Sampling method and descriptive statistical function in R language

sampling method

Common sampling methods

• Simple random sampling
• Stratified sampling
• Systematic sampling

#  Import data 
# 1  Finance   2  Architecture    3  Foreign Languages 
data <- read.csv("E:\\Github\\code-learning\\R\\data\\ The first 11 Period data \\data.csv")
#  According to the specialty and ID Sort 
data <- data[order(data$ major ,data$ID),]
head(data)

	major	ID	income
375	1	A001	6811
360	1	A002	3976
505	1	A003	2692
470	1	A004	8156
214	1	A005	2169
450	1	A006	6142

Simple random sampling

Simple random sampling is the most basic sampling method . It is divided into repeated sampling and non repeated sampling . The social survey adopts non repeated sampling .

sample(x,size,replace=FALSE,prob=NULL)

• x : Sample population
• size: Sample size
• replace: Whether it has been put back
• prob: Sampling probability , Default equal probability

Use sample The function sorts the data in ascending order

#  Sample the data serial number 
#  Extraction without return 10 Samples 
index_11 <- sample(1:nrow(data),10,replace = FALSE)
index_11
data[index_11,]

1. 202
2. 181
3. 392
4. 222
5. 22
6. 117
7. 190
8. 247
9. 135
10. 169

	major	ID	income
65	2	B102	8522
369	2	B081	8386
309	3	C092	6151
169	2	B122	6439
392	1	A022	4371
41	2	B017	4203
428	2	B090	5392
44	2	B147	3291
402	2	B035	7097
523	2	B069	8141

#  The withdrawal income returned is greater than 6000 Of 5 Samples 
index_12 <- sample(data$ID,5,replace = TRUE)
index_12

1. C118
2. A006
3. B117
4. B104
5. C087

#  Random sampling with unequal probability 
sample(c("a","b","c"),size = 10,replace = TRUE,
       prob = c(0.1,0.5,0.4))

1. 'c'
2. 'c'
3. 'b'
4. 'c'
5. 'b'
6. 'b'
7. 'b'
8. 'a'
9. 'c'
10. 'b'

Stratified sampling

Stratified sampling ： First, the population is divided into several sub populations according to one or several characteristics , Each sub population is called a layer ; Then several sub samples are randomly selected from each layer , These sub samples together are the samples of the population

strata(data, stratanames=NULL, size, method=c(“srswor”,“srswr”,“poisson”,“systematic”), pik,description=FALSE)

• stratanames: Hierarchical fields
• size: Sample size of each layer
• method:
  • srswor： Don't put back the random sample
  • srswr： Put back the random sample
  • poisson： Poisson sampling
  • systematic： Systematic sampling
• pik: The probability that each data is included in the sample , Only used in unequal probability sampling
• description: TRUE when , Display the number of samples and the total number

#  Import sampling
library(sampling)

#  Stratified sampling by discipline , Each extraction 1 individual ,2 individual ,3 individual , The method is to sample without putting it back , Display description information 
index_21 <- strata(data,stratanames = " major ",size=c(1,2,3),
                   method = "srswor",description = TRUE)
index_21

Stratum 1 

Population total and number of selected units: 100 1 
Stratum 2 

Population total and number of selected units: 200 2 
Stratum 3 

Population total and number of selected units: 300 3 
Number of strata  3 
Total number of selected units 6 

	major	ID_unit	Prob	Stratum
62	1	62	0.01	1
241	2	241	0.01	2
280	2	280	0.01	2
359	3	359	0.01	3
393	3	393	0.01	3
399	3	399	0.01	3

Systematic sampling

Also known as equidistant sampling . It is a variant of pure random sampling . In systematic sampling , First, change the whole from 1～N Serial numbers , And calculate the sampling distance K=N/n. In style N Is the total number of total units ,n Is sample size . And then in 1～K Take a random number from the list k1, As the first unit of the sample , Then take k1+K,k1+2K……, Until you smoke enough n Units .
Systematic sampling shall prevent periodic deviation , Because it will reduce the representativeness of the sample . for example , The list of military personnel is usually arranged by shift ,10 Class one , The monitor is No 1 name , If the sampling distance is also taken as 10 when , Then the sample is composed of soldiers or squad leaders .

data2=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),
matrix(rep("sc",70),70,1,byrow=TRUE))
data2=cbind.data.frame(data2,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)),
1000*runif(235))
names(data2)=c("state","region","income")

#  Use “income” Field to calculate the sampling probability of each population unit 
pik=inclusionprobabilities(data2$income,10)
#  Use systematic sampling to take samples （ The sample size is 10）
s=UPsystematic(pik) 
#  Extract observed data 
getdata(data2,s)

