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if (!require("pacman")) install.packages("pacman")Loading required package: pacmanHide / show the code
p_load(pacman,
kernlab,
tidyverse)
A silly headline? Maybe! But it has some clues about the topic!
If the population is Sampling! one sample from this population would be pling! right?
This whole article is all about this and how to do the sampling in R.
What I will not explain: 😒
- Definitions of sample and population
- Statistical need of this process
Needed Libraries
Some optional settings:
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options(scipen = 999, # Who likes scientifi notations anyway?!
digits = 3) # More than 3 digits will be needed when I'm going to MARSSimple Random Sampling
To make a basic slicing, you just need a variation of function slice() as slice_sample().
Let’s use spam dataset of HP Labs1:
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data(spam)
head(spam) make address all num3d our over remove internet order mail receive will
1 0.00 0.64 0.64 0 0.32 0.00 0.00 0.00 0.00 0.00 0.00 0.64
2 0.21 0.28 0.50 0 0.14 0.28 0.21 0.07 0.00 0.94 0.21 0.79
3 0.06 0.00 0.71 0 1.23 0.19 0.19 0.12 0.64 0.25 0.38 0.45
4 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
5 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
6 0.00 0.00 0.00 0 1.85 0.00 0.00 1.85 0.00 0.00 0.00 0.00
people report addresses free business email you credit your font num000
1 0.00 0.00 0.00 0.32 0.00 1.29 1.93 0.00 0.96 0 0.00
2 0.65 0.21 0.14 0.14 0.07 0.28 3.47 0.00 1.59 0 0.43
3 0.12 0.00 1.75 0.06 0.06 1.03 1.36 0.32 0.51 0 1.16
4 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
5 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 0.00
money hp hpl george num650 lab labs telnet num857 data num415 num85
1 0.00 0 0 0 0 0 0 0 0 0 0 0
2 0.43 0 0 0 0 0 0 0 0 0 0 0
3 0.06 0 0 0 0 0 0 0 0 0 0 0
4 0.00 0 0 0 0 0 0 0 0 0 0 0
5 0.00 0 0 0 0 0 0 0 0 0 0 0
6 0.00 0 0 0 0 0 0 0 0 0 0 0
technology num1999 parts pm direct cs meeting original project re edu
1 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
2 0 0.07 0 0 0.00 0 0 0.00 0 0.00 0.00
3 0 0.00 0 0 0.06 0 0 0.12 0 0.06 0.06
4 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
5 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
6 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
table conference charSemicolon charRoundbracket charSquarebracket
1 0 0 0.00 0.000 0
2 0 0 0.00 0.132 0
3 0 0 0.01 0.143 0
4 0 0 0.00 0.137 0
5 0 0 0.00 0.135 0
6 0 0 0.00 0.223 0
charExclamation charDollar charHash capitalAve capitalLong capitalTotal type
1 0.778 0.000 0.000 3.76 61 278 spam
2 0.372 0.180 0.048 5.11 101 1028 spam
3 0.276 0.184 0.010 9.82 485 2259 spam
4 0.137 0.000 0.000 3.54 40 191 spam
5 0.135 0.000 0.000 3.54 40 191 spam
6 0.000 0.000 0.000 3.00 15 54 spamIf we would want to take randomly just 200 emails (!) from this dataset, how many of them would be spam? Let’s randomly select 200 emails from spam dataset using slice_sample function:
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set.seed(42) # let's set the random seed for a cool value
random200 <-
spam %>%
select(type) %>% # lets not bother with other variables for now
slice_sample(n = 200) # gets random 400 records
glimpse(random200)Rows: 200
Columns: 1
$ type <fct> nonspam, nonspam, nonspam, spam, spam, spam, nonspam, nonspam, sp…How is the ratio of spam / non-spam ? Let’s have a look:
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table_of_counts <- table(random200$type)
table_of_counts # shows the counts
nonspam spam
128 72 Hide / show the code
prop.table(table_of_counts) # shows the proportion
nonspam spam
0.64 0.36 %36 of the randomly taken emails are spams! huge amount! What if we would check the whole data?
