QTM 151 - Introduction to Statistical Computing II

Lecture 05 - Boolean Logic and Conditional Statements

Danilo Freire

danilo.freire@emory.edu

Emory University

17 September, 2024

Nice to see you all again! 😊

Brief recap of last class 📚

Brief recap

In the last class, we did the following:

Introduced Matplotlib and NumPy libraries and loaded them with import matplotlib.pyplot as plt and import numpy as np
Created histograms and scatter plots with plt.hist() and plt.scatter()
Explored NumPy mathematical functions: np.log(), np.exp(), np.sin(), np.sqrt()
Created NumPy arrays and performed operations
- Example: np.array([1,2,3]), array1 + array2

Accessed array elements using indexing (e.g., array[1:3])
Performed scalar operations on arrays, such as array * 2 or array + 5
Computed summary statistics with np.mean(), np.std(), np.min(), np.max()
Discussed importance of random numbers in simulations
Generated random numbers: e.g., np.random.normal(loc=0, scale=1, size=10)
Plotted histograms of random variables with plt.hist()

Are you more comfortable with Python now? 🐍

Today’s class 📚

Today’s class

Today we will:

Learn about Boolean logic
Discuss the importance of conditional statements in programming
Understand how to use conditional statements in Python
Explore the if, elif, and else statements
Practice writing conditional statements in Python

Let’s get started! 🚀

Boolean logic 🧠

Boolean logic

A bit of history

Named after George Boole, a British mathematician and philosopher
Boole’s work on logic laid the foundation for modern computer science
Boolean logic is a branch of algebra that deals with true and false values
It is useful for computer programming because it is based on binary values
In Python, Boolean values are True and False
We use them to make decisions in our code

Testing expressions with text 🐍

True and False values

We can test whether two values are equal using the == operator (two equal signs)
For example, 5 == 5 returns True
We can also test whether two values are not equal using the != operator (exclamation mark followed by an equal sign)
Let’s see how this works in Python
First, let’s load the matplotlib and numpy libraries

import matplotlib.pyplot as plt
import numpy as np

# You can compare two strings by using a double "equal sign"
# This can be useful if you're trying to evaluate whether data was entered correctly

"Is this the real life?" == "is this just fantasy?"

False

Note: the order of the strings matter!

"ab" == "ba"

False

True and False values

Equality of strings is most useful when you’re comparing an unknown variable to a benchmark
Below, try switching the value of any_questions

any_questions = "no"
print(any_questions == "no")

True

any_questions = "yes" 
print(any_questions == "no")

False

Test for the presence of keywords in a sentence (`in` operator)

We can test whether a keyword is present in a sentence or a list using the in operator
For example, "apple" in "I like apples" returns True
Let’s see how this works in Python

"apple" in "I like apples"

True

keyword = "economic"
sentence = "The Federal Reserve makes forecasts about many economic outcomes"

keyword in sentence

# Try changing the keyword!

True

Now, let’s test whether a keyword is present in a list

current_month = "September"
list_summer_months = ["June","July","August"]

print(current_month in list_summer_months)
print('June' in list_summer_months)

False
True

Common pitfall when testing expressions

Be careful when testing expressions with text
Python is case-sensitive, so "apple" == "Apple" returns False
To avoid this, you can use the lower() method to convert all characters to lowercase
And please remember there is a difference between double equal signs == and single equal sign =

"apple" == "Apple"

False

"apple".lower() == "Apple".lower()

True

# A single vs double equality sign makes a BIG difference
# When you have a single equality (=) you are assignning the variable
# When you have a double equality (==) you are comparing two values
message_hello = "hello"

print(message_hello == "hello")

True

Try it out!

Now, let’s test whether you can identify the correct expression
Write code to check whether the string “red” is contained in the list: ["red","green","yellow","orange"] Appendix 01

So far so good? 🤔

Testing expressions with numbers 🐍

Testing expressions with numbers

Tests with numbers
- Strictly less than (<), less than or equal (<=)
- Equal (==)
- Strictly more than (>), greater than or equal to (>=)
Let’s see how this works in Python

x = 5

print(x < 5)
print(x <= 5)
print(x == 5)
print(x >= 5)
print(x > 5)

False
True
True
True
False

Validate a data type

We can test whether a variable is of a certain data type using the isinstance() function
For example, isinstance(5, int) returns True
Other data types include float, str, list, tuple, dict, set, bool

y = 10

print(isinstance(y,int))
print(isinstance(y,float))
print(isinstance(y,str))

