BIOL 297: Schedule for week of April 13-17

Last updated on Apr 14, 2020 3 min read

Assignments:

There will be a regular lab assignment on the normal distribution in R due by next Tuesday.
If you haven’t already, make sure you complete your proposal for the final that was due Friday.

Readings:

Whitlock & Schluter, Chapter 10: The normal distribution

Schedule

Note that on Tuesday, class will meet synchronously on Google Meet meet.google.com/foi-xwhi-ape. Class will be recorded and posted online if you are unable to attend. Remaining instruction will be asynchronous, meaning you can work at your own pace and desired time.

Tuesday, April 14 - synchronous

We will go over the Normal Distribution in more detail to prepare for analyzing continuous variables
We will go over the Class Project
Read chapter 10 from textbook
Watch pre-recorded lecture by Dr. Yaniv Brandvain:

PDF of slides are posted on Laulima

Thursday, April 16 - lab

Lab on the Normal Distribution in R (I will post by Wednesday night)
Join Google Meeting at 12: meet.google.com/vhq-qczv-dew

Code demo on the Normal distribution


# Demonstrate the Normal distribution

# Load libraries
library(dplyr)
library(ggplot2)

# Plot standard normal ----
df <- data.frame(Y = seq(-3, 3, 0.01))
df$prob_density <- dnorm(df$Y, mean = 0, sd = 1)
ggplot(df, aes(Y, prob_density)) +
  geom_area(fill = "tomato") +
  geom_line() +
  xlab("Value of numerical variable") +
  ylab("Probability density") +
  theme_bw()

# Integrate area between an interval ----
# Approximately 2/3 (68.3%) of probability falls within +/- 1 sd
pnorm(1, mean = 0, sd = 1) - pnorm(-1, mean = 0, sd = 1)

sigma <- 2
pnorm(sigma, mean = 0, sd = sigma) - pnorm(-sigma, mean = 0, sd = sigma)

mu <- 1
sigma <- 2
pnorm(sigma + mu, mean = mu, sd = sigma) - 
  pnorm(-sigma + mu, mean = mu, sd = sigma)

# Approximately 95% of probability falls within +/- 2 sd
mu <- 1
sigma <- 2
pnorm(2 * sigma + mu, mean = mu, sd = sigma) - 
  pnorm(-2 * sigma + mu, mean = mu, sd = sigma)

# Z-transform ----
# Convert any normal distribution to standard normal with mu = 0, sigma = 1

N <- 100 # our sample size
Y <- rnorm(100, mean = 100, sd = 10)
mu <- mean(Y)
mu

sigma <- sd(Y)
sigma

Z <- (Y - mu) / sigma
mean(Z)
sd(Z)

head(cbind(Y, Z))

df <- data.frame(
  value = c(Y, Z),
  facet = rep(c("Y", "Z"), each = N)
)
ggplot(df, aes(value)) +
  facet_grid(~ facet, scales = "free") +
  geom_histogram(fill = "tomato") +
  theme_bw()

# Transforming data ----
# data from OpenNahele
open_nahele <- read.csv("https://bdj.pensoft.net/article/download/suppl/4411035/")

# Plot raw data (right-skewed)
ggplot(open_nahele, aes(D95)) +
  geom_histogram(fill = "tomato") +
  theme_bw()

open_nahele$log_D95 <- log(open_nahele$D95)

# Plot transformed data
ggplot(open_nahele, aes(log_D95)) +
  geom_histogram(fill = "tomato") +
  theme_bw()

# Is that better? Use QQ plots
ggplot(open_nahele, aes(sample = D95)) +
  geom_qq() +
  geom_qq_line() +
  ggtitle("Not very normal") +
  theme_bw()

ggplot(open_nahele, aes(sample = log_D95)) +
  geom_qq() +
  geom_qq_line() +
  ggtitle("Normalish") +
  theme_bw()