Basic Statistics - (02) R[1]

 
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Basic Statistics - (02) R[1]

1. Bar Graph

  • Making A Bar Graph

    We easily can make graphs to visualize our data. Let’s visualize the number of manual and automatic transmissions in our car sample through a bar graph, using the function barplot(). The first argument of barplot() is a vector containing the heights of each bar. These heights correspond to the proportional frequencies of a desired measure in your data. You can obtain this information using the table() function.

    We are going to make a bar graph of the am (transmission) variable of the mtcars dataset. In this case, the height of the bars can be the frequency of manual and automatic transmission cars. Therefore, here we are going to use table() and barplot() to make this plot.

    Remember, you can select a specific variable using either $ or [,]. If you need to look at your data you can simply enter mtcars into your console, or if you just want to check the variables you can always enter str(mtcars) in your console.

    • Instructions

      • In your script, create an object called height using the frequencies of the am variable of the mtcars dataset
      • Use this variable and the barplot() function to create a bar plot of transmission types in our car sample

    • Answer

      #Assign the frequency of the mtcars variable "am" to a variable called "height"
str(mtcars)
height <- table(mtcars$am)
#Create a barplot of "height"
barplot(height)

      > #Assign the frequency of the mtcars variable "am" to a variable called "height"
> str(mtcars)
'data.frame':	32 obs. of  11 variables:
 $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
 $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
 $ disp: num  160 160 108 258 360 ...
 $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
 $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
 $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
 $ qsec: num  16.5 17 18.6 19.4 17 ...
 $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
 $ am  : Factor w/ 2 levels "0","1": 2 2 2 1 1 1 1 1 1 1 ...
 $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
 $ carb: num  4 4 1 1 2 1 4 2 2 4 ...
> height <- table(mtcars$am)
> #Create a barplot of "height"
> barplot(height)

  • Labelling A Bar Graph

    Now we’re going to add some labels to the bar graph, still using barplot(). The first argument of barplot() was a vector of the bar heights. Following this, we can add arguments to format the graph as necessary. For instance, barplot(height, argument1, argument2). Here we are going to add a label to the y axis using the argument ylab = "name here", and x axis labels to the bars using the argument names.arg = "vector of names here".

    • Instruction

      • Make a vector of the names of the bars using the c() command. Assign this to the variable barnames. Remember that the first bar is automatic and the second is manual.
      • Add the ylab = and names.arg = commands to your barplot(height) code
      • Label the y axis “number of cars” and use barnames to label the bars.
      • Remeber that arguments in a function are separated with a comma (e.g. function(argument1, argument2, argument3))

    • Answer

      # vector of bar heights
height <- table(mtcars$am)
# Make a vector of the names of the bars called "barnames"
barnames <- c("automatic","manual")
# Label the y axis "number of cars" and label the bars using barnames
barplot(height, ylab = "number of cars", names.arg = barnames)

2. Histograms

  • Making A Histogram

    It can be useful to plot frequencies as histograms to visualize the spread of our data.

    Let’s make a histogram of the number of carburetors in our mtcars dataset using the function hist(). The first argument of hist() is vector of values for which the histogram is desired. Following this, we can add arguments to format the graph as necessary. For instance, hist(variable, argument1, argument2)

    • Instruction

      • In your script, write a code to produce a histogram of the number of carburetors in each car using the variable carb of the data set mtcars.
      • Make the title of this histogram “Carburetors” by adding the argument main = "title*" inside your hist() function.
      • Remember, you can select a specific variable using either $ or [,]. If you need to look at your data you can simply enter mtcars into your console, or if you just want to check the variables you can always enter str(mtcars) in your console.

    • Answer

      # Make a histogram of the carb variable from the mtcars data set. Set the title to "Carburetors"
hist(mtcars$carb, main = "Carburetors")

  • Formatting Your Histogram

    Sometimes we have to change things because R’s default setting isn’t suitable for our graph. In the same way as we added a title argument to hist(), we can change the scale of the y-axis through adding the argument ylim followed by the range we want (e.g. for a scale from 0 to 50, we would say ylim = c(0,50)). We can also label the x-axis using the argument xlab = "title", or change the colour of the bars to blue with the argument col = "blue".

    • Instruction

      • Change the y axis scale from 0 to 20
      • Make the bars “red”
      • Label the x-axis “Number of Carburetors”
      • Remember that you should separate each argument with a comma

    • Answer

      # arguments to change the y-axis scale to 0 - 20, label the x-axis and colour the bars red
hist(mtcars$carb, ylim = c(0,20), xlab = "Number of Cuarburetors", col = "red", main = "Carburetors")

3. Mean and Median

  • mean()&median()

    We can measure the mean and median of a variable using the functions mean() and median(), using the variable in question as the first argument between brackets. Let’s try it out!