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table_of_counts_all <- table(spam$type)
table_of_counts_all # shows the counts
nonspam spam
2788 1813 Hide / show the code
prop.table(table_of_counts_all) # shows the proportion
nonspam spam
0.606 0.394 Surprisingly (maybe not surprisingly at all) ,our 200 observations has the similar spam/non-spam ratio with the all dataset!🥸
An alternative way also exists!
What if we don’t have the data frame but just only a vector! Then good old sample() comes to help!
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spam_or_not_spam <- spam$type # Creating a vector of spam or not spam column
random200_of_vector <-
sample(spam_or_not_spam, size = 200) # This time it's not "n" but "size"
table_of_counts <- table(random200_of_vector)
table_of_counts # shows the countsrandom200_of_vector
nonspam spam
111 89 Hide / show the code
prop.table(table_of_counts) # shows the proportionrandom200_of_vector
nonspam spam
0.555 0.445 As a result, just by writing couple of lines of code, we could have get random samples from our data and we saw that , at least in terms of spam/non spam ratio, our sample is nearly perfectly representing the all population data!
What we did is simple random sampling and works like a game of bingo. You start with your population of all numbers, and randomly pick them out one at a time until you have a winner or in our case, until you reach the defined sample size!
While using this technique, sometimes we can end up with 2 numbers in order like 6 and 7 being drawn in order, and sometimes we might end up with big gaps between numbers. If the game has numbers between 1 to 99, in first 15 draws, there could be no number over 50. We have no control on sample picking.
Systematic Sampling
Another alternative to what we did is systematic sampling. This samples the population at regular intervals. Which means, for example, let’s say we put all the numbers to a table. Instead of blindly drawing them from a bag, now we are picking every fifth number on the table. In this way, at least, we are being sure of each section of the table area is represented equally in the sample!
To demonstrate systematic sampling, we can add one column called rowid with rowid_to_column function:
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# Set the seed
set.seed(42)
spam2 <- spam %>%
# Add a row ID column
rowid_to_column
# View
head(spam2) rowid make address all num3d our over remove internet order mail receive
1 1 0.00 0.64 0.64 0 0.32 0.00 0.00 0.00 0.00 0.00 0.00
2 2 0.21 0.28 0.50 0 0.14 0.28 0.21 0.07 0.00 0.94 0.21
3 3 0.06 0.00 0.71 0 1.23 0.19 0.19 0.12 0.64 0.25 0.38
4 4 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31
5 5 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31
6 6 0.00 0.00 0.00 0 1.85 0.00 0.00 1.85 0.00 0.00 0.00
will people report addresses free business email you credit your font num000
1 0.64 0.00 0.00 0.00 0.32 0.00 1.29 1.93 0.00 0.96 0 0.00
2 0.79 0.65 0.21 0.14 0.14 0.07 0.28 3.47 0.00 1.59 0 0.43
3 0.45 0.12 0.00 1.75 0.06 0.06 1.03 1.36 0.32 0.51 0 1.16
4 0.31 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
5 0.31 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 0.00
money hp hpl george num650 lab labs telnet num857 data num415 num85
1 0.00 0 0 0 0 0 0 0 0 0 0 0
2 0.43 0 0 0 0 0 0 0 0 0 0 0
3 0.06 0 0 0 0 0 0 0 0 0 0 0
4 0.00 0 0 0 0 0 0 0 0 0 0 0
5 0.00 0 0 0 0 0 0 0 0 0 0 0
6 0.00 0 0 0 0 0 0 0 0 0 0 0
technology num1999 parts pm direct cs meeting original project re edu
