21 Статистичні функції

Автор

Юрій Клебан

21.1 Завантаження даних

library(tidyverse)

?msleep

msleep {ggplot2}

R Documentation

An updated and expanded version of the mammals sleep dataset

Description

This is an updated and expanded version of the mammals sleep dataset. Updated sleep times and weights were taken from V. M. Savage and G. B. West. A quantitative, theoretical framework for understanding mammalian sleep. Proceedings of the National Academy of Sciences, 104 (3):1051-1056, 2007.

Usage

msleep

Format

A data frame with 83 rows and 11 variables:

name: common name
genus
vore: carnivore, omnivore or herbivore?
order
conservation: the conservation status of the animal
sleep_total: total amount of sleep, in hours
sleep_rem: rem sleep, in hours
sleep_cycle: length of sleep cycle, in hours
awake: amount of time spent awake, in hours
brainwt: brain weight in kilograms
bodywt: body weight in kilograms

Details

Additional variables order, conservation status and vore were added from wikipedia.

[Package ggplot2 version 3.3.6 ]

head(msleep)

A tibble: 6 × 11
name	genus	vore	order	conservation	sleep_total	sleep_rem	sleep_cycle	awake	brainwt	bodywt
<chr>	<chr>	<chr>	<chr>	<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
Cheetah	Acinonyx	carni	Carnivora	lc	12.1	NA	NA	11.9	NA	50.000
Owl monkey	Aotus	omni	Primates	NA	17.0	1.8	NA	7.0	0.01550	0.480
Mountain beaver	Aplodontia	herbi	Rodentia	nt	14.4	2.4	NA	9.6	NA	1.350
Greater short-tailed shrew	Blarina	omni	Soricomorpha	lc	14.9	2.3	0.1333333	9.1	0.00029	0.019
Cow	Bos	herbi	Artiodactyla	domesticated	4.0	0.7	0.6666667	20.0	0.42300	600.000
Three-toed sloth	Bradypus	herbi	Pilosa	NA	14.4	2.2	0.7666667	9.6	NA	3.850

21.2 Перелік функцій

Функція	Опис
`range()`	Range (minimum and maximum) of vector
`min()`, `max()`	Minimum or maximum of vector
`mean()`, `median()`	Mean or median of vector
`sd()`	Standard deviation of vector
`table()`	Number of observations per level for a factor vector
`cor()`	Determine correlation(s) between two or more vectors
`summary()`	Summary statistics, depends on class

summary(msleep)

     name              genus               vore              order          
 Length:83          Length:83          Length:83          Length:83         
 Class :character   Class :character   Class :character   Class :character  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character  
                                                                            
                                                                            
                                                                            
                                                                            
 conservation        sleep_total      sleep_rem      sleep_cycle    
 Length:83          Min.   : 1.90   Min.   :0.100   Min.   :0.1167  
 Class :character   1st Qu.: 7.85   1st Qu.:0.900   1st Qu.:0.1833  
 Mode  :character   Median :10.10   Median :1.500   Median :0.3333  
                    Mean   :10.43   Mean   :1.875   Mean   :0.4396  
                    3rd Qu.:13.75   3rd Qu.:2.400   3rd Qu.:0.5792  
                    Max.   :19.90   Max.   :6.600   Max.   :1.5000  
                                    NA's   :22      NA's   :51      
     awake          brainwt            bodywt        
 Min.   : 4.10   Min.   :0.00014   Min.   :   0.005  
 1st Qu.:10.25   1st Qu.:0.00290   1st Qu.:   0.174  
 Median :13.90   Median :0.01240   Median :   1.670  
 Mean   :13.57   Mean   :0.28158   Mean   : 166.136  
 3rd Qu.:16.15   3rd Qu.:0.12550   3rd Qu.:  41.750  
 Max.   :22.10   Max.   :5.71200   Max.   :6654.000  
                 NA's   :27

msleep |> arrange(desc(bodywt)) |> tail()

