5 Basic statistics

5.1 The essentials of R

5.1.1 Manipulation of vector

library(tidyverse)
library(dplyr)
vec <- c(3,5,2,1,5,"O",NA)
length(unique(vec))

## [1] 6

num_vec <- as.numeric(vec)
log(num_vec)

## [1] 1.0986123 1.6094379 0.6931472 0.0000000 1.6094379        NA        NA

sum(c(num_vec, NA), na.rm=T)

## [1] 16

sort(num_vec, decreasing = T)

## [1] 5 5 3 2 1

is.na(num_vec)

## [1] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE

num_vec[!is.na(num_vec)]

## [1] 3 5 2 1 5

c(5,6) %in% vec

## [1]  TRUE FALSE

grepl("5", vec)

## [1] FALSE  TRUE FALSE FALSE  TRUE FALSE FALSE

5.1.2 Generate sequence or repeted sequece

seq(from = 0, to = 10, by = 0.5)

##  [1]  0.0  0.5  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  5.0  5.5  6.0  6.5  7.0
## [16]  7.5  8.0  8.5  9.0  9.5 10.0

rep(x = 1:3, times = 4)

##  [1] 1 2 3 1 2 3 1 2 3 1 2 3

rep(x = 1:3, each = 4)

##  [1] 1 1 1 1 2 2 2 2 3 3 3 3

5.1.3 Get directory and write data out and in

getwd()

## [1] "C:/Users/hed2/Downloads/mybook2/mybook2"

setwd(getwd())
write.csv(cars, "cars.csv", row.names=F)
dataframe  <- read.csv("cars.csv")

5.1.4 Function

my_func <- function(x){
  x_mod <- (x + 7) * 4
  return(x_mod)
}

my_func(num_vec)

## [1] 40 48 36 32 48 NA NA

5.1.5 Plot

plot(dist ~ speed, data=cars)

hist(cars$dist )

### Build model and plot

model <- lm(dist ~ speed, data=cars)
plot(dist ~ speed, data=cars)
abline(model)
abline(v = 25)
abline(h = 15)

### Rename names of columns

names(cars)

## [1] "speed" "dist"

names(cars) <- c("speed per hour", "total dist")

5.1.6 Class of dataframe

matrix <- as.matrix(cars)
df <- as.data.frame(matrix)
class(matrix)

## [1] "matrix" "array"

class(df)

## [1] "data.frame"

# tranform
t(matrix)

speed per hour	4	4	7	7	8	9	10	10	10	11	11	12	12	12	12	13	13	13	13	14	14	14	14	15	15	15	16	16	17	17	17	18	18	18	18	19	19	19	20	20	20	20	20	22	23	24	24	24	24	25
total dist	2	10	4	22	16	10	18	26	34	17	28	14	20	24	28	26	34	34	46	26	36	60	80	20	26	54	32	40	32	40	50	42	56	76	84	36	46	68	32	48	52	56	64	66	54	70	92	93	120	85

5.1.7 Generate new variable for dataframe (character)

paste0("raster_", 1:10)

##  [1] "raster_1"  "raster_2"  "raster_3"  "raster_4"  "raster_5"  "raster_6" 
##  [7] "raster_7"  "raster_8"  "raster_9"  "raster_10"

paste0("raster_", rep(x = 1:5, times = 10))

##  [1] "raster_1" "raster_2" "raster_3" "raster_4" "raster_5" "raster_1"
##  [7] "raster_2" "raster_3" "raster_4" "raster_5" "raster_1" "raster_2"
## [13] "raster_3" "raster_4" "raster_5" "raster_1" "raster_2" "raster_3"
## [19] "raster_4" "raster_5" "raster_1" "raster_2" "raster_3" "raster_4"
## [25] "raster_5" "raster_1" "raster_2" "raster_3" "raster_4" "raster_5"
## [31] "raster_1" "raster_2" "raster_3" "raster_4" "raster_5" "raster_1"
## [37] "raster_2" "raster_3" "raster_4" "raster_5" "raster_1" "raster_2"
## [43] "raster_3" "raster_4" "raster_5" "raster_1" "raster_2" "raster_3"
## [49] "raster_4" "raster_5"

df$group <- paste0("raster_", rep(x = 1:5, times = 10))
df$id <-  paste0("raster_",  1:50)

5.1.8 Create a new dataframe using ‘rnorm’ - random number from distribution

sample <-  round((rnorm(50,0, 1)),2)
group <- paste0("raster_", rep(x = 1:5, times = 10))

df_join <- data.frame(sample, group)
df_join$id <-  paste0("raster_",  1:50)

5.1.9 Left join two dataframes

library(dplyr)
data_all <- left_join(df, df_join, by="id")
head(data_all)

speed per hour	total dist	group.x	id	sample	group.y
4	2	raster_1	raster_1	-0.01	raster_1
4	10	raster_2	raster_2	-1.78	raster_2
7	4	raster_3	raster_3	-0.78	raster_3
7	22	raster_4	raster_4	0.13	raster_4
8	16	raster_5	raster_5	-0.71	raster_5
9	10	raster_1	raster_6	-0.04	raster_1