1 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
2 0 0.07 0 0 0.00 0 0 0.00 0 0.00 0.00
3 0 0.00 0 0 0.06 0 0 0.12 0 0.06 0.06
4 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
5 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
6 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
table conference charSemicolon charRoundbracket charSquarebracket
1 0 0 0.00 0.000 0
2 0 0 0.00 0.132 0
3 0 0 0.01 0.143 0
4 0 0 0.00 0.137 0
5 0 0 0.00 0.135 0
6 0 0 0.00 0.223 0
charExclamation charDollar charHash capitalAve capitalLong capitalTotal type
1 0.778 0.000 0.000 3.76 61 278 spam
2 0.372 0.180 0.048 5.11 101 1028 spam
3 0.276 0.184 0.010 9.82 485 2259 spam
4 0.137 0.000 0.000 3.54 40 191 spam
5 0.135 0.000 0.000 3.54 40 191 spam
6 0.000 0.000 0.000 3.00 15 54 spamHide / show the code
# Set the sample size to 200
sample_size <- 200
# Get the population size from spam
pop_size <- nrow(spam)
# Calculate the interval
interval <- pop_size %/% sample_size
interval[1] 23Using this interval in sampling:
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# Get row indexes for the sample
row_indexes <- seq_len(sample_size) * interval
spam_samp_systemetic <- spam %>%
# Add a row ID column
rowid_to_column() %>%
# Get 200 rows using systematic sampling
slice(row_indexes)
# See the result
head(spam_samp_systemetic) rowid make address all num3d our over remove internet order mail receive
1 23 0.00 0.00 0.00 0 2.94 0.00 0.00 0.00 0.00 0.00 0.00
2 46 0.15 0.45 1.05 0 0.45 0.00 0.00 1.81 0.60 0.75 0.00
3 69 0.30 0.00 0.61 0 0.00 0.00 0.00 0.00 0.00 0.92 0.30
4 92 0.47 0.31 0.47 0 0.05 0.13 0.05 0.26 0.44 0.76 0.26
5 115 0.12 1.76 0.63 0 0.88 0.00 0.12 0.50 0.25 3.90 0.50
6 138 1.00 0.00 0.33 0 0.66 0.66 0.00 0.00 0.00 0.00 0.00
will people report addresses free business email you credit your font num000
1 0.00 0.00 0.00 0.0 2.94 0.00 0 0.00 0.00 0.00 0 0.00
2 0.90 0.30 0.00 0.3 0.00 0.00 0 4.07 0.00 1.51 0 0.00
3 0.92 0.30 0.30 0.0 2.15 0.61 0 5.53 0.00 1.23 0 0.00
4 0.97 0.58 1.26 0.0 0.26 0.44 0 3.25 0.00 1.50 0 1.05
5 0.88 0.12 0.00 0.0 0.25 0.12 0 2.90 0.25 1.38 0 1.13
6 0.33 0.66 0.00 0.0 0.66 0.66 0 2.33 0.00 0.33 0 1.66
money hp hpl george num650 lab labs telnet num857 data num415 num85
1 0.00 0 0 0 0 0 0 0 0 0 0.0 0
2 0.30 0 0 0 0 0 0 0 0 0 0.0 0
3 0.30 0 0 0 0 0 0 0 0 0 0.3 0
4 0.34 0 0 0 0 0 0 0 0 0 0.0 0
5 0.12 0 0 0 0 0 0 0 0 0 0.0 0
6 0.33 0 0 0 0 0 0 0 0 0 0.0 0
technology num1999 parts pm direct cs meeting original project re edu table
1 0 0 0 0 0 0 0 0.00 0 0.00 0 0
2 0 0 0 0 0 0 0 0.00 0 0.15 0 0
3 0 0 0 0 0 0 0 0.00 0 0.30 0 0
4 0 0 0 0 0 0 0 0.00 0 0.02 0 0
5 0 0 0 0 0 0 0 0.12 0 0.00 0 0
6 0 0 0 0 0 0 0 0.00 0 0.00 0 0
conference charSemicolon charRoundbracket charSquarebracket charExclamation
1 0 0.404 0.404 0.000 0.809
2 0 0.000 0.250 0.000 1.318
3 0 0.000 0.100 0.000 1.053
4 0 0.004 0.066 0.000 0.322
5 0 0.019 0.379 0.159 0.000
6 0 0.000 0.060 0.000 0.120
charDollar charHash capitalAve capitalLong capitalTotal type
1 0.000 0.000 4.86 12 34 spam
2 0.068 0.000 5.30 130 774 spam
3 0.351 0.250 3.88 66 303 spam
4 0.764 0.159 6.10 193 3038 spam
5 0.119 0.000 4.16 38 507 spam
6 0.541 0.000 5.43 21 304 spamNotice the rowid jumps with the interval we found!👍😎
To check if there’s a problem with systematic sampling, we need to consider whether the data is sorted or has a pattern in the row order. If it does, the sample may not represent the whole population well. But don’t worry, we can solve this problem by shuffling the rows. This basically makes systematic sampling the same as simple random sampling.