True
False
False

Equality of vectors

We can test whether two vectors are equal using the == operator
For example, [1,2,3] == [1,2,3] returns True
Please note that the equality of vectors is done element-wise

vec_a = np.array([1,2,3])
vec_b = np.array([1,2,4])

vec_a == vec_b

array([ True,  True, False])

Try it out! 🚀
Define \(x= -1\). Check whether \(x^2 + 2x + 1 = 0\) is true Appendix 02
- Please remember that \(x^2\) is written as x**2 in Python
- Please note the difference between == and =

Testing multiple conditions 🐍

Testing multiple conditions

We can test multiple conditions using the and and or operators
The and operator returns True if both conditions are True
The or operator returns True if at least one condition is True

`not`: the negation operator

We can negate a condition using the not operator
The not operator returns True if the condition is False and vice versa
- Yes, it’s a bit confusing at first, but it’s intuitive once you see it in action
For instance, imagine that you want to know whether someone can vote in the US
- Here let’s assume the person is a national and we only care about age
- The person can vote if they are at least 18 years old

age  = 22

# Can this person legally vote in the US?
not (age < 18)

True

The not operator can be separated by a space and parentheses are not necessary
But parentheses can be helpful to organize your code logically

not age < 18

True

Condition A and B need to be satisfied: `&` operator

We can test multiple conditions using the & operator
The & operator returns True if both conditions are True
For example, 5 > 3 & 5 < 10 returns True

# We use the "&" symbol to separate "AND" conditions
age = 31

# Is this age between 20 and 30 (including these ages)?
( age >= 20 ) & (age <= 30)

False

Condition A or B needs to be satisfied: `|` operator

To test whether at least one condition is True, we use the | operator
For example, 5 > 3 | 5 > 10 returns True

# We use the "|" symbol to separate "OR" conditions.
age = 31

# Is this age higher than 20 or lower than 30?
( age >= 20 ) | (age <= 30)

True

# Another example
student_status = "freshman" 

# Is the student in the first two years of undergrad?
(student_status == "freshman") | (student_status == "sophomore")

True

Try it out! 🚀

Now, let’s test whether you can identify the correct expression

Write code that checks the following conditions:
- Whether age is strictly less than 20, or greater than 30
- Not in the age range 25-27 Appendix 03

Flow control: conditional statements 🐍

Flow control: conditional statements

If, elif, else

Conditional statements are used to make decisions in programming
The if statement is used to execute a block of code if a condition is True
The elif statement is used to execute a block of code if the first condition is False and the second condition is True
The else statement is used to execute a block of code if all other conditions are False
We use this a lot in data cleaning or data analysis to filter out data!

If statements

Test expression
- We type “if” followed by a logical condition and the “:” symbol.
- The “:” says: run the following command
Body of expression
- The “body” of the “if” statement needs to indented with four spaces
- You can indent text by pressing the “tab” button in your keyboard.
If the condition is true, a message will appear.
If the condition is false, then nothing happens

The if statement syntax is as follows:

if condition:
    Body

Another example:

# We start by defining a string
any_questions = "yes"

if any_questions == "yes":
    print("Need to give more explanations")

Need to give more explanations

If/else statements

When you have two possible outcomes

The else statement is used to execute a block of code if the condition is False
The else statement is always used in conjunction with the if statement
The else statement syntax is as follows:

if condition:
    Body
else:
    Body

For example, let’s say you want to know whether someone can vote in the US
- First, the person needs to be a national
- Second, the person needs to be at least 18 years old

age = 22
national = False

if national & (age >= 18):
    print("This person can vote in the US")
else:
    print("This person cannot vote in the US")

This person cannot vote in the US

Another example

# Here we want to change the colour of the histogram 
# based on a conditional statement

is_graph_red = False
how_many_classes = np.array([7,1,2,3,3,3,4,5,6])

if is_graph_red:
    plt.hist(x = how_many_classes, color="red")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show() 
else:
    plt.hist(x = how_many_classes, color="purple")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show()

The histogram will be red if is_graph_red is True, and purple otherwise

Try it out! 🚀

What happens if … ? Try the following:

Rerun the above code but change the value of is_graph_red.
What happens if you set a non-boolean value of is_graph_red?
Don’t include :
Don’t indent the body of the if Appendix 04