5.1.10 Select variables

select(data_all, group.x, id  )

group.x	id
raster_1	raster_1
raster_2	raster_2
raster_3	raster_3
raster_4	raster_4
raster_5	raster_5
raster_1	raster_6
raster_2	raster_7
raster_3	raster_8
raster_4	raster_9
raster_5	raster_10
raster_1	raster_11
raster_2	raster_12
raster_3	raster_13
raster_4	raster_14
raster_5	raster_15
raster_1	raster_16
raster_2	raster_17
raster_3	raster_18
raster_4	raster_19
raster_5	raster_20
raster_1	raster_21
raster_2	raster_22
raster_3	raster_23
raster_4	raster_24
raster_5	raster_25
raster_1	raster_26
raster_2	raster_27
raster_3	raster_28
raster_4	raster_29
raster_5	raster_30
raster_1	raster_31
raster_2	raster_32
raster_3	raster_33
raster_4	raster_34
raster_5	raster_35
raster_1	raster_36
raster_2	raster_37
raster_3	raster_38
raster_4	raster_39
raster_5	raster_40
raster_1	raster_41
raster_2	raster_42
raster_3	raster_43
raster_4	raster_44
raster_5	raster_45
raster_1	raster_46
raster_2	raster_47
raster_3	raster_48
raster_4	raster_49
raster_5	raster_50

5.1.11 Filter observations

raster_1 <- filter(data_all, group.x == "raster_1")
raster_1

speed per hour	total dist	group.x	id	sample	group.y
4	2	raster_1	raster_1	-0.01	raster_1
9	10	raster_1	raster_6	-0.04	raster_1
11	28	raster_1	raster_11	-0.31	raster_1
13	26	raster_1	raster_16	2.19	raster_1
14	36	raster_1	raster_21	1.45	raster_1
15	54	raster_1	raster_26	0.85	raster_1
17	50	raster_1	raster_31	1.11	raster_1
19	36	raster_1	raster_36	0.27	raster_1
20	52	raster_1	raster_41	-1.49	raster_1
24	70	raster_1	raster_46	-2.16	raster_1

speed_dist <- filter(data_all, data_all$`speed per hour` < 11 & data_all$`total dist` >= 10)
speed_dist

speed per hour	total dist	group.x	id	sample	group.y
4	10	raster_2	raster_2	-1.78	raster_2
7	22	raster_4	raster_4	0.13	raster_4
8	16	raster_5	raster_5	-0.71	raster_5
9	10	raster_1	raster_6	-0.04	raster_1
10	18	raster_2	raster_7	-0.47	raster_2
10	26	raster_3	raster_8	0.61	raster_3
10	34	raster_4	raster_9	1.17	raster_4

5.1.12 Append rows

rbind(raster_1,speed_dist)

speed per hour	total dist	group.x	id	sample	group.y
4	2	raster_1	raster_1	-0.01	raster_1
9	10	raster_1	raster_6	-0.04	raster_1
11	28	raster_1	raster_11	-0.31	raster_1
13	26	raster_1	raster_16	2.19	raster_1
14	36	raster_1	raster_21	1.45	raster_1
15	54	raster_1	raster_26	0.85	raster_1
17	50	raster_1	raster_31	1.11	raster_1
19	36	raster_1	raster_36	0.27	raster_1
20	52	raster_1	raster_41	-1.49	raster_1
24	70	raster_1	raster_46	-2.16	raster_1
4	10	raster_2	raster_2	-1.78	raster_2
7	22	raster_4	raster_4	0.13	raster_4
8	16	raster_5	raster_5	-0.71	raster_5
9	10	raster_1	raster_6	-0.04	raster_1
10	18	raster_2	raster_7	-0.47	raster_2
10	26	raster_3	raster_8	0.61	raster_3
10	34	raster_4	raster_9	1.17	raster_4

5.1.13 Create new variables instead of old variables

mutate(data_all, 
       sample = round(sample,1))

