Basic statistics assignment

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Problem 0.1

• random sample of size 10 from a standard Normal distribution

set.seed(1234)#for producing same results
x=rnorm(10);
x

##  [1] -1.2070657  0.2774292  1.0844412 -2.3456977  0.4291247  0.5060559
##  [7] -0.5747400 -0.5466319 -0.5644520 -0.8900378

Problem 0.1

• a logical vector indicating whether elements of the sample are greater than 0

x>0

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

Problem 0.1

• a character vector of length 10

chavec=c("one","two","three","four","five","six","seven","eight","nine","ten")
length(chavec)

## [1] 10

Problem 0.1

• a a factor vector of length 10, with 3 different factor “levels”

facvec=as.factor(c(rep("male",3),rep("female",4),rep("both",3)))
levels(facvec)

## [1] "both"   "female" "male"

dataframe

dt=data.frame(x=x,charve=chavec,facvec=facvec)
mean(dt$x)

## [1] -0.3831574

The only mean that we get is for the numeric variable x. The other two (character and factor) generate errors when called.

Problem 2: palmerpenguins

library(dplyr) # data cleaning package
library(corrplot) # for correlation plot
library(GGally) #
library(psych)
data("penguins", package = "palmerpenguins")#reading in the required data
df=penguins#assigning a new name to it
cat("The data has",dim(df)[1],"rows","and",dim(df)[2],"columns")

## The data has 344 rows and 8 columns

colnames(df)#it gives the columns names

## [1] "species"           "island"            "bill_length_mm"   
## [4] "bill_depth_mm"     "flipper_length_mm" "body_mass_g"      
## [7] "sex"               "year"

#Summary stats
summary(penguins)

##       species          island    bill_length_mm  bill_depth_mm  
##  Adelie   :152   Biscoe   :168   Min.   :32.10   Min.   :13.10  
##  Chinstrap: 68   Dream    :124   1st Qu.:39.23   1st Qu.:15.60  
##  Gentoo   :124   Torgersen: 52   Median :44.45   Median :17.30  
##                                  Mean   :43.92   Mean   :17.15  
##                                  3rd Qu.:48.50   3rd Qu.:18.70  
##                                  Max.   :59.60   Max.   :21.50  
##                                  NA's   :2       NA's   :2      
##  flipper_length_mm  body_mass_g       sex           year     
##  Min.   :172.0     Min.   :2700   female:165   Min.   :2007  
##  1st Qu.:190.0     1st Qu.:3550   male  :168   1st Qu.:2007  
##  Median :197.0     Median :4050   NA's  : 11   Median :2008  
##  Mean   :200.9     Mean   :4202                Mean   :2008  
##  3rd Qu.:213.0     3rd Qu.:4750                3rd Qu.:2009  
##  Max.   :231.0     Max.   :6300                Max.   :2009  
##  NA's   :2         NA's   :2

#plots
psych::pairs.panels(penguins)

we drop empty observations in sex variable

penguins <- penguins %>% filter(sex == 'male' | sex == 'female')
summary(penguins)

##       species          island    bill_length_mm  bill_depth_mm  
##  Adelie   :146   Biscoe   :163   Min.   :32.10   Min.   :13.10  
##  Chinstrap: 68   Dream    :123   1st Qu.:39.50   1st Qu.:15.60  
##  Gentoo   :119   Torgersen: 47   Median :44.50   Median :17.30  
##                                  Mean   :43.99   Mean   :17.16  
##                                  3rd Qu.:48.60   3rd Qu.:18.70  
##                                  Max.   :59.60   Max.   :21.50  
##  flipper_length_mm  body_mass_g       sex           year     
##  Min.   :172       Min.   :2700   female:165   Min.   :2007  
##  1st Qu.:190       1st Qu.:3550   male  :168   1st Qu.:2007  
##  Median :197       Median :4050                Median :2008  
##  Mean   :201       Mean   :4207                Mean   :2008  
##  3rd Qu.:213       3rd Qu.:4775                3rd Qu.:2009  
##  Max.   :231       Max.   :6300                Max.   :2009

penguins %>% group_by(species) %>% tally()

## # A tibble: 3 × 2
##   species       n
##   <fct>     <int>
## 1 Adelie      146
## 2 Chinstrap    68
## 3 Gentoo      119

penguins %>%group_by(species) %>% summarise_if(is.numeric, funs(mean,median)) %>% knitr::kable()

species	bill_length_mm_mean	bill_depth_mm_mean	flipper_length_mm_mean	body_mass_g_mean	year_mean	bill_length_mm_median	bill_depth_mm_median	flipper_length_mm_median	body_mass_g_median	year_median
Adelie	38.82397	18.34726	190.1027	3706.164	2008.055	38.85	18.40	190	3700	2008
Chinstrap	48.83382	18.42059	195.8235	3733.088	2007.971	49.55	18.45	196	3700	2008
Gentoo	47.56807	14.99664	217.2353	5092.437	2008.067	47.40	15.00	216	5050	2008

Penguins distributions

table(penguins$species, penguins$island)

##            
##             Biscoe Dream Torgersen
##   Adelie        44    55        47
##   Chinstrap      0    68         0
##   Gentoo       119     0         0

chisq.test(table(penguins$species, penguins$island)) # meaningful difference

## 
##  Pearson's Chi-squared test
## 
## data:  table(penguins$species, penguins$island)
## X-squared = 284.59, df = 4, p-value < 2.2e-16

ggplot(penguins, aes(x = island, y = species, color = species)) +
  geom_jitter(size = 3)  +ggtitle('Penguins by Island')

ggplot(data = penguins) + geom_point(mapping = aes(x = flipper_length_mm, y = bill_length_mm, color = species)) +
facet_wrap(~species) + geom_smooth(mapping = aes(x = flipper_length_mm, y = bill_length_mm)) + 
labs(title = "Bill vs flipper length by species")