TUTORIAL 2 - Literate Programming and Anscombe’s Quartet

MORE QUARTO!

Do the summary statistics reveal the truth? Or are they FILLED WITH LIES? A simple demonstration with Anscombe’s Quartet.

ANSCOMBE’S QUARTET

The purpose of this assignment is to demonstrate how summary statistics can sometimes be misleading and how data visualization helps us understand our dataset.

The Data

Anscombe’s Quartet is comprised of four pairs of x,y data:

library(ggplot2)
library(grid)
library(gridExtra)
library(datasets)
library(tidyverse)
library(dplyr)

datasets::anscombe

   x1 x2 x3 x4    y1   y2    y3    y4
1  10 10 10  8  8.04 9.14  7.46  6.58
2   8  8  8  8  6.95 8.14  6.77  5.76
3  13 13 13  8  7.58 8.74 12.74  7.71
4   9  9  9  8  8.81 8.77  7.11  8.84
5  11 11 11  8  8.33 9.26  7.81  8.47
6  14 14 14  8  9.96 8.10  8.84  7.04
7   6  6  6  8  7.24 6.13  6.08  5.25
8   4  4  4 19  4.26 3.10  5.39 12.50
9  12 12 12  8 10.84 9.13  8.15  5.56
10  7  7  7  8  4.82 7.26  6.42  7.91
11  5  5  5  8  5.68 4.74  5.73  6.89

Example Hypotheses

1. Eric has four replicates in which he is measuring the expression of two proteins (x, y) on 11 samples.
2. Cody has four replicates in which he is measuring gene expression of two genes (x, y) in 11 cell images.
3. Ronald has four replicates in which he is measuring a blood protein (x) and a malaria marker (y) in 11 patients.

Your hypothesis is that the four replicates do not differ in the correlation between x and y.

Summary Statistics

tidy_anscombe <- anscombe %>%
 pivot_longer(cols = everything(),
              names_to = c(".value", "set"),
              names_pattern = "(.)(.)")
tidy_anscombe_summary <- tidy_anscombe %>%
  group_by(set) %>%
  summarise(across(.cols = everything(),
                   .fns = lst(min,max,median,mean,sd,var),
                   .names = "{col}_{fn}"))
#> `summarise()` ungrouping output (override with `.groups` argument)

vars<-c("set", "x_mean", "x_var",  "y_mean", "y_var")
thing<- as.data.frame(tidy_anscombe_summary[vars])
knitr::kable(thing)

set	x_mean	x_var	y_mean	y_var
1	9	11	7.500909	4.127269
2	9	11	7.500909	4.127629
3	9	11	7.500000	4.122620
4	9	11	7.500909	4.123249

Visualization reveals hidden patterns!

ggplot(tidy_anscombe,
       aes(x = x,
           y = y)) +
  geom_point() +
  geom_point(data = tidy_anscombe_summary, aes(x=x_mean, y = y_mean, color = "red", size = 5),
             show.legend = FALSE)+
  facet_wrap(~set) +
  geom_smooth(method = "lm", se = FALSE)

`geom_smooth()` using formula = 'y ~ x'