Assignment 2 RMarkdown

1. Load Necessary Packages

“include=FALSE” hides code chunk
Tidyverse, knitr, kableExtra loaded

2. Read in the penguins.csv

“suppressMessages” hides preview of data

suppressMessages(penguins <- read_csv("penguins.csv"))

3. Data Wrangling

“filter” tool selects only observations of male penguins
“group_by” tool groups penguins by island
“summarize” tool finds the mean and sd of penguin masses of each island
“1” indicates rounding to 1 decimal place
“length” gives the sample size for each island (# of observed penguins per island)

p_1 <- penguins %>% 
  filter(Sex == "MALE") %>% 
  group_by(Island) %>% 
  summarize(
    mean_wt = round(mean(Body_Mass), 1),
    sd_wt = round(sd(Body_Mass), 1),
    length(Body_Mass)
  )

4. Create a Finalized Table of the Summary Data

“kable” creates table drawing from p_1
“col.names” renames column titles
“kable_styling” stripes color of rows, “hover” highlights the row the cursor is covering, “bordered” gives the table borders, “full_width” scales the table properly
“row_spec”, “0” specifies the header row, color and background gives the white and blue colors
“column_spec” “1” specifies the island column, and bolds the island name

kable(p_1, col.names = c("Island","Mean Body Mass (g)","SD Mean Body Mass (g)","Sample Size (# of Obs. Penguins)")) %>% 
  kable_styling(bootstrap_options = c("striped", "hover", "bordered", full_width = F)) %>% 
  row_spec(0, color = "white", background = "skyblue") %>% 
  column_spec(1, bold = T)

Island	Mean Body Mass (g)	SD Mean Body Mass (g)	Sample Size (# of Obs. Penguins)
Biscoe	4050.0	355.6	22
Dream	4045.5	330.5	28
Torgersen	4034.8	372.5	23

5. Create Side-by-Side Histograms for Male Penguin Body Masses

For side-by-side histograms, created new subset p_2
“filter” tool filters for only male penguin observations
“group_by” tool groups the penguin observations by the island
ggplot creates new graph titled mass_histogram, calling the p_2 subset and selecting the Body_Mass column for the x axis
“geom_histogram” calls for the graph to be a histogram, “fill” gives different fill colors to each island, “bins = 8” selects for 8 total histogram bins derived using the rice rule and n=73, “color = white” gives white borders to each bin
“facet_wrap” separates the histograms by island, “scale = free” allows for different y-axis scale on each histogram

p_2 <- penguins %>% 
  filter(Sex == "MALE") %>% 
  group_by(Island)

mass_histogram <- ggplot(p_2, aes(x = Body_Mass)) +
  geom_histogram(aes(fill = Island), bins = 8, color = "white") +
  facet_wrap(~ Island, scale = "free")

mass_histogram

6. Create Side-by-Side Quantile-Quantile Plots for Male Penguin Body Masses

ggplot creates new graph calling on p_2 subset, specicying the sample data from the Body_Mass column
“geom_qq” specifys geometry as a qq plot with the Island grouping
“facet_wrap” separates the graphs by Island, and “scale = free” allows for the scale of each graph to match the data

mass_quantile <- ggplot(p_2, aes(sample = Body_Mass)) +
  geom_qq(aes(fill = Island)) +
  facet_wrap(~ Island, scale = "free")

mass_quantile

7. Explain T or Z Distribution

To determine the confidence levels for the sample data collected, I would use the T-Distribution because we do not know the population standard deviation (only the sample), and the population samples appear to be normally distributed

8. Find the 95% Confidence Intervals for Mean Male Penguin Body Mass

New subset “Biscoe” created using p_2 subset, filtering for only observations at Biscoe Island
New subset “Dream” created using p_2 subset, filtering for only observations at Dream Island
“t.test” tool runs t.tests on biscoe and dream subsets, specificed for Body_Mass

Biscoe <- p_2 %>% 
  filter(Island == "Biscoe")

Dream <- p_2 %>% 
  filter(Island == "Dream")

biscoe_ci <- t.test(Biscoe$Body_Mass)

dream_ci <- t.test(Dream$Body_Mass)

Mean Male Penguin Body Mass for Biscoe Isalnd (n = 22) is 4050 g, with a 95% confidence interval of [3892, 4208].

Mean Male Penguin Body Mass for Dream Island (n = 28) is 4045.5 g, with a 95% confidence interval of [3917,4174].

9. Two-Sample T-Test Comparing Mean Body Mass at Biscoe and Dream Islands

“t.test” tool performs a two-sided t-test on the body_mass data from the Biscoe and Dream subets, output below

bodymass_t <- t.test(Biscoe$Body_Mass, Dream$Body_Mass)

bodymass_t

## 
##  Welch Two Sample t-test
## 
## data:  Biscoe$Body_Mass and Dream$Body_Mass
## t = 0.045448, df = 43.575, p-value = 0.964
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -193.5580  202.4866
## sample estimates:
## mean of x mean of y 
##  4050.000  4045.536

Male Penguin Body Mass at the two Islands, Biscoe (n=22) and Dream (n=28), do not differ significantly (t(43.5) = .0455, p = .964). From the observed samples, the mean body mass at Biscoe Island (4050 g) only differs from the mean at Dream Island (4045.5 g) by 4.5 g. Thus, there is a 96.4% chance that the two samples were drawn from populations with the same mean.

10. One-Tailed T-Test for Male Body Mass at Biscoe Island

“t.test” tool performs one-tailed t-test using 4200 g as the true mean, and the alternative hypthosis being that the true mean is actually less than 4200 g, output below

biscoe_t_oneside <- t.test(Biscoe$Body_Mass, mu = 4200, alternative = "less")

biscoe_t_oneside

## 
##  One Sample t-test
## 
## data:  Biscoe$Body_Mass
## t = -1.9787, df = 21, p-value = 0.03056
## alternative hypothesis: true mean is less than 4200
## 95 percent confidence interval:
##      -Inf 4180.445
## sample estimates:
## mean of x 
##      4050

The journal “Penguin Research” claims that the mean body mass of adult male Adiele penguins at Biscoe Island is 4200 g. However, our study sample (n = 22) resulted in a sample mean body mass of 4050 g. A one-tailed t-test at a 95% confidence interval (t(21) = -1.98, p = .03) was significant to show that the mean body mass of adult male Penguins at Biscoe Island is less than 4200 g. The results suggest that if the true mean were 4200 g, there is only a 3% chance that a mean sample body mass of 4050 g could have been ramdonly selected, and thus, the true mean body mass is likely less than 4200 g.

11. Finalized Box & Whisper plot with Overlaying Jitter for Male Penguin Body Mass

“ggplot” creates a new boxplot with jitter (geom_jitter) stored as penguin_boxplot
alpha changes the opaqueness of the fill, show.legened = F removes the legend, fill=island gives each island a different color
jitter is adjusted by width and opaqueness
labs adjusts axis and titles

penguin_boxplot <- ggplot(p_2, aes(x = Island, y = Body_Mass)) +
  geom_boxplot(aes(fill = Island), alpha = 0.8, show.legend = F) +
  geom_jitter(width = 0.1, alpha = 0.8) +
  labs(x = "Penguin Observations by Island (n (B) = 22, n (D) = 28, n (T) = 23)", y = "Body Mass (g)", title = "Male Adiele Penguin Body Mass Observations (Created by Chase Brewster)")

penguin_boxplot