Hypothesis testing; Why we use it and When we use it

What is Hypothesis Testing?

Hypothesis testing is a way to use statistics to decide if something about a large group (population) is true based on a smaller group (sample). You start with two ideas: the null hypothesis (H₀, like "there's no difference") and the alternative hypothesis (H₁, like "there is a difference"). Then, you collect data, do some math, and see if the data supports rejecting the null hypothesis.

Why Do We Use It?

We use hypothesis testing to make sure decisions are based on data, not just guesses. It helps figure out if what we see (like a drug working better) is real or just random luck. This is crucial in fields like science to test theories, in business to compare products, or in medicine to check if treatments work.

When Do We Use It?

You use hypothesis testing whenever you need to make a call about a population from a sample, such as:

1. Comparing two groups, like testing if a new teaching method improves test scores.
2. Seeing if a treatment works, like checking if a new drug lowers blood pressure.
3. Finding if variables are related, like seeing if exercise affects heart rate.
4. Examples include drug testing, market research, or quality control in manufacturing.

Surprising Detail: It Doesn't Prove Anything

A surprising thing is that rejecting the null hypothesis doesn't prove the alternative is true - it just means the data doesn't fit the null hypothesis. Also, not rejecting the null doesn't mean it's true; it just means we don't have enough evidence against it.

Key Points

1. Hypothesis testing is a statistical method to make decisions about a population using sample data.
2. We use it to see if a claim or theory is likely true, helping avoid guesses based on chance.
3. It's used when comparing groups, testing treatments, or finding relationships in data, like in science, business, or medicine.