13 13. Automatic (or “implicit”) conversions - numeric to logical - logical to numeric

13.1 Automatic (or “implicit”) conversions from numeric to logical

If R sees a logical value where it expects a numeric value then R will automatically interpret the logical value as a numeric value in the following way

TRUE is interpreted as a 1 and
FALSE is interpreted as a 0 (zero)

In the following example, the arithmetic operators (e.g. +,-,*,/,%%,%/%,^) expect that both of their “operands” will be numbers. However, in the following examples one or both of the operands are TRUE or FALSE. Therefore, R interprets TRUE as a 1 and FALSE as a 0 (zero). See the examples:

TRUE + 100    # interprets as 1 + 100

[1] 101

FALSE * 100    # interprets as 0 * 100

[1] 0

30 + FALSE    # interprets as 30 + 0

[1] 30

FALSE + TRUE + TRUE + FALSE + TRUE # interprets as 0+1+1+0+1

[1] 3

x=10
y=15
(x>y) * 100 # result is 0 * 100, or just 0

[1] 0

# EXPLANATION: 
#
# step 1: x>y is 10>15. This produces FALSE
# step 2: the * requires numbers so the FALSE is
#         converted to a number. R converts FALSE to 0.

x = 200
y = 0.3
(x>y) * 100   # result is 1 * 100, or just 100

[1] 100

# EXPLANATION: 
#
# step 1: x>y is 200>0.3. This produces TRUE
# step 2: the * requires numbers so the TRUE must be
#         converted to a number. R converts TRUE to 1.

13.2 sum( LOGICAL_VECTOR )

The sum function expects numbers. If you provide sum with logicals they get converted to numbers.

sum ( c( FALSE, TRUE, TRUE, FALSE) )   # same as sum(0,1,1,0)

[1] 2

Think about it …

sum( LOGICAL_VECTOR ) results in the number* of values* that are TRUE

13.3 mean( LOGICAL VECTOR )

The mean function expects numbers. If you provide mean with logicals they get converted to numbers.

mean ( c( TRUE, FALSE, TRUE, TRUE) )  # same as mean(1,0,1,1)

[1] 0.75

Think about it …

mean( LOGICAL_VECTOR ) results in the percent* of values* that are TRUE

13.4 — Practice —

13.4.1 QUESTION

##########################################################################.
# QUESTION: grades is a vector that contains grades of students on a test.
#
#           (a) write a command to show the number of students who got an 80 or above.
#
#           (b) write a command to show the percent of the class who got an 80 or above
# 
#           (c) show the grades that were 80 or above
##########################################################################.

ANSWER (a) - Click here for answer

#-----------------------------------------------------------------------------------.
# ANSWER: (a) write a command to show the number of students who got an 80 or above.
#-----------------------------------------------------------------------------------.

# EXAMPLE 1
grades = c(85, 80, 79, 65, 55, 72, 90, 95)
sum ( grades >= 80 )

[1] 4

# Original:  sum ( grades >= 80 )
#         :  sum ( c(85, 80, 79, 65, 55, 72, 90, 95) >= 80 )
#         :  sum ( c(85>=80, 80>=80, 79>=80, 65>=80, 55>=80, 72>=80, 90>=80, 95>=80))
#         :  sum ( c(TRUE, TRUE, FALSE,  FALSE,  FALSE,  FALSE, TRUE, TRUE))
#         :  sum ( c(1,1,0,0,0,0,1,1))
#            4


# EXAMPLE 2
grades = c(45, 78, 78, 85, 88)   
sum ( grades >= 80 )

[1] 2

ANSWER (b) - Click here for answer

#-------------------------------------------------------------------------------------.
# ANSWER: (b) write a command to show the percent of the class who got an 80 or above
#-------------------------------------------------------------------------------------.

# EXAMPLE 1
grades = c(85, 80, 79, 65, 55, 72, 90, 95)
# YOUR CODE GOES HERE       # 0.5

# ONE WAY
mean( grades >= 80 )

[1] 0.5

# Original:  mean ( grades >= 80 )
#         :  mean ( c(85, 80, 79, 65, 55, 72, 90, 95) >= 80 )
#         :  mean ( c(85>=80, 80>=80, 79>=80, 65>=80, 55>=80, 72>=80, 90>=80, 95>=80))
#         :  mean ( c(TRUE, TRUE, FALSE,  FALSE,  FALSE,  FALSE, TRUE, TRUE))
#         :  mean ( c(1,1,0,0,0,0,1,1))
#            0.5

# ANOTHER WAY

sum( grades>= 80) / length(grades)

[1] 0.5

# EXAMPLE 2
grades = c(45, 78, 78, 85, 88)   
# YOUR CODE GOES HERE       # 0.4

ANSWER (c) - Click here for answer

#-------------------------------------------------------------------------------------.
# ANSWER: (c) show the grades that were 80 or above
#-------------------------------------------------------------------------------------.

# EXAMPLE 1
grades = c(85, 80, 79, 65, 55, 72, 90, 95)

# ANSWER       
grades[grades>=80]    # 85 80 90 95

[1] 85 80 90 95

# Original:   grades[grades>=80]
#             grades[c(85, 80, 79, 65, 55, 72, 90, 95)>=80]
#             grades[c(85>=80, 80>=80, 79>=80, 65>=80, 55>=80, 72>=80, 90>=80, 95>=80)]
#             grades[c(85>=80, 80>=80, 79>=80, 65>=80, 55>=80, 72>=80, 90>=80, 95>=80)]
#         :   grades[c(TRUE, TRUE, FALSE,  FALSE,  FALSE,  FALSE, TRUE, TRUE)]
#             85 80 90 95

# EXAMPLE 2
grades = c(45, 78, 78, 85, 88)   
# ANSWER       
grades[grades>=80]    # 85 88

[1] 85 88

13.4.2 QUESTION

##########################################################################.
# QUESTION: Add up the grades that are above 80
##########################################################################.