A tibble: 6 × 11
name	genus	vore	order	conservation	sleep_total	sleep_rem	sleep_cycle	awake	brainwt	bodywt
<chr>	<chr>	<chr>	<chr>	<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
Big brown bat	Eptesicus	insecti	Chiroptera	lc	19.7	3.9	0.1166667	4.3	0.00030	0.023
House mouse	Mus	herbi	Rodentia	nt	12.5	1.4	0.1833333	11.5	0.00040	0.022
Deer mouse	Peromyscus	NA	Rodentia	NA	11.5	NA	NA	12.5	NA	0.021
Greater short-tailed shrew	Blarina	omni	Soricomorpha	lc	14.9	2.3	0.1333333	9.1	0.00029	0.019
Little brown bat	Myotis	insecti	Chiroptera	NA	19.9	2.0	0.2000000	4.1	0.00025	0.010
Lesser short-tailed shrew	Cryptotis	omni	Soricomorpha	lc	9.1	1.4	0.1500000	14.9	0.00014	0.005

mean(msleep$sleep_total)      # Mean
median(msleep$sleep_total)    # Median
max(msleep$sleep_total)       # Max
min(msleep$sleep_total)       # Min
sd(msleep$sleep_total)        # Standard deviation
var(msleep$sleep_total)       # Variance
quantile(msleep$sleep_total)  # Various quantiles

10.433734939759

10.1

19.9

1.9

4.45035699057058

19.8056773435204

0%: 1.9
25%: 7.85
50%: 10.1
75%: 13.75
100%: 19.9

msleep[msleep$sleep_total > 8,]

