in-class ex 7
jenny hsu
2020-09-18
0.1 Introduction
Ten subjects were played tones at each of 5 loudnesses, in random order. Subjects were asked to draw a line on paper whose length matched the loudness of the tone. Each subject repeated each loudness 3 times, for a total of 30 trials per subject. Here is the mean of the 3 log-lengths for each loudness, the sd of the three log-lengths, and the number of replications, which is always 3.
A data frame with 50 observations on the following 5 variables.
subject
a factor with unique values for each subject
loudness
either 50, 60, 70, 80 or 90 db. Decibels are a logrithmic scale
y
a numeric vector giving the mean of the log-lengths of three lines drawn.
sd
a numeric vector, giving the sd of the three log lengths
n
a numeric vector, equal to the constant value 3
0.2 Data management
data(Stevens, package="alr4")library(tidyverse)
library(lme4)glimpse(Stevens)Rows: 50
Columns: 5
$ subject <fct> A, A, A, A, A, B, B, B, B, B, C, C, C, C, C, D, D, D, D, D...
$ loudness <dbl> 50, 60, 70, 80, 90, 50, 60, 70, 80, 90, 50, 60, 70, 80, 90...
$ y <dbl> 0.379, 1.727, 3.016, 3.924, 4.413, 0.260, 0.833, 2.009, 2....
$ sd <dbl> 0.507, 0.904, 0.553, 0.363, 0.092, 0.077, 0.287, 0.396, 0....
$ n <dbl> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3...0.3 OLS regression lines over 10 subjects
0.4 Visualization
ggplot(data=Stevens, aes(x=loudness, y=y)) +
geom_point(alpha=0.5) +
stat_smooth(method="lm", formula=y ~ x, se=F) +
facet_grid(. ~ subject) +
labs(x="Loudness (in db)",
y="Mean Line length (in log)") +
theme_minimal() 