Click here for answer

grades = c(45, 78, 78, 85, 88)   

# ANSWER
sum ( grades[grades>=80] )

[1] 173

13.5 Automatic (or “implicit”) conversions from logical to numeric

To convert numeric values to logical values, R uses slightly different rules.

If R sees a numeric value where it expects a logical value (i.e. TRUE or FALSE) then R will automatically interpret the numeric value as a logical (i.e. TRUE or FALSE) value in the following way

0 (zero) is interpreted as FALSE
any nonzero number (e.g. 92, -0.243, etc) is interpreted as a TRUE

13.5.1 Quick review of ifelse(LOGICAL_VALUE, SOME_VALUE, ANOTHER_VALUE)

Recall that the ifelse function expects a logical value (i.e. TRUE or FALSE) as the first argument. The following are some simple examples:
x = 10
y = 3
ifelse(x>y, 100, 200)   # 100
[1] 100
x = 10 
y = 15
ifelse(x>y, 100, 200)    # 200
[1] 200
ifelse(c(x>y, x>100), "apple", "pear")  # 1st argument has 2 logical values
[1] "pear" "pear"

When the ifelse function contains numbers in the first argument, then the numbers are converted into logicals using the rules stated above (0 becomes FALSE; non-zero becomes TRUE). See the following examples:

ifelse(97, 100, 200)  # 97 is converted to TRUE, result is 100

[1] 100

ifelse(-3.2, 100, 200)  # -97 is also converted to TRUE, result is 100

[1] 100

ifelse(0, 100, 200)    # 0 is converted to FALSE, result is 200

[1] 200

x=0
y=100

ifelse(x, 100, 200)    # ifelse(0,100,200)     same as ifelse(FALSE, 100, 200)

[1] 200

ifelse(x*y, 100, 200)  # ifelse(100*0,100,200) same as ifelse(FALSE, 100, 200)

[1] 200

ifelse(y+x, 100, 200)  # ifelse(100+0,100,200) same as ifelse(TRUE, 100, 200)

[1] 100

# This one is tricky.
ifelse(TRUE+FALSE*FALSE, 100, 200)

[1] 100

# EXPLANATION:
# original:      ifelse(TRUE+FALSE*FALSE, 100, 200)  
# becomes:       ifelse(1+0*0, 100, 200)  
# order of ops:  ifelse(1+0, 100, 200)
#                ifelse(1, 100, 200)
# final result:  100

13.6 Review - numeric vs logical indexing - no conversions happen

Remember that an index can be a numeric vector or a logical vector. Therefore, TRUE / FALSE vectors will NOT be converted to 1’s and 0’s in an index.

# Start with some data
grades = c(60,70,80,90,100)

# The following uses a logical index to extract those values
# that correspond to the TRUE values in the index.
grades[c(FALSE, TRUE, FALSE, TRUE, TRUE)]  # 70 90 100

[1]  70  90 100

# The following uses a numeric index. Here the first value
# is extracted a few times. An index of 0 is ignored.
grades[c(0,1,0,1,1)]  # 60 60 60

[1] 60 60 60

13.7 –Practice–

What’s going to be displayed by the following? Why?

13.7.1 QUESTION 1

grades = c(60,70,80,90,100)
grades[c(1, 0, 0, 1)]

Click here to see the output …

grades = c(60,70,80,90,100)
grades[c(1, 0, 0, 1)]

[1] 60 60

EXPLANATION - a zero index is ignored.

13.7.2 QUESTION 2

grades = c(60,70,80,90,100)
grades[c(1, FALSE, FALSE, TRUE)]

Click here to see the output …

grades = c(60,70,80,90,100)
grades[c(1, FALSE, FALSE, TRUE)]

[1] 60 60

# EXPLANATION - A vector must contain all the same type of data.
#   If you try to mix logical and numeric values in the same vector then
#   Logical values are converted to numeric (TRUE becomes 1, FALSE becomes 0). 
#   Therefore, this selects the first and fourth elements from the vector. 
#   A zero index is ignored.

13.7.3 QUESTION 3

c( TRUE, 999, FALSE )

Click here for answer

c( TRUE, 999, FALSE )

[1]   1 999   0

# EXPLANATION - You cannot mix logical values and numbers in a
#    vector, TRUE becomes 1 and FALSE becomes 0

13.7.4 QUESTION 4

sum(c(TRUE, FALSE, TRUE, TRUE))

Click here for answer

sum(c(TRUE, FALSE, TRUE, TRUE))

[1] 3

# EXPLANATION 
#   same as sum(c(1,0,1,1))
#   If you try to do math with logicals they become numbers
#   (TRUE becomes 1, FALSE becomes 0)

13.7.5 QUESTION 5

mean(c(TRUE, FALSE, TRUE, TRUE))

Click here for answer

mean(c(TRUE, FALSE, TRUE, TRUE))

[1] 0.75

# EXPLANATION 
#   same as mean(c(1,0,1,1))