A tibble: 61 × 11
name	genus	vore	order	conservation	sleep_total	sleep_rem	sleep_cycle	awake	brainwt	bodywt
<chr>	<chr>	<chr>	<chr>	<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
Cheetah	Acinonyx	carni	Carnivora	lc	12.1	NA	NA	11.9	NA	50.000
Owl monkey	Aotus	omni	Primates	NA	17.0	1.8	NA	7.0	0.01550	0.480
Mountain beaver	Aplodontia	herbi	Rodentia	nt	14.4	2.4	NA	9.6	NA	1.350
Greater short-tailed shrew	Blarina	omni	Soricomorpha	lc	14.9	2.3	0.1333333	9.1	0.00029	0.019
Three-toed sloth	Bradypus	herbi	Pilosa	NA	14.4	2.2	0.7666667	9.6	NA	3.850
Northern fur seal	Callorhinus	carni	Carnivora	vu	8.7	1.4	0.3833333	15.3	NA	20.490
Dog	Canis	carni	Carnivora	domesticated	10.1	2.9	0.3333333	13.9	0.07000	14.000
Guinea pig	Cavis	herbi	Rodentia	domesticated	9.4	0.8	0.2166667	14.6	0.00550	0.728
Grivet	Cercopithecus	omni	Primates	lc	10.0	0.7	NA	14.0	NA	4.750
Chinchilla	Chinchilla	herbi	Rodentia	domesticated	12.5	1.5	0.1166667	11.5	0.00640	0.420
Star-nosed mole	Condylura	omni	Soricomorpha	lc	10.3	2.2	NA	13.7	0.00100	0.060
African giant pouched rat	Cricetomys	omni	Rodentia	NA	8.3	2.0	NA	15.7	0.00660	1.000
Lesser short-tailed shrew	Cryptotis	omni	Soricomorpha	lc	9.1	1.4	0.1500000	14.9	0.00014	0.005
Long-nosed armadillo	Dasypus	carni	Cingulata	lc	17.4	3.1	0.3833333	6.6	0.01080	3.500
North American Opossum	Didelphis	omni	Didelphimorphia	lc	18.0	4.9	0.3333333	6.0	0.00630	1.700
Big brown bat	Eptesicus	insecti	Chiroptera	lc	19.7	3.9	0.1166667	4.3	0.00030	0.023
European hedgehog	Erinaceus	omni	Erinaceomorpha	lc	10.1	3.5	0.2833333	13.9	0.00350	0.770
Patas monkey	Erythrocebus	omni	Primates	lc	10.9	1.1	NA	13.1	0.11500	10.000
Western american chipmunk	Eutamias	herbi	Rodentia	NA	14.9	NA	NA	9.1	NA	0.071
Domestic cat	Felis	carni	Carnivora	domesticated	12.5	3.2	0.4166667	11.5	0.02560	3.300
Galago	Galago	omni	Primates	NA	9.8	1.1	0.5500000	14.2	0.00500	0.200
Mongoose lemur	Lemur	herbi	Primates	vu	9.5	0.9	NA	14.5	NA	1.670
Thick-tailed opposum	Lutreolina	carni	Didelphimorphia	lc	19.4	6.6	NA	4.6	NA	0.370
Macaque	Macaca	omni	Primates	NA	10.1	1.2	0.7500000	13.9	0.17900	6.800
Mongolian gerbil	Meriones	herbi	Rodentia	lc	14.2	1.9	NA	9.8	NA	0.053
Golden hamster	Mesocricetus	herbi	Rodentia	en	14.3	3.1	0.2000000	9.7	0.00100	0.120
Vole	Microtus	herbi	Rodentia	NA	12.8	NA	NA	11.2	NA	0.035
House mouse	Mus	herbi	Rodentia	nt	12.5	1.4	0.1833333	11.5	0.00040	0.022
Little brown bat	Myotis	insecti	Chiroptera	NA	19.9	2.0	0.2000000	4.1	0.00025	0.010
Round-tailed muskrat	Neofiber	herbi	Rodentia	nt	14.6	NA	NA	9.4	NA	0.266
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
Northern grasshopper mouse	Onychomys	carni	Rodentia	lc	14.5	NA	NA	9.5	NA	0.028
Rabbit	Oryctolagus	herbi	Lagomorpha	domesticated	8.4	0.9	0.4166667	15.6	0.01210	2.500
Chimpanzee	Pan	omni	Primates	NA	9.7	1.4	1.4166667	14.3	0.44000	52.200
Tiger	Panthera	carni	Carnivora	en	15.8	NA	NA	8.2	NA	162.564
Jaguar	Panthera	carni	Carnivora	nt	10.4	NA	NA	13.6	0.15700	100.000
Lion	Panthera	carni	Carnivora	vu	13.5	NA	NA	10.5	NA	161.499
Baboon	Papio	omni	Primates	NA	9.4	1.0	0.6666667	14.6	0.18000	25.235
Desert hedgehog	Paraechinus	NA	Erinaceomorpha	lc	10.3	2.7	NA	13.7	0.00240	0.550
Potto	Perodicticus	omni	Primates	lc	11.0	NA	NA	13.0	NA	1.100
Deer mouse	Peromyscus	NA	Rodentia	NA	11.5	NA	NA	12.5	NA	0.021
Phalanger	Phalanger	NA	Diprotodontia	NA	13.7	1.8	NA	10.3	0.01140	1.620
Potoroo	Potorous	herbi	Diprotodontia	NA	11.1	1.5	NA	12.9	NA	1.100
Giant armadillo	Priodontes	insecti	Cingulata	en	18.1	6.1	NA	5.9	0.08100	60.000
Laboratory rat	Rattus	herbi	Rodentia	lc	13.0	2.4	0.1833333	11.0	0.00190	0.320
African striped mouse	Rhabdomys	omni	Rodentia	NA	8.7	NA	NA	15.3	NA	0.044
Squirrel monkey	Saimiri	omni	Primates	NA	9.6	1.4	NA	14.4	0.02000	0.743
Eastern american mole	Scalopus	insecti	Soricomorpha	lc	8.4	2.1	0.1666667	15.6	0.00120	0.075
Cotton rat	Sigmodon	herbi	Rodentia	NA	11.3	1.1	0.1500000	12.7	0.00118	0.148
Mole rat	Spalax	NA	Rodentia	NA	10.6	2.4	NA	13.4	0.00300	0.122
Arctic ground squirrel	Spermophilus	herbi	Rodentia	lc	16.6	NA	NA	7.4	0.00570	0.920
Thirteen-lined ground squirrel	Spermophilus	herbi	Rodentia	lc	13.8	3.4	0.2166667	10.2	0.00400	0.101
Golden-mantled ground squirrel	Spermophilus	herbi	Rodentia	lc	15.9	3.0	NA	8.1	NA	0.205
Musk shrew	Suncus	NA	Soricomorpha	NA	12.8	2.0	0.1833333	11.2	0.00033	0.048
Pig	Sus	omni	Artiodactyla	domesticated	9.1	2.4	0.5000000	14.9	0.18000	86.250
Short-nosed echidna	Tachyglossus	insecti	Monotremata	NA	8.6	NA	NA	15.4	0.02500	4.500
Eastern american chipmunk	Tamias	herbi	Rodentia	NA	15.8	NA	NA	8.2	NA	0.112
Tenrec	Tenrec	omni	Afrosoricida	NA	15.6	2.3	NA	8.4	0.00260	0.900
Tree shrew	Tupaia	omni	Scandentia	NA	8.9	2.6	0.2333333	15.1	0.00250	0.104
Arctic fox	Vulpes	carni	Carnivora	NA	12.5	NA	NA	11.5	0.04450	3.380
Red fox	Vulpes	carni	Carnivora	NA	9.8	2.4	0.3500000	14.2	0.05040	4.230