If/elif/else statements

The last conditional statement is the elif statement
The elif statement is used to execute a block of code if the first condition is False and the second condition is True
It is just like another if statement, but it is used when you have more than two possible outcomes
The elif statement syntax is as follows:

if condition:
    Body
elif condition:
    Body
else:
    Body

Example

years_in_program = 1

if years_in_program == 1:
    print("This student is a freshman")
elif years_in_program == 2:
    print("This student is a sophomore")
elif years_in_program == 3:
    print("This student is a junior")
else:
    print("This student is a senior")

This student is a freshman

And that’s it for today! 🎉

Questions? 🤔

Try this at home! 🏠

Practice writing conditional statements in Python

Create a variable called “points” with a value between 0 and 100
Write a flow with “if”, “elif” and “else” to assign the letter grade
In the body, store the output in a new variable called “letter_grade”
Print the letter grade at the end

Important

Check that it works by trying different values of “points”!

Thank you very much and see you next time! 🙏

Appendix 01

colors = ["red","green","yellow","orange"]

"red" in colors

True

Back to the main text

Appendix 02

x = -1

x**2 + 2*x + 1 == 0

True

Back to the main text

Appendix 03

Whether age (age = 31) is strictly less than 20, or greater than 30
Not in the age range 25-27

age = 31

(age < 20) | (age > 30)

True

(age < 25) | (age > 27)

True

The second answer uses | because & evaluates both statements at the same time, and one cannot be less than 25 and greater than 27 at the same time. Therefore, it must be |.

Back to the main text

Appendix 04

What happens if is_graph_red is set to True?

is_graph_red = True
how_many_classes = np.array([7,1,2,3,3,3,4,5,6])

if is_graph_red:
    plt.hist(x = how_many_classes, color="red")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show() 
else:
    plt.hist(x = how_many_classes, color="purple")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show()

Back to the main text

Appendix 04 - Continued

What happens if you set a non-boolean value of is_graph_red?

It is considered True if it is not zero

is_graph_red = 39
how_many_classes = np.array([7,1,2,3,3,3,4,5,6])

if is_graph_red:
    plt.hist(x = how_many_classes, color="red")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show() 
else:
    plt.hist(x = how_many_classes, color="purple")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show()

Back to the main text

Appendix 04 - Continued

What happens if you don’t include :?

You will get a syntax error

is_graph_red = True
how_many_classes = np.array([7,1,2,3,3,3,4,5,6])

if is_graph_red
    plt.hist(x = how_many_classes, color="red")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show() 
else:
    plt.hist(x = how_many_classes, color="purple")
    plt.title("Count of students in each category")
    plt.xlabel("How many classes are you taking?")
    plt.show()

Back to the main text

Appendix 04 - Continued

What happens if you don’t indent the body of the if?

You will get another syntax error

is_graph_red = True
how_many_classes = np.array([7,1,2,3,3,3,4,5,6])

if is_graph_red:
plt.hist(x = how_many_classes, color="red")
plt.title("Count of students in each category")
plt.xlabel("How many classes are you taking?")
plt.show() 
else:
plt.hist(x = how_many_classes, color="purple")
plt.title("Count of students in each category")
plt.xlabel("How many classes are you taking?")
plt.show()

Back to the main text

QTM 151 - Introduction to Statistical Computing II

Nice to see you all again! 😊

Brief recap of last class 📚

Brief recap

In the last class, we did the following:

Are you more comfortable with Python now? 🐍

Today’s class 📚

Today’s class

Boolean logic 🧠

Boolean logic

A bit of history

Testing expressions with text 🐍

True and False values

True and False values

Test for the presence of keywords in a sentence (in operator)

Common pitfall when testing expressions

Try it out!

So far so good? 🤔

Testing expressions with numbers 🐍

Testing expressions with numbers

Validate a data type

Equality of vectors

Testing multiple conditions 🐍

Testing multiple conditions

not: the negation operator

Condition A and B need to be satisfied: & operator

Condition A or B needs to be satisfied: | operator

Try it out! 🚀

Flow control: conditional statements 🐍

Flow control: conditional statements

If, elif, else

If statements

If/else statements

When you have two possible outcomes

Another example

Try it out! 🚀

If/elif/else statements

Example

And that’s it for today! 🎉

Questions? 🤔

Try this at home! 🏠

Thank you very much and see you next time! 🙏

Appendix 01

Appendix 02

Appendix 03

Appendix 04

Appendix 04 - Continued

Appendix 04 - Continued

Appendix 04 - Continued

Test for the presence of keywords in a sentence (`in` operator)

`not`: the negation operator

Condition A and B need to be satisfied: `&` operator

Condition A or B needs to be satisfied: `|` operator