Lab 1: Intro to R

library(tidyverse)
library(openintro)

Exercise 1

arbuthnot$girls

##  [1] 4683 4457 4102 4590 4839 4820 4928 4605 4457 4952 4784 5332 5200 4910 4617
## [16] 3997 3919 3395 3536 3181 2746 2722 2840 2908 2959 3179 3349 3382 3289 3013
## [31] 2781 3247 4107 4803 4881 5681 4858 4319 5322 5560 5829 5719 6061 6120 5822
## [46] 5738 5717 5847 6203 6033 6041 6299 6533 6744 7158 7127 7246 7119 7214 7101
## [61] 7167 7302 7392 7316 7483 6647 6713 7229 7767 7626 7452 7061 7514 7656 7683
## [76] 5738 7779 7417 7687 7623 7380 7288

Exercise 2

There is an overall increasing trend in the number of girls baptized over the period from 1629 to 1710, although the number fluctuates substantially from year to year. The number of girls baptized was relatively low during the earlier years, generally around 3,000–5,000, and increased to more than 7,000 in many of the later years. Therefore, the plot suggests that the number of girls baptized generally increased over time.

ggplot(data = arbuthnot, aes(x = year, y = girls)) + 
  geom_point()

ggplot(data = arbuthnot, aes(x = year, y = girls)) + 
  geom_line()

Exercise 3

The plot shows that the proportion of boys born is generally greater than 0.5, meaning that boys were born in a slightly greater proportion than girls during most of the years in the Arbuthnot dataset. However, the proportion fluctuates from year to year. Overall, the data support Arbuthnot’s observation that boys were born in greater numbers than girls.

arbuthnot <- arbuthnot %>%
  mutate(total = boys + girls)

arbuthnot <- arbuthnot %>%
  mutate(boy_ratio = boys / total)

ggplot(data = arbuthnot, aes(x = year, y = boy_ratio)) +
  geom_line()

data('present', package='openintro')

arbuthnot %>%
  summarize(min = min(boys), max = max(boys))

## # A tibble: 1 × 2
##     min   max
##   <int> <int>
## 1  2890  8426

Exercise 4

The dataset contains birth records from 1940 through 2002.

The dimensions of the data frame are:

63 rows (observations) 3 columns (variables)

The variable names are:

year boys girls

range(present$year)

## [1] 1940 2002

dim(present)

## [1] 63  3

names(present)

## [1] "year"  "boys"  "girls"

glimpse(present)

## Rows: 63
## Columns: 3
## $ year  <dbl> 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950…
## $ boys  <dbl> 1211684, 1289734, 1444365, 1508959, 1435301, 1404587, 1691220, 1…
## $ girls <dbl> 1148715, 1223693, 1364631, 1427901, 1359499, 1330869, 1597452, 1…

Exercise 5

The birth counts in the present dataset are much larger than those in the Arbuthnot dataset.

In the Arbuthnot data, the average number of boys born per year is approximately 5,907, while the average number of girls is approximately 5,535. In contrast, the present-day U.S. dataset has approximately 1.89 million boys and 1.79 million girls born per year.

Therefore, the two datasets are not of a similar magnitude. The U.S. birth counts are hundreds of times larger, which is expected because Arbuthnot’s data represent baptism records from London, whereas the present dataset represents births across the entire United States.

present %>%
  summarize(
    mean_boys = mean(boys),
    mean_girls = mean(girls)
  )

## # A tibble: 1 × 2
##   mean_boys mean_girls
##       <dbl>      <dbl>
## 1  1885600.   1793915.

arbuthnot %>%
  summarize(
    mean_boys = mean(boys),
    mean_girls = mean(girls)
  )

## # A tibble: 1 × 2
##   mean_boys mean_girls
##       <dbl>      <dbl>
## 1     5907.      5535.

Exercise 6

The plot shows that the proportion of boys born in the United States is generally slightly greater than 0.5 throughout the period from 1940 to 2002. Thus, boys were generally born in greater proportion than girls.

This means that Arbuthnot’s observation also holds for the United States: the number of male births is slightly higher than the number of female births. However, the difference is relatively small, and the proportion fluctuates somewhat from year to year.

The OpenIntro documentation itself uses a boys-to-girls ratio plot for this dataset, consistent with this analysis.

present <- present %>%
  mutate(total = boys + girls)

present <- present %>%
  mutate(boy_ratio = boys / total)

ggplot(data = present, aes(x = year, y = boy_ratio)) +
  geom_line()

Exercise 7

The year with the highest total number of births was 1961.

In 1961:

Boys = 2,186,274 Girls = 2,082,052 Total = 4,268,326 births

present <- present %>%
  mutate(total = boys + girls)

present %>%
  arrange(desc(total))

## # A tibble: 63 × 5
##     year    boys   girls   total boy_ratio
##    <dbl>   <dbl>   <dbl>   <dbl>     <dbl>
##  1  1961 2186274 2082052 4268326     0.512
##  2  1960 2179708 2078142 4257850     0.512
##  3  1957 2179960 2074824 4254784     0.512
##  4  1959 2173638 2071158 4244796     0.512
##  5  1958 2152546 2051266 4203812     0.512
##  6  1962 2132466 2034896 4167362     0.512
##  7  1956 2133588 2029502 4163090     0.513
##  8  1990 2129495 2028717 4158212     0.512
##  9  1991 2101518 2009389 4110907     0.511
## 10  1963 2101632 1996388 4098020     0.513
## # ℹ 53 more rows

present %>%
  arrange(desc(total)) %>%
  select(year, boys, girls, total)

## # A tibble: 63 × 4
##     year    boys   girls   total
##    <dbl>   <dbl>   <dbl>   <dbl>
##  1  1961 2186274 2082052 4268326
##  2  1960 2179708 2078142 4257850
##  3  1957 2179960 2074824 4254784
##  4  1959 2173638 2071158 4244796
##  5  1958 2152546 2051266 4203812
##  6  1962 2132466 2034896 4167362
##  7  1956 2133588 2029502 4163090
##  8  1990 2129495 2028717 4158212
##  9  1991 2101518 2009389 4110907
## 10  1963 2101632 1996388 4098020
## # ℹ 53 more rows

```