The trick in here is to use prop argument of the slice_sample() function. Normally, we use it to say like “take %10 of the data randomly” by assigning 0.1 to it. It will start randomly picking 1 by one until it reaches %10 of the population. What if we put 1 instead? It will mean “take %100 of the data randomly” which it will pick the data randomly until all the data is picked. Which basically means, data will be shuffled
This is the original data:
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head(spam) make address all num3d our over remove internet order mail receive will
1 0.00 0.64 0.64 0 0.32 0.00 0.00 0.00 0.00 0.00 0.00 0.64
2 0.21 0.28 0.50 0 0.14 0.28 0.21 0.07 0.00 0.94 0.21 0.79
3 0.06 0.00 0.71 0 1.23 0.19 0.19 0.12 0.64 0.25 0.38 0.45
4 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
5 0.00 0.00 0.00 0 0.63 0.00 0.31 0.63 0.31 0.63 0.31 0.31
6 0.00 0.00 0.00 0 1.85 0.00 0.00 1.85 0.00 0.00 0.00 0.00
people report addresses free business email you credit your font num000
1 0.00 0.00 0.00 0.32 0.00 1.29 1.93 0.00 0.96 0 0.00
2 0.65 0.21 0.14 0.14 0.07 0.28 3.47 0.00 1.59 0 0.43
3 0.12 0.00 1.75 0.06 0.06 1.03 1.36 0.32 0.51 0 1.16
4 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
5 0.31 0.00 0.00 0.31 0.00 0.00 3.18 0.00 0.31 0 0.00
6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 0.00
money hp hpl george num650 lab labs telnet num857 data num415 num85
1 0.00 0 0 0 0 0 0 0 0 0 0 0
2 0.43 0 0 0 0 0 0 0 0 0 0 0
3 0.06 0 0 0 0 0 0 0 0 0 0 0
4 0.00 0 0 0 0 0 0 0 0 0 0 0
5 0.00 0 0 0 0 0 0 0 0 0 0 0
6 0.00 0 0 0 0 0 0 0 0 0 0 0
technology num1999 parts pm direct cs meeting original project re edu
1 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
2 0 0.07 0 0 0.00 0 0 0.00 0 0.00 0.00
3 0 0.00 0 0 0.06 0 0 0.12 0 0.06 0.06
4 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
5 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
6 0 0.00 0 0 0.00 0 0 0.00 0 0.00 0.00
table conference charSemicolon charRoundbracket charSquarebracket
1 0 0 0.00 0.000 0
2 0 0 0.00 0.132 0
3 0 0 0.01 0.143 0
4 0 0 0.00 0.137 0
5 0 0 0.00 0.135 0
6 0 0 0.00 0.223 0
charExclamation charDollar charHash capitalAve capitalLong capitalTotal type
1 0.778 0.000 0.000 3.76 61 278 spam
2 0.372 0.180 0.048 5.11 101 1028 spam
3 0.276 0.184 0.010 9.82 485 2259 spam
4 0.137 0.000 0.000 3.54 40 191 spam
5 0.135 0.000 0.000 3.54 40 191 spam
6 0.000 0.000 0.000 3.00 15 54 spamLet’s shuffle the rows:
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# Shuffle the rows of attrition_pop then add row IDs
spam_shuffled <- spam %>%
slice_sample(prop = 1)
head(spam_shuffled) make address all num3d our over remove internet order mail receive will
