9.1. Conditional Statements

In many situations, actions and results depends on a specific set of conditions being satisfied. For example, individuals in randomized controlled trials receive the treatment if they have been assigned to the treatment group. A gambler makes money if she wins her bet.

In this section we will learn how to describe such situations using code. A conditional statement is a multi-line statement that allows Python to choose among different alternatives based on the truth value of an expression. While conditional statements can appear anywhere, they appear most often within the body of a function in order to express alternative behavior depending on argument values.

A conditional statement always begins with an if header, which is a single line followed by an indented body. The body is only executed if the expression directly following if (called the if expression) evaluates to a true value. If the if expression evaluates to a false value, then the body of the if is skipped.

Let us start defining a function that returns the sign of a number.

def sign(x):
    
    if x > 0:
        return 'Positive'

sign(3)

'Positive'

This function returns the correct sign if the input is a positive number. But if the input is not a positive number, then the if expression evaluates to a false value, and so the return statement is skipped and the function call has no value.

sign(-3)

So let us refine our function to return Negative if the input is a negative number. We can do this by adding an elif clause, where elif if Python’s shorthand for the phrase “else, if”.

def sign(x):
    
    if x > 0:
        return 'Positive'
    
    elif x < 0:
        return 'Negative'

Now sign returns the correct answer when the input is -3:

sign(-3)

'Negative'

What if the input is 0? To deal with this case, we can add another elif clause:

def sign(x):
    
    if x > 0:
        return 'Positive'
    
    elif x < 0:
        return 'Negative'
    
    elif x == 0:
        return 'Neither positive nor negative'

sign(0)

'Neither positive nor negative'

Equivalently, we can replace the final elif clause by an else clause, whose body will be executed only if all the previous comparisons are false; that is, if the input value is equal to 0.

def sign(x):
    
    if x > 0:
        return 'Positive'
    
    elif x < 0:
        return 'Negative'
    
    else:
        return 'Neither positive nor negative'

sign(0)

'Neither positive nor negative'

9.1.1. The General Form

A conditional statement can also have multiple clauses with multiple bodies, and only one of those bodies can ever be executed. The general format of a multi-clause conditional statement appears below.

if <if expression>:
    <if body>
elif <elif expression 0>:
    <elif body 0>
elif <elif expression 1>:
    <elif body 1>
...
else:
    <else body>

There is always exactly one if clause, but there can be any number of elif clauses. Python will evaluate the if and elif expressions in the headers in order until one is found that is a true value, then execute the corresponding body. The else clause is optional. When an else header is provided, its else body is executed only if none of the header expressions of the previous clauses are true. The else clause must always come at the end (or not at all).

9.1.2. Example: Betting on a Die

Suppose I bet on a roll of a fair die. The rules of the game:

• If the die shows 1 spot or 2 spots, I lose a dollar.

• If the die shows 3 spots or 4 spots, I neither lose money nor gain money.

• If the die shows 5 spots or 6 spots, I gain a dollar.

We will now use conditional statements to define a function one_bet that takes the number of spots on the roll and returns my net gain.

def one_bet(x):
    """Returns my net gain if the die shows x spots"""
    if x <= 2:
        return -1
    elif x <= 4:
        return 0
    elif x <= 6:
        return 1

Let’s check that the function does the right thing for each different number of spots.

one_bet(1), one_bet(2), one_bet(3), one_bet (4), one_bet(5), one_bet(6)

(-1, -1, 0, 0, 1, 1)

As a review of how conditional statements work, let’s see what one_bet does when the input is 3.

• First it evaluates the if expression, which is 3 <= 2 which is False. So one_bet doesn’t execute the if body.

• Then it evaluates the first elif expression, which is 3 <= 4, which is True. So one_bet executes the first elif body and returns 0.

• Once the body has been executed, the process is complete. The next elif expression is not evaluated.

If for some reason we use an input greater than 6, then the if expression evaluates to False as do both of the elif expressions. So one_bet does not execute the if body nor the two elif bodies, and there is no value when you make the call below.

one_bet(17)

To play the game based on one roll of a die, you can use np.random.choice to generate the number of spots and then use that as the argument to one_bet. Run the cell a few times to see how the output changes.

one_bet(np.random.choice(np.arange(1, 7)))

-1

At this point it is natural to want to collect the results of all the bets so that we can analyze them. In the next section we develop a way to do this without running the cell over and over again.