Comparing Arbutnot’s Baptisms to Present Day Births

Arbuthnot’s Baptism Data

The Arbuthnot data set refers to Dr. John Arbuthnot, an 18th century physician, writer, and mathematician. He was interested in the ratio of newborn boys to newborn girls, so he gathered the baptism records for children born in London for every year from 1629 to 1710.

A summary of Arbuthnot’s baptism data set for girls and boys:

source("more/arbuthnot.R")
head(arbuthnot)
##   year boys girls
## 1 1629 5218  4683
## 2 1630 4858  4457
## 3 1631 4422  4102
## 4 1632 4994  4590
## 5 1633 5158  4839
## 6 1634 5035  4820
dim(arbuthnot)
## [1] 82  3
names(arbuthnot)
## [1] "year"  "boys"  "girls"

Present Day Birth Records in the US

The Present data set contains trend analysis of the sex ratios at birth in the US from 19049 to 2002.

Question 1:

What are the dimensions of the data frame and what are the variable or column names?

The present data set contains 63 rows and 3 columns which are named year, boys, and girls.

source("more/present.R")
head(present)
##   year    boys   girls
## 1 1940 1211684 1148715
## 2 1941 1289734 1223693
## 3 1942 1444365 1364631
## 4 1943 1508959 1427901
## 5 1944 1435301 1359499
## 6 1945 1404587 1330869
dim(present)
## [1] 63  3
names(present)
## [1] "year"  "boys"  "girls"

What years are included in this data set?

The birth data ranges from 1940 to 2002.

min(present$year)
## [1] 1940
max(present$year)
## [1] 2002

Question 2: How do these counts compare to Arbuthnot’s?

Total number of baptisms per year

The total number of baptisms for boys and girls for the period from 1629 to 1710.

plot(arbuthnot$year, arbuthnot$boys + arbuthnot$girls, type = "l")

Total number of births per year

The total number of births for boys and girls for the period from 1940 to 2002.

plot(present$year, present$boys + present$girls, type = "l")

Are they on a similar scale?

Scale for Baptism data

min(arbuthnot$boys + arbuthnot$girls)
## [1] 5612
max(arbuthnot$boys + arbuthnot$girls)
## [1] 16145

Scale for modern US birth data

min(present$boys + present$girls)
## [1] 2360399
max(present$boys + present$girls)
## [1] 4268326

Ratio of min and max births to baptisms

The scale of present day births is several hundred times the scale of baptisms.

min(present$boys + present$girls)/min(arbuthnot$boys + arbuthnot$girls)
## [1] 420.5985
max(present$boys + present$girls)/max(arbuthnot$boys + arbuthnot$girls)
## [1] 264.3745

Question 3: Make a plot that displays the boy-to-girl ratio for every year in the data set. What do you see?

Early on the number of boys born is higher than girls, but as the years progress the proportion of boys to girls gets closer to being equal.

Plot of ratio of boy to girl ratio

plot(present$year, present$boys/present$girls, type = "l")

Proportion of boys to girls

There are more boys born than girls during the entire period of the data set, but the proportion of boys gets smaller over time.

present$boys/(present$boys + present$girls)
##  [1] 0.5133386 0.5131376 0.5141926 0.5138001 0.5135613 0.5134745 0.5142562
##  [8] 0.5134883 0.5131024 0.5130881 0.5130778 0.5126891 0.5124173 0.5130027
## [15] 0.5125423 0.5123716 0.5125011 0.5123550 0.5120462 0.5120713 0.5119269
## [22] 0.5122088 0.5117064 0.5128408 0.5115250 0.5124656 0.5118474 0.5121866
## [29] 0.5130068 0.5129073 0.5133154 0.5126337 0.5124973 0.5127013 0.5133340
## [36] 0.5130513 0.5127982 0.5128057 0.5128266 0.5126110 0.5128692 0.5125792
## [43] 0.5123372 0.5126648 0.5122425 0.5126849 0.5124035 0.5121951 0.5121931
## [50] 0.5121286 0.5121179 0.5112054 0.5121992 0.5121845 0.5116894 0.5119398
## [57] 0.5114951 0.5116337 0.5115255 0.5119072 0.5117182 0.5111665 0.5117154
plot(present$year, present$boys/(present$boys + present$girls), type = "l")

Question 4: In what year did we see the most total number of births in the U.S.?

The year with the greatest number of total births is 1961.

present$totalBirths = present$boys + present$girls
present[ present$totalBirths == max(present$totalBirths), ]
##    year    boys   girls totalBirths
## 22 1961 2186274 2082052     4268326