    • Instruction

      • In the editor calculate the mean and median miles per gallon (mpg) of the mtcars data set
      • Remember, you can select a specific variable using either $ or [,]. If you need to look at your data you can simply enter mtcars into your console, or if you just want to check the variables you can always enter str(mtcars) in your console.

    • Answer

      str(mtcars)
# Calculate the mean miles per gallon
mean(mtcars$mpg)
# Calculate the median miles per gallon
median(mtcars$mpg)

      > str(mtcars)
'data.frame':	32 obs. of  11 variables:
 $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
 $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
 $ disp: num  160 160 108 258 360 ...
 $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
 $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
 $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
 $ qsec: num  16.5 17 18.6 19.4 17 ...
 $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
 $ am  : Factor w/ 2 levels "0","1": 2 2 2 1 1 1 1 1 1 1 ...
 $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
 $ carb: num  4 4 1 1 2 1 4 2 2 4 ...
> # Calculate the mean miles per gallon
> mean(mtcars$mpg)
[1] 20.09062
> # Calculate the median miles per gallon
> median(mtcars$mpg)
[1] 19.2

4. Mode

  • sort()

    Sometimes it is useful to look at the the most frequent value in a data set, known as the ‘mode’. R doesn’t have a standard function for mode, but we can calculate the mode easily using the table() function, which you might be familiar with now.

    When you have a large data set, the output of table() might be too long to manually identify which value is the mode. In this case it can be useful to use the sort() function, which arranges a vector or factor into ascending order. (You can add the argument decreasing = TRUE to sort() if you want to arrange it in to descending order.)

    Lets use sort() and table() to find the mode of the carb variable of mtcars.

    • Instruction

      • Produce a frequency table of carb from mtcars in descending order of frequency
      • Remember that you should separate arguments with a comma

    • Answer

      # Produce a sorted frequency table of `carb` from `mtcars`
table(mtcars$carb)
sort(table(mtcars$carb), decreasing = TRUE)

      > # Produce a sorted frequency table of `carb` from `mtcars`
> table(mtcars$carb)
    
 1  2  3  4  6  8 
 7 10  3 10  1  1
> sort(table(mtcars$carb), decreasing = TRUE)
    
 2  4  1  3  6  8 
10 10  7  3  1  1

5. Range

  • max()&min()

    The range of a variable is the difference between the highest and lowest value. We can find these values using max() and min() on the variables of our choice. The value returned tells us which row (or case) contains the requested value. We can then index this case to find the desired values. Remember, you can index using [].

    • Instructions

      • In your script, assign the minimum value of mtcars$mpg to x
      • In your script, assign the maximum value of mtcars$mpg to y
      • In your script, use the values of x and y to calculate the range of miles per gallon.

    • Answer

      # Minimum value
x <- min(mtcars$mpg)
# Maximum value
y <- max(mtcars$mpg)
# Calculate the range of mpg using x and y
y
x
y - x

      > # Minimum value
> x <- min(mtcars$mpg)
> # Maximum value
> y <- max(mtcars$mpg)
> # Calculate the range of mpg using x and y
> y
[1] 33.9
> x
[1] 10.4
> y - x
[1] 23.5

6. Quartiles

  • quartile()

    You can calculate the quartiles in your data set using the function quantile(). The output of quantile() gives you the lowest value, first quartile, second quartile, third quartile and highest value. 25% of your data lies below the first quartile value, 50% lies below the second quartile, and 75% lies below the third quartile value. Let’s see for ourselves!

    • Instruction

      • In your console, calculate the quartiles of the variable qsec from mtcars using the quantile() function.
      • From the output, answer the questions in your script.

    • Answer

      quantile(range(0,10))
quantile(mtcars$qsec)

      > quantile(range(0,10))
  0%  25%  50%  75% 100% 
 0.0  2.5  5.0  7.5 10.0
> quantile(mtcars$qsec)
     0%     25%     50%     75%    100% 
14.5000 16.8925 17.7100 18.9000 22.9000

  • boxplot()&IQR()

    To better visualise your data’s quartiles you can create a boxplot using the function boxplot() (in the same way as you used hist() and barplot()). Similarly, you can calculate the interquartile range manually by subtracting the value of the third quartile from the value of the first quartile, or we can use the function IQR() on your variable of interest. Let’s try out making a boxplot and calculating the interquartile range of the mtcars variable qsec.