2609 0 0 0.00 0 0.00 0 0.00 0 0.0 0.00 0 2.85
4069 0 0 0.00 0 0.00 0 0.00 0 0.0 0.00 0 0.00
2369 0 0 0.00 0 0.77 0 0.00 0 0.0 0.00 0 0.00
1098 0 0 0.40 0 0.00 0 0.20 0 0.8 0.20 0 0.40
1252 0 0 0.72 0 0.72 0 0.72 0 0.0 0.00 0 0.00
634 0 0 0.00 0 0.00 0 0.00 0 0.0 1.49 0 1.49
people report addresses free business email you credit your font num000
2609 0.00 0.00 0.0 0.0 0 0 0.00 0.00 0.00 0 0
4069 0.00 0.00 0.0 0.0 0 0 0.00 0.00 0.00 0 0
2369 0.00 0.00 0.0 0.0 0 0 1.55 0.00 0.77 0 0
1098 0.00 1.41 0.2 0.4 0 0 3.44 3.03 2.22 0 0
1252 0.72 0.00 0.0 0.0 0 0 1.45 0.00 1.45 0 0
634 0.00 0.00 0.0 0.0 0 0 7.46 0.00 1.49 0 0
money hp hpl george num650 lab labs telnet num857 data num415 num85
2609 0.00 0 0 0.00 0 0 0 0 0 0 0 0
4069 0.00 0 0 0.00 0 0 0 0 0 0 0 0
2369 0.77 0 0 0.77 0 0 0 0 0 0 0 0
1098 0.40 0 0 0.00 0 0 0 0 0 0 0 0
1252 0.72 0 0 0.00 0 0 0 0 0 0 0 0
634 0.00 0 0 0.00 0 0 0 0 0 0 0 0
technology num1999 parts pm direct cs meeting original project re edu
2609 0 0 0 0 0 0 0 0 0 0.00 0.00
4069 0 0 0 0 0 0 0 0 0 0.00 4.00
2369 0 0 0 0 0 0 0 0 0 1.55 0.77
1098 0 0 0 0 0 0 0 0 0 0.00 0.00
1252 0 0 0 0 0 0 0 0 0 0.00 0.00
634 0 0 0 0 0 0 0 0 0 0.00 0.00
table conference charSemicolon charRoundbracket charSquarebracket
2609 0 0 0.000 0.000 0
4069 0 0 0.000 0.684 0
2369 0 0 0.000 0.490 0
1098 0 0 0.033 0.066 0
1252 0 0 0.000 0.364 0
634 0 0 0.000 0.000 0
charExclamation charDollar charHash capitalAve capitalLong capitalTotal
2609 0.480 0.000 0 2.00 7 26
4069 0.000 0.000 0 1.12 2 9
2369 0.196 0.000 0 3.16 10 79
1098 0.133 0.066 0 2.70 30 192
1252 0.729 0.121 0 7.78 32 249
634 0.000 0.000 0 2.69 15 35
type
2609 nonspam
4069 nonspam
2369 nonspam
1098 spam
1252 spam
634 spamNow let’s overwrite the rowids starting one and we will have shuffled order:
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spam_shuffled <- spam_shuffled %>%
rowid_to_column()
head(spam_shuffled) rowid make address all num3d our over remove internet order mail receive
1 1 0 0 0.00 0 0.00 0 0.00 0 0.0 0.00 0
2 2 0 0 0.00 0 0.00 0 0.00 0 0.0 0.00 0
3 3 0 0 0.00 0 0.77 0 0.00 0 0.0 0.00 0
4 4 0 0 0.40 0 0.00 0 0.20 0 0.8 0.20 0
5 5 0 0 0.72 0 0.72 0 0.72 0 0.0 0.00 0
6 6 0 0 0.00 0 0.00 0 0.00 0 0.0 1.49 0
will people report addresses free business email you credit your font num000
1 2.85 0.00 0.00 0.0 0.0 0 0 0.00 0.00 0.00 0 0
2 0.00 0.00 0.00 0.0 0.0 0 0 0.00 0.00 0.00 0 0
3 0.00 0.00 0.00 0.0 0.0 0 0 1.55 0.00 0.77 0 0
4 0.40 0.00 1.41 0.2 0.4 0 0 3.44 3.03 2.22 0 0
5 0.00 0.72 0.00 0.0 0.0 0 0 1.45 0.00 1.45 0 0
6 1.49 0.00 0.00 0.0 0.0 0 0 7.46 0.00 1.49 0 0
money hp hpl george num650 lab labs telnet num857 data num415 num85
1 0.00 0 0 0.00 0 0 0 0 0 0 0 0
