DATASCI 5.3

What is the null hypothesis (H₀)?

A default claim that assumes no difference or no effect (we start by believing this).

What is the alternative hypothesis (Hₐ)?

The claim we are trying to find evidence for (a difference or effect).

What is the goal of hypothesis testing?

To see if there is strong enough evidence to reject H₀.

If we fail to reject H₀, what does it mean?

There is not enough evidence against H₀ (NOT that H₀ is true).

What is the null value (p₀)?

The value we compare our sample result to.

What happens if the null value is inside a confidence interval?

We fail to reject H₀.

What happens if the null value is outside a confidence interval?

We reject H₀.

What is a Type 1 Error?

Rejecting H₀ when it is actually true.

What is a Type 2 Error?

Failing to reject H₀ when Hₐ is actually true.

What happens when you reduce one type of error?

The other type of error usually increases.

What is the significance level (α)?

The probability of making a Type 1 error (commonly 0.05).

What does α = 0.05 mean?

We accept a 5% chance of incorrectly rejecting H₀.

What is a p-value?

The probability of getting results as extreme as ours if H₀ is true.

When do we reject H₀ using the p-value?

When p-value < α.

When do we fail to reject H₀ using the p-value?

When p-value > α.

Why do we use p₀ (not p̂) in hypothesis tests?

Because we assume H₀ is true when calculating.

What is the null distribution?

The distribution of possible results assuming H₀ is true.

Steps to find a p-value?

1. Assume H₀ is true

2. Find how extreme your result is

3. Find the probability (area in tail)

What are the 4 steps of a hypothesis test?

1. Prepare

2. Check

3. Calculate

4. Conclude

When should you use a smaller α (like 0.01)?

When a Type 1 error is very serious.

When should you use a larger α (like 0.10)?

When a Type 2 error is more serious.

How can you reduce Type 2 error?

Increase sample size.

What is statistical significance?

The result is unlikely due to chance.

What is practical significance?

The result is important in real life.

an something be statistically significant but not important?

Yes (especially with large sample sizes).

What is a one-sided test?

Tests if a parameter is only greater OR only less than a value.

What is a two-sided test?

Tests if a parameter is different (either direction).

Why are one-sided tests risky?

They can ignore important results in the opposite direction.

Main idea of hypothesis testing?

Start skeptical → use data → decide if evidence is strong enough.