Simulating Data in R
Same Seating Chart!
Statistical Distributions
Recall from your statistics classes…
A random variable is a value we don’t know until we take a sample.
- Coin flip: could be heads (0) or tails (1)
- Person’s height: could be anything from 0 feet to 10 feet.
- Annual income of a US worker: could be anything from $0 to $1.6 billion
The distribution of a random variable tells us its possible values and how likely they are to occur.
- Coin flip: 50% chance of heads and tails.
- Heights follow a bell curve centered at 5 foot 7.
- Most American workers make under $100,000.
Statistical Distributions with Names!
Uniform Distribution
- When you know the range of values, but not much else.
- All values in the range are equally likely to occur.
Normal Distribution
- When you expect values to fall near the center.
- Frequency of values follows a bell shaped curve.
t-Distribution
- A slightly wider bell curve.
- Basically used in the same context as the Normal distribution, but more common with real data (when the standard deviation is unknown).
Chi-Square Distribution
- Somewhat skewed, and only allows values above zero.
- Used in testing count data.
Binomial Distribution
- Appears when you have two possible outcomes, and you are counting how many times each outcome occurred.
- This is a discrete distribution, as there can only be whole number values!
Simulate a Dataset
We can generate fake data based on the assumption that a variable follows a certain distribution.
- We randomly sample observations from the distribution.
age <- runif(1000, min = 15, max = 75)Since there is randomness involved, we will get a different result each time we run the code.
runif(3, min = 15, max = 75)[1] 51.12011 48.62721 73.48332runif(3, min = 15, max = 75)[1] 48.79667 72.64916 29.31348To make a reproducible random sample, we first set the seed:
set.seed(93401)
runif(3, min = 15, max = 75)[1] 20.84739 51.61768 42.68515set.seed(93401)
runif(3, min = 15, max = 75)[1] 20.84739 51.61768 42.68515set.seed(435)
fake_data <- tibble(names = charlatan::ch_name(1000),
height = rnorm(1000, mean = 67, sd = 3),
age = runif(1000, min = 15, max = 75),
measure = rbinom(1000, size = 1, prob = 0.6)
) |>
mutate(supports_measure_A = ifelse(measure == 1, "yes", "no"))
head(fake_data)# A tibble: 6 × 5
names height age measure supports_measure_A
<chr> <dbl> <dbl> <int> <chr>
1 Elbridge Kautzer 67.4 66.3 1 yes
2 Brandon King 65.0 61.5 0 no
3 Phyllis Thompson 68.1 53.8 1 yes
4 Humberto Corwin 67.5 33.9 1 yes
5 Theresia Koelpin 71.4 16.1 1 yes
6 Hayden O'Reilly-Johns 66.2 37.0 0 no Check to see the ages look uniformly distributed.
Code
fake_data |>
ggplot(mapping = aes(x = age,
fill = supports_measure_A)) +
geom_histogram(show.legend = F) +
facet_wrap(~ supports_measure_A,
ncol = 1) +
scale_fill_brewer(palette = "Paired") +
theme_bw() +
labs(x = "Age (years)",
y = "",
subtitle = "Number of Individuals Supportng Measure A for Different Ages",)