	ID_unit	state	region	income
14	14	nc	1	172.0453
38	38	nc	1	341.7052
59	59	nc	1	616.9244
87	87	nc	1	331.2421
107	107	nc	2	150.9538
127	127	nc	2	993.4834
152	152	nc	3	992.7680
179	179	sc	1	854.8830
201	201	sc	2	638.2734
222	222	sc	2	919.4055

Describe statistics

Sometimes we just want to quickly browse the descriptive statistical characteristics of the data , If the calculation of one input function is very troublesome ,R Many functions are provided in , Multiple statistics can be displayed at once

summary function

summary() Is a function of the system itself , Include minimum and maximum values , Median , The median , Frequency statistics of quartile and category data .

vars <- c("mpg","hp","wt")
summary(mtcars[vars])

      mpg              hp              wt       
 Min.   :10.40   Min.   : 52.0   Min.   :1.513  
 1st Qu.:15.43   1st Qu.: 96.5   1st Qu.:2.581  
 Median :19.20   Median :123.0   Median :3.325  
 Mean   :20.09   Mean   :146.7   Mean   :3.217  
 3rd Qu.:22.80   3rd Qu.:180.0   3rd Qu.:3.610  
 Max.   :33.90   Max.   :335.0   Max.   :5.424  

Hmisc In bag describe function

This function provides the number of variables and observations , Number of missing values , Number of unique values , Average , Each quantile value , Five maximum and minimum values .

library(Hmisc)
describe(mtcars[vars])

mtcars[vars] 

 3  Variables      32  Observations
--------------------------------------------------------------------------------
mpg 
       n  missing distinct     Info     Mean      Gmd      .05      .10 
      32        0       25    0.999    20.09    6.796    12.00    14.34 
     .25      .50      .75      .90      .95 
   15.43    19.20    22.80    30.09    31.30 

lowest : 10.4 13.3 14.3 14.7 15.0, highest: 26.0 27.3 30.4 32.4 33.9
--------------------------------------------------------------------------------
hp 
       n  missing distinct     Info     Mean      Gmd      .05      .10 
      32        0       22    0.997    146.7    77.04    63.65    66.00 
     .25      .50      .75      .90      .95 
   96.50   123.00   180.00   243.50   253.55 

lowest :  52  62  65  66  91, highest: 215 230 245 264 335
--------------------------------------------------------------------------------
wt 
       n  missing distinct     Info     Mean      Gmd      .05      .10 
      32        0       29    0.999    3.217    1.089    1.736    1.956 
     .25      .50      .75      .90      .95 
   2.581    3.325    3.610    4.048    5.293 

lowest : 1.513 1.615 1.835 1.935 2.140, highest: 3.845 4.070 5.250 5.345 5.424
--------------------------------------------------------------------------------

pastecs In bag stat.desc function

This function can calculate a wide variety of descriptive statistics .
stat.desc(x,basic=TRUE,desc=TRUE,norm=FALSE,p=0.95)

• basic: Calculate all the values , control , The number of missing values , And min max , Range and sum .
• desc: Calculate the median , Average , Standard error of mean value , The confidence of the mean value is 95% The confidence interval of , variance , Standard deviation and coefficient of variation
• norm: Returns the normal distribution statistic （ skewness , kurtosis , Statistical significance ） and shapiro-Wilk Normal test results
• p: confidence interval

library(pastecs)
stat.desc(mtcars[vars],norm = TRUE)

	mpg	hp	wt
nbr.val	32.0000000	32.00000000	32.00000000
nbr.null	0.0000000	0.00000000	0.00000000
nbr.na	0.0000000	0.00000000	0.00000000
min	10.4000000	52.00000000	1.51300000
max	33.9000000	335.00000000	5.42400000
range	23.5000000	283.00000000	3.91100000
sum	642.9000000	4694.00000000	102.95200000
median	19.2000000	123.00000000	3.32500000
mean	20.0906250	146.68750000	3.21725000
SE.mean	1.0654240	12.12031731	0.17296847
CI.mean.0.95	2.1729465	24.71955013	0.35277153
var	36.3241028	4700.86693548	0.95737897
std.dev	6.0269481	68.56286849	0.97845744
coef.var	0.2999881	0.46740771	0.30412851
skewness	0.6106550	0.72602366	0.42314646
skew.2SE	0.7366922	0.87587259	0.51048252
kurtosis	-0.3727660	-0.13555112	-0.02271075
kurt.2SE	-0.2302812	-0.08373853	-0.01402987
normtest.W	0.9475647	0.93341934	0.94325772
normtest.p	0.1228814	0.04880824	0.09265499

All in all ,R There are many descriptive statistical functions in , These are just a few of them . Those who are interested can explore , Find your habit and use one

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