Mastering Hypothesis Testing with R: Understanding and Performing T-tests

Lesson Introduction

Welcome to our exciting lesson! We'll be diving into Hypothesis Testing using R. Even though it might sound intricate, think of it as deciding whether a toy is worth buying based on its reviews. Our focus will be the T-test, which helps us determine if two groups differ significantly. R has a useful function, the t.test(), to assist us in conducting these tests quickly and accurately. By the end of this lesson, you'll understand Hypothesis Testing, know what a T-test is and be able to conduct a T-test using R. So, let's get started!

What is Hypothesis Testing?

Imagine owning a café and introducing a new blueberry muffin recipe. You believe this new recipe makes the muffins more popular, increasing their sales. To confirm this, you decide to use hypothesis testing. Null Hypothesis (H0): The null hypothesis is our initial statement that there is no change, effect, or difference. In this case, it would be, "The new blueberry muffin recipe does not increase sales." It's like saying, "Our change didn’t do anything. Things are the same." Alternative Hypothesis (HA): The alternative hypothesis is what you are trying to prove. It suggests that there is an effect, a change, or a difference. For the café scenario, it would be, "The new blueberry muffin recipe increases sales." This is like saying, "Yes, our change made a difference. Things are not the same." Think of the null hypothesis as maintaining the status quo or believing nothing has changed until proven otherwise. The alternative hypothesis is your bet against the status quo, proposing that a change has occurred.

How Does a T-test Work?

Let's better understand the T-test. It examines whether the mean values of two groups truly differ. This is similar to testing whether two pots of coffee have different temperatures because one is under an AC vent or if it's just a coincidence. The T-test presents us with two important values: the t-statistic and the p-value . The t-statistic represents the size of the difference relative to the variation in your sample data. In simpler terms, a larger t-statistic indicates a more significant difference in the mean values of the two groups. The p-value reflects the probability that the results happened by chance. If the p-value is less than 0.05, we usually conclude that the difference is statistically significant, not due to chance.

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ages <- c(28, 32, 25, 25, 27, 27, 27, 29, 30, 31, 33)  # mean = 28.5
H1_test <- t.test(ages, mu = 30)

print(H1_test$statistic)  # t-statistic: -1.788854 
print(H1_test$p.value)  # p-value: 0.1039

ages <- c(28, 32, 25, 25, 27, 27, 27, 29, 30, 31, 33)  # mean = 28.5
H1_test <- t.test(ages, mu = 30)

print(H1_test$statistic)  # t-statistic: -1.788854 
print(H1_test$p.value)  # p-value: 0.1039

set.seed(1234)
ages <- rnorm(90, mean=33, sd=5)  # mean = 33
H1_test <- t.test(ages, mu = 30)

print(H1_test$statistic)  # t-statistic: 3.519
print(H1_test$p.value)  # p-value: 0.0006

set.seed(1234)
ages <- rnorm(90, mean=33, sd=5)  # mean = 33
H1_test <- t.test(ages, mu = 30)

print(H1_test$statistic)  # t-statistic: 3.519
print(H1_test$p.value)  # p-value: 0.0006

team_A_hours <- c(8.5, 7.5, 8, 8, 8, 8, 8, 8.5, 9)
team_B_hours <- c(9, 8, 9, 9, 9, 9, 9, 9, 9.5)
H1_test <- t.test(team_A_hours, team_B_hours)

print(H1_test$statistic)  # t-statistic: -4
print(H1_test$p.value)  # p-value: 0.001

team_A_hours <- c(8.5, 7.5, 8, 8, 8, 8, 8, 8.5, 9)
team_B_hours <- c(9, 8, 9, 9, 9, 9, 9, 9, 9.5)
H1_test <- t.test(team_A_hours, team_B_hours)

print(H1_test$statistic)  # t-statistic: -4
print(H1_test$p.value)  # p-value: 0.001

ages <- c(28, 32, 25, 25, 27, 27, 27, 29, 30, 31, 33)  # mean = 28.5
H1_test <- t.test(ages, mu = 30)

print(H1_test$statistic)  # t-statistic: -1.788854 
print(H1_test$p.value)  # p-value: 0.1039

set.seed(1234)
ages <- rnorm(90, mean=33, sd=5)  # mean = 33
H1_test <- t.test(ages, mu = 30)

print(H1_test$statistic)  # t-statistic: 3.519
print(H1_test$p.value)  # p-value: 0.0006

team_A_hours <- c(8.5, 7.5, 8, 8, 8, 8, 8, 8.5, 9)
team_B_hours <- c(9, 8, 9, 9, 9, 9, 9, 9, 9.5)
H1_test <- t.test(team_A_hours, team_B_hours)

print(H1_test$statistic)  # t-statistic: -4
print(H1_test$p.value)  # p-value: 0.001

Lesson Introduction

What is Hypothesis Testing?

How Does a T-test Work?

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One-Sample T-test

Two-Sample T-test

Summary