sum(msleep$sleep_total > 8)   # Frequency (count)
mean(msleep$sleep_total > 8)  # Relative frequency (proportion)

0.734939759036145

mean(msleep$sleep_rem)

<NA>

mean(msleep$sleep_rem, na.rm = TRUE)

1.87540983606557

cor(msleep$sleep_total, msleep$sleep_rem)

<NA>

cor(msleep$sleep_total, msleep$sleep_rem, use = "complete.obs")

0.751754999228714

table(msleep$vore)


  carni   herbi insecti    omni 
     19      32       5      20

proportions(table(msleep$vore))


     carni      herbi    insecti       omni 
0.25000000 0.42105263 0.06578947 0.26315789

# Counts:
table(msleep$vore, msleep$conservation)

# Proportions, per row:
proportions(table(msleep$vore, msleep$conservation),
            margin = 1)

         
          cd domesticated en lc nt vu
  carni    1            2  1  5  1  4
  herbi    1            7  2 10  3  3
  insecti  0            0  1  2  0  0
  omni     0            1  0  8  0  0

         
                  cd domesticated         en         lc         nt         vu
  carni   0.07142857   0.14285714 0.07142857 0.35714286 0.07142857 0.28571429
  herbi   0.03846154   0.26923077 0.07692308 0.38461538 0.11538462 0.11538462
  insecti 0.00000000   0.00000000 0.33333333 0.66666667 0.00000000 0.00000000
  omni    0.00000000   0.11111111 0.00000000 0.88888889 0.00000000 0.00000000

TASK

Load ggplot2 using library(ggplot2) if you have not already done so. Then do the following:

View the documentation for the diamonds data and read about different the variables.

Check the data structures: how many observations and variables are there and what type of variables (numeric, categorical, etc.) are there?

Compute summary statistics (means, median, min, max, counts for categorical variables). Are there any missing values?

plot(msleep$sleep_total, msleep$sleep_rem)

library(ggplot2)
ggplot(msleep, aes(x = sleep_total, y = sleep_rem)) + geom_point()

Warning message:
"Removed 22 rows containing missing values (geom_point)."

plot(msleep$sleep_total, msleep$sleep_rem, pch = 16)
grid()

ggplot(msleep, aes(sleep_total, sleep_rem, colour = vore)) +
      geom_point() +
      xlab("Total sleep time (h)")

Warning message:
"Removed 22 rows containing missing values (geom_point)."

