5 Numbers

I know you know what numbers are, and we’ve already seen that we have two types of numbers in R: integers and doubles; so, let’s move to see them in action.

Operations

First of all, here is how to do basic mathematical operation in R:

# Plus, minus, multiply, divide
5 + 4 - 2 * 3 / 2

[1] 6

# Power
4 ** 3

[1] 64

# Logarithm
log(100) # base e

[1] 4.60517

log10(100) # base 10

[1] 2

log2(100) # base 2

[1] 6.643856

log(100, base = 3) # choose the base

[1] 4.191807

# Natural exponential
exp(2)

[1] 7.389056

# Square root
sqrt(9)

[1] 3

An interesting operator is the modulus (%%) which returns the remainder of a division, for example:

7 %% 3

[1] 1

This can be useful to evaluate if a number is even or odd by calculating the remainder of the division x / 2 (so using x %% 2): if it is 0, the number x is even, otherwise it is odd.

11 %% 2

[1] 1

12 %% 2

[1] 0

Rounding

Another thing that we usually want to do is to round decimal number, especially after log transformation or division. To do so, we have 3 functions:

# Round to n decimal places
round(x = 1/3, digits = 2)

[1] 0.33

# Round to upper integer
ceiling(10.2)

[1] 11

# Round to lower integer
floor(14.9)

[1] 14

Look how ceiling and floor do not take into account the decimal part, even if it is greater or lower than 0.5.

Tranform to type number

Sometimes you want to transform a string that contains a number to a numeric type in R. I know we haven’t covered strings yet (next chapter will be on them), but let’s do a bit step forward now just to see this super useful function, that we use a lot when dealing with dataframes.
To do so, we’ll use the function called as.numeric()

mystring <- "15" # This is a character, can you guess why R interpret it as a character?
typeof(mystring)

[1] "character"

mynumber <- as.numeric(mystring)
typeof(mynumber)

[1] "double"

Wow, you will find this super super super useful.

Exercises

Let’s now put in practice what we have seen in this chapter and in the previous (remember? the script… I want you to write a script with these exercises and save it)

Exercise 5.1 The results of a Real-Time PCR indicate that your triplicates for FOXP1 have these Ct: 22.4, 22.31, 22.24. Calculate the mean value and print it rounded to 2 decimal places.

Solution

# calculator solution
mean_result_calc <- (22.4 + 22.31 + 22.24) / 3
mean_result_calc <- round(mean_result_calc, digits = 2)
print(mean_result_calc)

[1] 22.32

# BETTER solution
rep1 <- 22.4
rep2 <- 22.31
rep3 <- 22.24
n_rep <- 3

mean_res_better <- (rep1 + rep2 + rep3) / n_rep
mean_res_better_round <- round(mean_res_better, digits = 2)
print(mean_res_better_round)

[1] 22.32

The second solution is better because every number is stored in a variable, that you then use to calculate the mean value.

Exercise 5.2 Now calculate the sd of the data of exercise 5.1 and print the value rounded to upper integer, to lower integer and to a 4-digit decimal.

Solution

# Use only better solution, first calculate the variance
var_calc <- ((rep1 - mean_res_better)^2 + (rep2 - mean_res_better)^2 + (rep3 - mean_res_better)^2) / (n_rep - 1)

# Now let's calculate sd
sd_calc <- sqrt(var_calc)

sd_calc_ceil <- ceiling(sd_calc)
print(sd_calc_ceil)

[1] 1

sd_calc_floor <- floor(sd_calc)
print(sd_calc_floor)

[1] 0

sd_calc_round <- round(sd_calc, digits = 4)
print(sd_calc_round)

[1] 0.0802

Ok, now you’re ready to learn about strings, let’s go.