyr group_by/summarize

pen %>% group_by(species) %>% 
  summarize(n=n(), 
            mean = mean(bill_depth_mm, na.rm = TRUE), 
            median = median(bill_depth_mm, na.rm = TRUE), 
            sd = sd(bill_depth_mm, na.rm = TRUE), 
            IQR = IQR(bill_depth_mm, na.rm = TRUE)) %>%
  knitr::kable(digits=2) # for nice table format printing
species n mean median sd IQR
Adelie 152 18.35 18.40 1.22 1.5
Chinstrap 68 18.42 18.45 1.14 1.9
Gentoo 124 14.98 15.00 0.98 1.5

Option 2: grouped tbl_summary

tbl_summary(pen, 
            include = "bill_depth_mm", 
            by = "species", 
            statistic = list(
              all_continuous() ~ "{mean} ({sd})"
    ))
Characteristic Adelie
N = 1521		 Chinstrap
N = 681		 Gentoo
N = 1241
bill_depth_mm 18.35 (1.22) 18.42 (1.14) 14.98 (0.98)
    Unknown 1 0 1
1 Mean (SD)

Got LOTS of categories? See the help page for an alternative view.

The distribution of bill depth are fairly normal for each species, with some higher end values causing a slight right skew for Adelie and Gentoo. Gentoo penguins have lower average bill depth compared to Adelie or Chinstrap (15.0mm vs 18.3 and 18.4mm respectively). Chinstrap however have a larger IQR at 1.9 compared to 1.5 for the others.

Q ~ Q Association

This example explores the association between the length of a penguins flipper and it’s body mass. The quantitative response variable is body mass(body_mass_g) and the quantitative explanatory variable is flipper length (flipper_length_mm).

cor(pen$flipper_length_mm, pen$body_mass_g, 
    use="pairwise.complete.obs") # calculate the correlation
[1] 0.8712018
ggplot(pen, aes(x=flipper_length_mm, y=body_mass_g)) + geom_point() + 
  geom_smooth(se=FALSE, col="brown") + geom_smooth(se=FALSE, method="lm") +
  theme_bw()

There is a positive association between flipper length and body mass of a penguin. The correlation coefficient is 0.87, and the form of the relationship is relatively linear.