source("http://www.openintro.org/stat/data/arbuthnot.R")
type arbuthnot
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
7 1635 5106 4928
8 1636 4917 4605
9 1637 4703 4457
10 1638 5359 4952
11 1639 5366 4784
12 1640 5518 5332
13 1641 5470 5200
14 1642 5460 4910
15 1643 4793 4617
16 1644 4107 3997
17 1645 4047 3919
18 1646 3768 3395
19 1647 3796 3536
20 1648 3363 3181
21 1649 3079 2746
22 1650 2890 2722
23 1651 3231 2840
24 1652 3220 2908
25 1653 3196 2959
26 1654 3441 3179
27 1655 3655 3349
28 1656 3668 3382
29 1657 3396 3289
30 1658 3157 3013
31 1659 3209 2781
32 1660 3724 3247
33 1661 4748 4107
34 1662 5216 4803
35 1663 5411 4881
36 1664 6041 5681
37 1665 5114 4858
38 1666 4678 4319
39 1667 5616 5322
40 1668 6073 5560
41 1669 6506 5829
42 1670 6278 5719
43 1671 6449 6061
44 1672 6443 6120
45 1673 6073 5822
46 1674 6113 5738
47 1675 6058 5717
48 1676 6552 5847
49 1677 6423 6203
50 1678 6568 6033
51 1679 6247 6041
52 1680 6548 6299
53 1681 6822 6533
54 1682 6909 6744
55 1683 7577 7158
56 1684 7575 7127
57 1685 7484 7246
58 1686 7575 7119
59 1687 7737 7214
60 1688 7487 7101
61 1689 7604 7167
62 1690 7909 7302
63 1691 7662 7392
64 1692 7602 7316
65 1693 7676 7483
66 1694 6985 6647
67 1695 7263 6713
68 1696 7632 7229
69 1697 8062 7767
70 1698 8426 7626
71 1699 7911 7452
72 1700 7578 7061
73 1701 8102 7514
74 1702 8031 7656
75 1703 7765 7683
76 1704 6113 5738
77 1705 8366 7779
78 1706 7952 7417
79 1707 8379 7687
80 1708 8239 7623
81 1709 7840 7380
82 1710 7640 7288
dim(arbuthnot)
[1] 82 3
names(arbuthnot)
[1] "year" "boys" "girls"
arbuthnot$boys
[1] 5218 4858 4422 4994 5158 5035 5106 4917 4703 5359 5366 5518 5470 5460
[15] 4793 4107 4047 3768 3796 3363 3079 2890 3231 3220 3196 3441 3655 3668
[29] 3396 3157 3209 3724 4748 5216 5411 6041 5114 4678 5616 6073 6506 6278
[43] 6449 6443 6073 6113 6058 6552 6423 6568 6247 6548 6822 6909 7577 7575
[57] 7484 7575 7737 7487 7604 7909 7662 7602 7676 6985 7263 7632 8062 8426
[71] 7911 7578 8102 8031 7765 6113 8366 7952 8379 8239 7840 7640
Exercise 1 The number of girls baptised each year
plot(x=arbuthnot$year, y=arbuthnot$girls)
or to connect them with a line we use the third “l” and other variables for fun, for instance:
plot(x=arbuthnot$year, y=arbuthnot$girls, type="l")
plot(x=arbuthnot$year, y=arbuthnot$girls, type="c")
plot(x=arbuthnot$year, y=arbuthnot$girls, type="b")
Exercise 2 Is there an apparent trend in the number of girls baptized over the years? Yes, there is a definite increase in girls baptisms over this sample. Basic R calculator example:
5218+4683
[1] 9901
To see the total number of baptisms for boys and girls, R will compute all sums simultaneously
arbuthnot$boys+arbuthnot$girls
[1] 9901 9315 8524 9584 9997 9855 10034 9522 9160 10311 10150
[12] 10850 10670 10370 9410 8104 7966 7163 7332 6544 5825 5612
[23] 6071 6128 6155 6620 7004 7050 6685 6170 5990 6971 8855
[34] 10019 10292 11722 9972 8997 10938 11633 12335 11997 12510 12563
[45] 11895 11851 11775 12399 12626 12601 12288 12847 13355 13653 14735
[56] 14702 14730 14694 14951 14588 14771 15211 15054 14918 15159 13632
[67] 13976 14861 15829 16052 15363 14639 15616 15687 15448 11851 16145
[78] 15369 16066 15862 15220 14928
To make a “l” plot of total Baptisms per year we can execute these commands: Also, as shown you do not have to specify the arguments that x is first and y is next as we did on last plot. It is assumed to come in this order.
plot(arbuthnot$year, arbuthnot$boys+arbuthnot$girls,type="l")
We can compute the baptism ratio in 1629 by using the numbers and / like below:
5218/4683
## [1] 1.114
or we can type out or act on the vectors for each year to do the same task
arbuthnot$boys/arbuthnot$girls
[1] 1.114 1.090 1.078 1.088 1.066 1.045 1.036 1.068 1.055 1.082 1.122
[12] 1.035 1.052 1.112 1.038 1.028 1.033 1.110 1.074 1.057 1.121 1.062
[23] 1.138 1.107 1.080 1.082 1.091 1.085 1.033 1.048 1.154 1.147 1.156
[34] 1.086 1.109 1.063 1.053 1.083 1.055 1.092 1.116 1.098 1.064 1.053
[45] 1.043 1.065 1.060 1.121 1.035 1.089 1.034 1.040 1.044 1.024 1.059
[56] 1.063 1.033 1.064 1.072 1.054 1.061 1.083 1.037 1.039 1.026 1.051
[67] 1.082 1.056 1.038 1.105 1.062 1.073 1.078 1.049 1.011 1.065 1.075
[78] 1.072 1.090 1.081 1.062 1.048
Here we compute the proprtion of newborns that are boys:
5218/(5218+4683)
## [1] 0.527
or for all years at the same time also:
arbuthnot$boys/(arbuthnot$boys+arbuthnot$girls)
[1] 0.5270 0.5215 0.5188 0.5211 0.5160 0.5109 0.5089 0.5164 0.5134 0.5197
[11] 0.5287 0.5086 0.5127 0.5265 0.5094 0.5068 0.5080 0.5260 0.5177 0.5139
[21] 0.5286 0.5150 0.5322 0.5255 0.5193 0.5198 0.5218 0.5203 0.5080 0.5117
[31] 0.5357 0.5342 0.5362 0.5206 0.5257 0.5154 0.5128 0.5200 0.5134 0.5220
[41] 0.5274 0.5233 0.5155 0.5129 0.5106 0.5158 0.5145 0.5284 0.5087 0.5212
[51] 0.5084 0.5097 0.5108 0.5060 0.5142 0.5152 0.5081 0.5155 0.5175 0.5132
[61] 0.5148 0.5200 0.5090 0.5096 0.5064 0.5124 0.5197 0.5136 0.5093 0.5249
[71] 0.5149 0.5177 0.5188 0.5120 0.5027 0.5158 0.5182 0.5174 0.5215 0.5194
[81] 0.5151 0.5118
Exercise 3 Now, make a plot of the proportion of boys over time.
plot (arbuthnot$boys/(arbuthnot$boys+arbuthnot$girls),type="l")
It looks like the proportion of boys over the same time period has declined a bit.
Using R for comparisons like: <, >, =
Do boys outnumber girls in each year?
arbuthnot$boys>arbuthnot$girls
[1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[15] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[29] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[43] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[57] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
[71] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
HOW COOL!! It is showing logical data, TRUE or FALSE
X out and SAVE