21.3 Інші методи

library(psych)
describe(msleep)

A psych: 11 × 13
	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
name*	1	83	42.0000000	24.1039416	42.0000000	42.00000000	31.13460000	1.0000000	83.000	82.000000	0.00000000	-1.2434523	2.64575131
genus*	2	83	40.2530120	22.5176589	41.0000000	40.44776119	28.16940000	1.0000000	77.000	76.000000	-0.05639775	-1.2520857	2.47163416
vore*	3	76	2.3421053	1.1260862	2.0000000	2.30645161	1.48260000	1.0000000	4.000	3.000000	0.41786835	-1.2479239	0.12917095
order*	4	83	11.2771084	6.1511713	15.0000000	11.53731343	4.44780000	1.0000000	19.000	18.000000	-0.37717341	-1.5460760	0.67517877
conservation*	5	54	3.7777778	1.3127340	4.0000000	3.77272727	0.74130000	1.0000000	6.000	5.000000	-0.13522194	-0.5048689	0.17864046
sleep_total	6	83	10.4337349	4.4503570	10.1000000	10.38358209	5.04084000	1.9000000	19.900	18.000000	0.05230964	-0.7074466	0.48849014
sleep_rem	7	61	1.8754098	1.2982881	1.5000000	1.70816327	1.18608000	0.1000000	6.600	6.500000	1.46161590	2.7342493	0.16622875
sleep_cycle	8	32	0.4395833	0.3586801	0.3333333	0.37628205	0.23474500	0.1166667	1.500	1.383333	1.49498905	1.5749153	0.06340629
awake	9	83	13.5674699	4.4520852	13.9000000	13.61716418	5.04084000	4.1000000	22.100	18.000000	-0.05133450	-0.7073810	0.48867984
brainwt	10	56	0.2815814	0.9764137	0.0124000	0.06602717	0.01784309	0.0001400	5.712	5.711860	4.62750025	20.9636487	0.13047877
bodywt	11	83	166.1363494	786.8397316	1.6700000	20.48743284	2.43442920	0.0050000	6654.000	6653.995000	7.10016261	53.7180357	86.36688086

describe(
          msleep, 
          fast = TRUE, 
          quant = c(0.25, 0.50, 0.75), 
          ranges = FALSE, 
)

A psych: 11 × 8
	vars	n	mean	sd	se	Q0.25	Q0.5	Q0.75
	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
name	1	83	NaN	NA	NA	NA	NA	NA
genus	2	83	NaN	NA	NA	NA	NA	NA
vore	3	76	NaN	NA	NA	NA	NA	NA
order	4	83	NaN	NA	NA	NA	NA	NA
conservation	5	54	NaN	NA	NA	NA	NA	NA
sleep_total	6	83	10.4337349	4.4503570	0.48849014	7.8500000	10.1000000	13.7500000
sleep_rem	7	61	1.8754098	1.2982881	0.16622875	0.9000000	1.5000000	2.4000000
sleep_cycle	8	32	0.4395833	0.3586801	0.06340629	0.1833333	0.3333333	0.5791667
awake	9	83	13.5674699	4.4520852	0.48867984	10.2500000	13.9000000	16.1500000
brainwt	10	56	0.2815814	0.9764137	0.13047877	0.0029000	0.0124000	0.1255000
bodywt	11	83	166.1363494	786.8397316	86.36688086	0.1740000	1.6700000	41.7500000

21.3.1 Описова статистика для групи

describe(
          msleep ~ vore,
          fast = TRUE, 
          quant = c(0.25, 0.50, 0.75), 
          ranges = FALSE, omit = TRUE
)