speed per hour	total dist	group.x	id	sample	group.y
4	2	raster_1	raster_1	0.0	raster_1
4	10	raster_2	raster_2	-1.8	raster_2
7	4	raster_3	raster_3	-0.8	raster_3
7	22	raster_4	raster_4	0.1	raster_4
8	16	raster_5	raster_5	-0.7	raster_5
9	10	raster_1	raster_6	0.0	raster_1
10	18	raster_2	raster_7	-0.5	raster_2
10	26	raster_3	raster_8	0.6	raster_3
10	34	raster_4	raster_9	1.2	raster_4
11	17	raster_5	raster_10	-0.8	raster_5
11	28	raster_1	raster_11	-0.3	raster_1
12	14	raster_2	raster_12	1.4	raster_2
12	20	raster_3	raster_13	-2.2	raster_3
12	24	raster_4	raster_14	-0.3	raster_4
12	28	raster_5	raster_15	2.1	raster_5
13	26	raster_1	raster_16	2.2	raster_1
13	34	raster_2	raster_17	0.2	raster_2
13	34	raster_3	raster_18	-0.9	raster_3
13	46	raster_4	raster_19	0.2	raster_4
14	26	raster_5	raster_20	-0.7	raster_5
14	36	raster_1	raster_21	1.4	raster_1
14	60	raster_2	raster_22	-0.8	raster_2
14	80	raster_3	raster_23	0.4	raster_3
15	20	raster_4	raster_24	0.6	raster_4
15	26	raster_5	raster_25	-0.8	raster_5
15	54	raster_1	raster_26	0.8	raster_1
16	32	raster_2	raster_27	-0.8	raster_2
16	40	raster_3	raster_28	0.6	raster_3
17	32	raster_4	raster_29	1.1	raster_4
17	40	raster_5	raster_30	-1.0	raster_5
17	50	raster_1	raster_31	1.1	raster_1
18	42	raster_2	raster_32	-0.5	raster_2
18	56	raster_3	raster_33	0.3	raster_3
18	76	raster_4	raster_34	0.2	raster_4
18	84	raster_5	raster_35	-0.4	raster_5
19	36	raster_1	raster_36	0.3	raster_1
19	46	raster_2	raster_37	-1.2	raster_2
19	68	raster_3	raster_38	-0.1	raster_3
20	32	raster_4	raster_39	0.8	raster_4
20	48	raster_5	raster_40	-2.2	raster_5
20	52	raster_1	raster_41	-1.5	raster_1
20	56	raster_2	raster_42	-1.2	raster_2
20	64	raster_3	raster_43	-1.6	raster_3
22	66	raster_4	raster_44	0.4	raster_4
23	54	raster_5	raster_45	-1.0	raster_5
24	70	raster_1	raster_46	-2.2	raster_1
24	92	raster_2	raster_47	-0.6	raster_2
24	93	raster_3	raster_48	-0.4	raster_3
24	120	raster_4	raster_49	0.9	raster_4
25	85	raster_5	raster_50	-1.1	raster_5

5.1.14 summarise statistics

 summarise(data_all,
          mean_speed = mean(sample),
          max_dist = max( "total dist" ))

mean_speed	max_dist
-0.1862	total dist

5.1.15 Group dataframe then summarise statistics

data_all_group <-   group_by(data_all, group.x)   
 summarise(data_all_group, 
          mean_speed = mean(sample),
          max_dist = max( "total dist" ))

mean_speed	max_dist
-0.1862	total dist

5.1.16 Ungroup then summarise statistics

ungroup_data <- ungroup( data_all_group)
 summarise(  ungroup_data , 
          mean_speed = mean(sample),
          max_dist = max( "total dist" ))

mean_speed	max_dist
-0.1862	total dist

5.1.17 Summary linear regression model

mod1 <- lm(cars$`total dist` ~ cars$`speed per hour` )
summary(mod1) 

## 
## Call:
## lm(formula = cars$`total dist` ~ cars$`speed per hour`)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.069  -9.525  -2.272   9.215  43.201 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           -17.5791     6.7584  -2.601   0.0123 *  
## cars$`speed per hour`   3.9324     0.4155   9.464 1.49e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared:  0.6511, Adjusted R-squared:  0.6438 
## F-statistic: 89.57 on 1 and 48 DF,  p-value: 1.49e-12

5.1.18 Create frequency table

table(data_all_group$`speed per hour`,data_all_group$group.x  )

/	raster_1	raster_2	raster_3	raster_4	raster_5
4	1	1	0	0	0
7	0	0	1	1	0
8	0	0	0	0	1
9	1	0	0	0	0
10	0	1	1	1	0
11	1	0	0	0	1
12	0	1	1	1	1
13	1	1	1	1	0
14	1	1	1	0	1
15	1	0	0	1	1
16	0	1	1	0	0
17	1	0	0	1	1
18	0	1	1	1	1
19	1	1	1	0	0
20	1	1	1	1	1
22	0	0	0	1	0
23	0	0	0	0	1
24	1	1	1	1	0
25	0	0	0	0	1

5.1.19 Value and variable label

table(iris$Species)

setosa	versicolor	virginica
50	50	50

iris$Species <- factor(iris$Species,labels = c( "setosanew","versicolornew","virginianew"))
table(iris$Species)

setosanew	versicolornew	virginianew
50	50	50

library(Hmisc)

label(iris$Species) <- "Species types"
table(iris$Species)

setosanew	versicolornew	virginianew
50	50	50

5.1.20 Recode a variable

irisifelse <-  iris%>% 
mutate(Sepal.Length2 = ifelse(Sepal.Length < 6 , "level1", ifelse(Sepal.Length < 7 , "level2", Sepal.Length)))

table(irisifelse$Sepal.Length2)

7	7.1	7.2	7.3	7.4	7.6	7.7	7.9	level1	level2
1	1	3	1	1	1	4	1	83	54

5.2 Central Limit Theorem

see here

5.3 Common statistical distribution

see here