2 0.00 0 0 0.00 0 0 0 0 0 0 0 0
3 0.77 0 0 0.77 0 0 0 0 0 0 0 0
4 0.40 0 0 0.00 0 0 0 0 0 0 0 0
5 0.72 0 0 0.00 0 0 0 0 0 0 0 0
6 0.00 0 0 0.00 0 0 0 0 0 0 0 0
technology num1999 parts pm direct cs meeting original project re edu
1 0 0 0 0 0 0 0 0 0 0.00 0.00
2 0 0 0 0 0 0 0 0 0 0.00 4.00
3 0 0 0 0 0 0 0 0 0 1.55 0.77
4 0 0 0 0 0 0 0 0 0 0.00 0.00
5 0 0 0 0 0 0 0 0 0 0.00 0.00
6 0 0 0 0 0 0 0 0 0 0.00 0.00
table conference charSemicolon charRoundbracket charSquarebracket
1 0 0 0.000 0.000 0
2 0 0 0.000 0.684 0
3 0 0 0.000 0.490 0
4 0 0 0.033 0.066 0
5 0 0 0.000 0.364 0
6 0 0 0.000 0.000 0
charExclamation charDollar charHash capitalAve capitalLong capitalTotal
1 0.480 0.000 0 2.00 7 26
2 0.000 0.000 0 1.12 2 9
3 0.196 0.000 0 3.16 10 79
4 0.133 0.066 0 2.70 30 192
5 0.729 0.121 0 7.78 32 249
6 0.000 0.000 0 2.69 15 35
type
1 nonspam
2 nonspam
3 nonspam
4 spam
5 spam
6 spamProportional stratified sampling
Before we discussed stratified sampling in this article. So if you want to know more about it, please have a look to it first.
What we didn’t discuss in there was doing it by proportion or by sample size.
- We will use proportional stratified sampling on
mtcars, grouped bycylindersof the cars - Then we will ungroup the stratified sample.
Let’s first see the distribution of the groups:
Hide / show the code
# From previous step
mtcars %>%
count(cyl, sort = TRUE) %>%
mutate(percent = 100 * n / sum(n)) cyl n percent
1 8 14 43.8
2 4 11 34.4
3 6 7 21.9So, our sample should include similar ratio from these groups. Let’s see what happens:
Hide / show the code
# Use proportional stratified sampling to get 30% of each cylinder group
mtcars_stratified <- mtcars %>%
group_by(cyl) %>%
slice_sample(prop =0.3) %>%
ungroup()
mtcars_stratified# A tibble: 9 × 11
mpg cyl disp hp drat wt qsec vs am gear carb
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 30.4 4 75.7 52 4.93 1.62 18.5 1 1 4 2
2 21.5 4 120. 97 3.7 2.46 20.0 1 0 3 1
3 26 4 120. 91 4.43 2.14 16.7 0 1 5 2
4 19.2 6 168. 123 3.92 3.44 18.3 1 0 4 4
5 19.7 6 145 175 3.62 2.77 15.5 0 1 5 6
6 10.4 8 472 205 2.93 5.25 18.0 0 0 3 4
7 17.3 8 276. 180 3.07 3.73 17.6 0 0 3 3
8 16.4 8 276. 180 3.07 4.07 17.4 0 0 3 3
9 14.7 8 440 230 3.23 5.34 17.4 0 0 3 4Let’s compare the groups in terms of ratios:
Hide / show the code
mtcars %>%
count(cyl, sort = TRUE) %>%
mutate(percent = 100 * n / sum(n)) cyl n percent
1 8 14 43.8
2 4 11 34.4
3 6 7 21.9Hide / show the code
mtcars_stratified %>%
count(cyl, sort = TRUE) %>%
mutate(percent = 100 * n / sum(n))# A tibble: 3 × 3
cyl n percent
<dbl> <int> <dbl>
1 8 4 44.4
2 4 3 33.3
3 6 2 22.2As we see, each group represented in the similar proportion between population and sample.
