Penguins and T-tests

#Install and load packages
library(tidyverse)
library(stats)
library(rrcov)
library(readxl)#Reads excel data

Part 1. Use tidyverse to create a summary dataset that shows the average of bill_length_mm, bill_depth_mm, and flipper_length_mm by species

df <- read_excel("homework_2_penguins.xlsx")

# copy original data into working dataframe, ignore NAs, and format categorical info
penguins <- na.omit(df)
penguins[sapply(penguins, is.character)] <- lapply(penguins[sapply(penguins, is.character)], as.factor)
penguins$year <- as.factor(penguins$year)

summary(penguins)
##       species          island    bill_length_mm  bill_depth_mm  
##  Adelie   :146   Biscoe   :163   Min.   :32.10   Min.   :13.10  
##  Chinstrap: 68   Dream    :123   1st Qu.:39.50   1st Qu.:15.60  
##  Gentoo   :119   Torgersen: 47   Median :44.50   Median :17.30  
##                                  Mean   :43.99   Mean   :17.16  
##                                  3rd Qu.:48.60   3rd Qu.:18.70  
##                                  Max.   :59.60   Max.   :21.50  
##  flipper_length_mm  body_mass_g       sex        year    
##  Min.   :172       Min.   :2700   female:165   2007:103  
##  1st Qu.:190       1st Qu.:3550   male  :168   2008:113  
##  Median :197       Median :4050                2009:117  
##  Mean   :201       Mean   :4207                          
##  3rd Qu.:213       3rd Qu.:4775                          
##  Max.   :231       Max.   :6300

The data has penguin body data for three species collected at three islands over three years. It is almost equally divided between females and males.

Let’s put this information into a new dataframe by species and summarize the body size variables.

p_summary <- penguins %>%
  group_by(species) %>%
  summarise(
    ave_bill_length_mm = mean(bill_length_mm),
    ave_bill_depth_mm = mean(bill_depth_mm),
    ave_flipper_length_mm = mean(flipper_length_mm),
    ave_body_mass_g = mean(body_mass_g)
  )
p_summary
## # A tibble: 3 × 5
##   species   ave_bill_length_mm ave_bill_depth_mm ave_flipper_length_mm
##   <fct>                  <dbl>             <dbl>                 <dbl>
## 1 Adelie                  38.8              18.3                  190.
## 2 Chinstrap               48.8              18.4                  196.
## 3 Gentoo                  47.6              15.0                  217.
## # ℹ 1 more variable: ave_body_mass_g <dbl>

Part 2. Create boxplots that compare penguins by sex for bill_length_mm, bill_depth_mm, and flipper_length_mm

# create plot for bill length vs. sex
ggplot(data=penguins, aes(y=bill_length_mm, x=sex)) +
  geom_boxplot() + 
  theme_classic() +
    scale_x_discrete("Sex", labels = c("Female", "Male")) +
  scale_y_continuous("Bill Length (mm)", breaks=seq(30,60,by=5)) +
  theme(panel.grid.major.y = element_line(color = "gray",
                                        size = 0.25,
                                        linetype = 1)) +
  ggtitle("Comparison of Penguin Bill Length and Sex")

# create plot for bill depth vs. sex
ggplot(data=penguins, aes(y=bill_depth_mm, x=sex)) +
  geom_boxplot() + 
  theme_classic() +
    scale_x_discrete("Sex", labels = c("Female", "Male")) +
  scale_y_continuous("Bill Depth (mm)", breaks=seq(13,23,by=1)) +
  theme(panel.grid.major.y = element_line(color = "gray",
                                        size = 0.25,
                                        linetype = 1)) +
  ggtitle("Comparison of Penguin Bill Depth and Sex")

# create plot for flipper length vs. sex
ggplot(data=penguins, aes(y=flipper_length_mm, x=sex)) +
  geom_boxplot() + 
  theme_classic() +
    scale_x_discrete("Sex", labels = c("Female", "Male")) +
  scale_y_continuous("Flipper Length (mm)", breaks=seq(170,235,by=10)) +
  theme(panel.grid.major.y = element_line(color = "gray",
                                        size = 0.25,
                                        linetype = 1)) +
  ggtitle("Comparison of Penguin Flipper Length and Sex")

Part 3. Run t.tests to compare penguins by sex for bill_length_mm, bill_depth_mm, and flipper_length_mm

Is there a significant difference between the sexes for bill length, bill depth, and flipper length? Performing t-tests on the grouped data will return p-values. If the p-values is small, traditionally < 0.05, then there is statistical evidence that there is a difference between the two groups.

t.test(bill_length_mm ~ sex, data = penguins)
## 
##  Welch Two Sample t-test
## 
## data:  bill_length_mm by sex
## t = -6.6725, df = 329.29, p-value = 1.066e-10
## alternative hypothesis: true difference in means between group female and group male is not equal to 0
## 95 percent confidence interval:
##  -4.865676 -2.649908
## sample estimates:
## mean in group female   mean in group male 
##             42.09697             45.85476
t.test(bill_depth_mm ~ sex, data = penguins)
## 
##  Welch Two Sample t-test
## 
## data:  bill_depth_mm by sex
## t = -7.309, df = 330.88, p-value = 2.036e-12
## alternative hypothesis: true difference in means between group female and group male is not equal to 0
## 95 percent confidence interval:
##  -1.860077 -1.071157
## sample estimates:
## mean in group female   mean in group male 
##             16.42545             17.89107
t.test(flipper_length_mm ~ sex, data = penguins)
## 
##  Welch Two Sample t-test
## 
## data:  flipper_length_mm by sex
## t = -4.8079, df = 325.28, p-value = 2.336e-06
## alternative hypothesis: true difference in means between group female and group male is not equal to 0
## 95 percent confidence interval:
##  -10.064811  -4.219821
## sample estimates:
## mean in group female   mean in group male 
##             197.3636             204.5060

For all three variables the p-values are << 0.05, which means there is a statistical difference between the size of these features and the sex of the penguins.