    • Instruction

      • Use the boxplot() function on the variable qsec of mtcars
      • Calculate the interquartile range of qsec from mtcars using IQR()

    • Answers

      # Make a boxplot of qsec
boxplot(mtcars$qsec)
# Calculate the interquartile range of qsec
IQR(mtcars$qsec)

      boxplot

      > # Make a boxplot of qsec
> boxplot(mtcars$qsec)
> # Calculate the interquartile range of qsec
> IQR(mtcars$qsec)
[1] 2.0075

  • IQR outliers

    In the boxplot you created you can see a circle above the boxplot. This indicates an outlier. We can calculate an outlier as a value 1.5 * IQR above the third quartile, or 1.5 * IQR below the first quartile. Let’s try it out with the qsec variable from mtcars.

    • Instructions

      • In your console, find the value of the interquartile range of the qsec variable of mtcars using IQR().
      • In your console, find the values of the first and third quartiles of the qsec variable of mtcars using quantile()
      • In your console, calculate the upper threshold value for an outlier. Report this value in your script.

    • Answer

      iqr <--IQR(mtcars$qsec)
quartile<--quantile(mtcars$qsec)
iqr
quartile
quartile[2]
quartile[3]
# What is the threshold value for an outlier below the first quartile?
quartile[2]-1.5*iqr
# What is the threshold value for an outlier above the third quartile?
quartile[4]+1.5*iqr
    

      > iqr <--IQR(mtcars$qsec)
> quartile<--quantile(mtcars$qsec)
> iqr
[1] -2.0075
> quartile
      0%      25%      50%      75%     100% 
-14.5000 -16.8925 -17.7100 -18.9000 -22.9000
> quartile[2]
     25% 
-16.8925
> quartile[3]
   50% 
-17.71
> # What is the threshold value for an outlier below the first quartile?
> quartile[2]-1.5*iqr
      25% 
-13.88125
> # What is the threshold value for an outlier above the third quartile?
> quartile[4]+1.5*iqr
      75% 
-21.91125

7. Standard Deviation

  • sd()

    We can also measure the spread of data through the standard deviation. You can calculate these using the function sd(), which takes a vector of the variable in question as its first argument. Let’s try it out!

    • Instruction

      • In your script, find the standard deviation and interquartile ranges of horsepower (hp) and miles per gallon (mpg)
      • Submit, and take a look at the values

    • Answer

      # Find the IQR of horsepower
IQR(mtcars$hp)
# Find the standard deviation of horsepower
sd(mtcars$hp)
# Find the IQR of miles per gallon
IQR(mtcars$mpg)
# Find the standard deviation of miles per gallon
sd(mtcars$mpg)

      > # Find the IQR of horsepower
> IQR(mtcars$hp)
[1] 83.5
> # Find the standard deviation of horsepower
> sd(mtcars$hp)
[1] 68.56287
> # Find the IQR of miles per gallon
> IQR(mtcars$mpg)
[1] 7.375
> # Find the standard deviation of miles per gallon
> sd(mtcars$mpg)
[1] 6.026948

8. Z-score

We can calculate the z-score for a given value (X) as (X - mean) / standard deviation. In R you can do this with a whole variable at once by putting the variable name in the place of X. Let’s try this!

  • Instruction

    • In your script, calculate the z-score of the mpg variable of the mtcars data set
    • Remember to put brackets around (X - mean)/standard deviation

  • Answer

    # Calculate the z-scores of mpg
sd<-sd(mtcars$mpg)
mean <-mean(mtcars$mpg)
zscore <- (mtcars$mpg - mean)/sd
zscore
str(zscore)

    > # Calculate the z-scores of mpg
> sd<-sd(mtcars$mpg)
> mean <-mean(mtcars$mpg)
> zscore <- (mtcars$mpg - mean)/sd
> zscore
 [1]  0.15088482  0.15088482  0.44954345  0.21725341 -0.23073453 -0.33028740
 [7] -0.96078893  0.71501778  0.44954345 -0.14777380 -0.38006384 -0.61235388
[13] -0.46302456 -0.81145962 -1.60788262 -1.60788262 -0.89442035  2.04238943
[19]  1.71054652  2.29127162  0.23384555 -0.76168319 -0.81145962 -1.12671039
[25] -0.14777380  1.19619000  0.98049211  1.71054652 -0.71190675 -0.06481307
[31] -0.84464392  0.21725341
> str(zscore)
 num [1:32] 0.151 0.151 0.45 0.217 -0.231 ...