Equal counts stratified sampling
Instead of this, no matter the numbers in the population, you can say like, ” I just want to see 3 cars from each cylinder type”. Then, you can use equal counts as below:
Hide / show the code
# From previous step
mtcars_equal <- mtcars %>%
group_by(cyl) %>%
slice_sample(n = 3) %>%
ungroup()
mtcars_equal# A tibble: 9 × 11
mpg cyl disp hp drat wt qsec vs am gear carb
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 22.8 4 141. 95 3.92 3.15 22.9 1 0 4 2
2 32.4 4 78.7 66 4.08 2.2 19.5 1 1 4 1
3 21.5 4 120. 97 3.7 2.46 20.0 1 0 3 1
4 21.4 6 258 110 3.08 3.22 19.4 1 0 3 1
5 19.7 6 145 175 3.62 2.77 15.5 0 1 5 6
6 21 6 160 110 3.9 2.62 16.5 0 1 4 4
7 14.3 8 360 245 3.21 3.57 15.8 0 0 3 4
8 14.7 8 440 230 3.23 5.34 17.4 0 0 3 4
9 18.7 8 360 175 3.15 3.44 17.0 0 0 3 2Let’s check the counts:
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mtcars_equal %>%
count(cyl, sort = TRUE) %>%
mutate(percent = 100 * n / sum(n))# A tibble: 3 × 3
cyl n percent
<dbl> <int> <dbl>
1 4 3 33.3
2 6 3 33.3
3 8 3 33.3Weighted Sampling
Stratified sampling gives you guidelines on how likely it is to select rows from your dataset within specific subgroups. A broader approach to this is weighted sampling, where you can set rules for the probability of selecting individual rows. In weighted sampling, the likelihood of choosing a particular row is directly tied to its weight value. So, the higher the weight, the greater the chances of picking that row.
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# this code weights by the physical weight of the cars, so heavy cars are more likely to get
# selected
mtcars %>% slice_sample(weight_by = wt, n = 5) mpg cyl disp hp drat wt qsec vs am gear carb
Merc 450SE 16.4 8 276 180 3.07 4.07 17.4 0 0 3 3
Hornet Sportabout 18.7 8 360 175 3.15 3.44 17.0 0 0 3 2
Toyota Corona 21.5 4 120 97 3.70 2.46 20.0 1 0 3 1
Merc 450SLC 15.2 8 276 180 3.07 3.78 18.0 0 0 3 3
Pontiac Firebird 19.2 8 400 175 3.08 3.85 17.1 0 0 3 2Cluster Sampling
Stratified sampling has a drawback that requires data collection from all subgroups within the population. The challenge arises when the data collection process is costly, such as when physical travel is needed to obtain the required information. This expense can make the analysis financially burdensome.
However, there is a more cost-effective option called cluster sampling. With cluster sampling, you can limit the number of subgroups involved by randomly selecting a smaller subset through simple random sampling. Within each selected subgroup, you can then perform simple random sampling as before. This approach provides comparable results while reducing the expenses associated with collecting data from every single subgroup.
Let’s see the cut sizes in diamonds dataset:
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diamonds %>%
distinct(cut)# A tibble: 5 × 1
cut
<ord>
1 Ideal
2 Premium
3 Good
4 Very Good
5 Fair Now randomly pick some cut categories:
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# Create clusters based on diamond cut
clusters <- diamonds %>%
distinct(cut) %>%
sample_n(size = 3) %>%
pull(cut)
clusters[1] Good Fair Ideal
Levels: Fair < Good < Very Good < Premium < IdealNow we can use only these randomly picked subgroups and perform simple random sampling:
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# Perform cluster sampling
cluster_sample <- diamonds %>%
filter(cut %in% clusters) %>%
slice_sample(n = 100, replace = FALSE)
head(cluster_sample)# A tibble: 6 × 10
carat cut color clarity depth table price x y z
<dbl> <ord> <ord> <ord> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
1 3.02 Fair I I1 65.2 56 10577 9.11 9.02 5.91
2 0.34 Ideal I SI1 60.2 57 589 4.54 4.5 2.72
3 1.27 Ideal F VS2 61 59 9547 6.96 6.98 4.25
4 0.54 Ideal F VVS2 61 54 2231 5.28 5.3 3.23
5 0.43 Ideal D VS2 60.7 57 1129 4.91 4.88 2.97
6 1.01 Ideal F SI2 61.3 57 3777 6.4 6.35 3.91Hide / show the code
summary(cluster_sample$cut) Fair Good Very Good Premium Ideal
6 17 0 0 77 As we see, only 3 subgroups exists and they are randomly picked.
Conclusion
When it comes to real life data analysis, usually data is not big, it’s huge! So you will have to make some sampling one wa or another. As you can see, there are different methods you can use but they all depends on what type of data you have and how it’s collected. In the end, main objective is being away as much as possible from any kind of bias! (Which is , believe or not, one of the hardest things…)
I hope you enjoyed!😉