HYPOTHESIS TESTING IN R

NULL & ALTERNATE HYPOTHESIS, ERROR TYPES, T-TEST
1

R

MEDIUM

last hacked on Jan 24, 2019

Null and Alternate Hypothesis

Null Hypothesis: Ho

This is your default assumption or belief.

Alternate Hypothesis: H1

Notion that is rival to our default assumption or belief.

We attempt to test, statistically, whether Ho is True, or False.

From our data analysis, we then proceed to either not reject or reject our Ho. If we reject Ho, we do so in favor of H1; and vice-versa.

Type I and II Errors

We can make mistakes while choosing to reject or not reject, however; and this is why we have Type I and Type II errors.

When Ho is True

• If we do not reject Ho, then we are making the correct decision.

• If we reject the null hypothesis, then we are making the Type I error.

When Ho is False

• If we reject Ho, then we are making the correct decision.

• If we do not reject Ho, then we are making the Type II error.

Implementation

We will employ the Student's t-Test to determine whether we should either reject or not reject Ho.

Specifically, we will use the t.test() function. Before diving in, let's take a look at a preview of docs:

?t.test
t.test {stats}  R Documentation
Student's t-Test

Description

Performs one and two sample t-tests on vectors of data.

Usage

t.test(x, ...)

## Default S3 method:
t.test(x, y = NULL,
alternative = c("two.sided", "less", "greater"),
mu = 0, paired = FALSE, var.equal = FALSE,
conf.level = 0.95, ...)

...

Now let's mock a data set, called test_data1. Next, we will compute its t.test.

test_data1 <- c(55, 60, 62, 63, 65, 66, 68, 69, 70, 71, 75, 80)
t.test(test_data1)
One Sample t-test

data:  test_data1
t = 34.357, df = 11, p-value = 1.522e-12
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
62.70778 71.29222
sample estimates:
mean of x
67

Here, (having provided no further arguments) our alternative hypothesis is such that the true mean is not equal to 0. More elegantly:

• H1 (alternative hypothesis) : true mean is not equal to 0, therefore:
• Ho (null hypothesis) : true mean is equal to zero.

Since our p-value is less than .05, we reject Ho.

Therefore we are accepting our alternate hypothesis, which is that our true mean is not equal to 0.