 Descriptive statistics by group 
vore: carni
             vars  n  mean     sd    se Q0.25  Q0.5 Q0.75
name            1 19   NaN     NA    NA    NA    NA    NA
genus           2 19   NaN     NA    NA    NA    NA    NA
vore            3 19   NaN     NA    NA    NA    NA    NA
order           4 19   NaN     NA    NA    NA    NA    NA
conservation    5 14   NaN     NA    NA    NA    NA    NA
sleep_total     6 19 10.38   4.67  1.07  6.25 10.40 13.00
sleep_rem       7 10  2.29   1.86  0.59  1.33  1.95  3.05
sleep_cycle     8  5  0.37   0.03  0.01  0.35  0.38  0.38
awake           9 19 13.63   4.68  1.07 11.00 13.60 17.75
brainwt        10  9  0.08   0.10  0.03  0.02  0.04  0.07
bodywt         11 19 90.75 182.07 41.77  3.34 20.49 93.00
------------------------------------------------------------ 
vore: herbi
             vars  n   mean      sd     se Q0.25  Q0.5 Q0.75
name            1 32    NaN      NA     NA    NA    NA    NA
genus           2 32    NaN      NA     NA    NA    NA    NA
vore            3 32    NaN      NA     NA    NA    NA    NA
order           4 32    NaN      NA     NA    NA    NA    NA
conservation    5 26    NaN      NA     NA    NA    NA    NA
sleep_total     6 32   9.51    4.88   0.86  4.30 10.30 14.22
sleep_rem       7 24   1.37    0.92   0.19  0.60  0.95  1.97
sleep_cycle     8 12   0.42    0.32   0.09  0.18  0.22  0.69
awake           9 32  14.49    4.88   0.86  9.78 13.70 19.70
brainwt        10 20   0.62    1.57   0.35  0.01  0.01  0.24
bodywt         11 32 366.88 1244.08 219.92  0.19  1.23 39.00
------------------------------------------------------------ 
vore: insecti
             vars n  mean    sd    se Q0.25  Q0.5 Q0.75
name            1 5   NaN    NA    NA    NA    NA    NA
genus           2 5   NaN    NA    NA    NA    NA    NA
vore            3 5   NaN    NA    NA    NA    NA    NA
order           4 5   NaN    NA    NA    NA    NA    NA
conservation    5 3   NaN    NA    NA    NA    NA    NA
sleep_total     6 5 14.94  5.92  2.65  8.60 18.10 19.70
sleep_rem       7 4  3.52  1.93  0.96  2.08  3.00  4.45
sleep_cycle     8 3  0.16  0.04  0.02  0.14  0.17  0.18
awake           9 5  9.06  5.92  2.65  4.30  5.90 15.40
brainwt        10 5  0.02  0.03  0.02  0.00  0.00  0.03
bodywt         11 5 12.92 26.39 11.80  0.02  0.07  4.50
------------------------------------------------------------ 
vore: omni
             vars  n  mean    sd   se Q0.25  Q0.5 Q0.75
name            1 20   NaN    NA   NA    NA    NA    NA
genus           2 20   NaN    NA   NA    NA    NA    NA
vore            3 20   NaN    NA   NA    NA    NA    NA
order           4 20   NaN    NA   NA    NA    NA    NA
conservation    5  9   NaN    NA   NA    NA    NA    NA
sleep_total     6 20 10.93  2.95 0.66  9.10  9.90 10.93
sleep_rem       7 18  1.96  1.01 0.24  1.25  1.85  2.30
sleep_cycle     8 11  0.59  0.47 0.14  0.26  0.50  0.71
awake           9 20 13.07  2.95 0.66 13.07 14.10 14.90
brainwt        10 17  0.15  0.32 0.08  0.00  0.01  0.18
bodywt         11 20 12.72 24.69 5.52  0.18  0.95  7.60

** Refs **

https://www.agroninfo.com/computing-summary-statistics-in-r/