What is Hypothesis Testing ? Math, Statistics for data science, machine learning

Summary

This video explains hypothesis testing in a simple and accessible way, using examples like drug testing and coin flipping. It introduces key concepts such as null and alternative hypotheses, and how they are used to test claims. Through examples of drug A vs. drug B, astrology, and scientific breakthroughs, the video highlights the importance of rejecting randomness in scientific claims. The speaker emphasizes the need for skepticism and critical thinking in hypothesis testing to prove if a claim is truly valid or just a result of chance.

Takeaways

• 😀 Hypothesis testing helps scientists and companies prove claims by eliminating randomness and ensuring that observed effects are real.
• 😀 The null hypothesis (H₀) is the default belief that there is no effect or difference, and it is tested to be rejected in favor of the alternative hypothesis.
• 😀 The alternative hypothesis (H₁ or Ha) is the claim or theory being tested, and it contrasts with the null hypothesis.
• 😀 In drug testing, you start with a small sample size, but larger sample sizes are needed to draw valid conclusions about a population.
• 😀 Randomness can often trick us into thinking there is an underlying reason behind an event when, in fact, it’s just chance (like flipping a coin).
• 😀 Hypothesis testing eliminates the element of randomness, allowing scientists to confidently state that an effect is real and not due to chance.
• 😀 The null hypothesis represents the established fact, and you begin your tests with skepticism toward new claims (like drug B being more effective than drug A).
• 😀 In hypothesis testing, if you reject the null hypothesis, you automatically prove the alternative hypothesis to be true (e.g., drug B is better than drug A).
• 😀 Hypothesis testing is akin to a courtroom trial, where the defendant is assumed innocent (null hypothesis) until proven guilty (alternative hypothesis).
• 😀 Historical beliefs, like the Earth being the center of the universe, were disproven through hypothesis testing, which led to the establishment of new truths (e.g., heliocentric model).
• 😀 Techniques such as Z-test, T-test, and Chi-Square tests are commonly used in hypothesis testing to eliminate randomness and validate claims with data.

Q & A

What is hypothesis testing?

Hypothesis testing is a scientific method used to determine whether there is enough evidence to support a claim or theory. It involves testing an idea (the alternative hypothesis) by assuming the opposite (the null hypothesis) and using data to determine if the null hypothesis can be rejected.

Why can't we just roll out Drug B to millions of people to test its effectiveness?

Testing on millions of people is impractical at first. Instead, smaller sample sizes are used to conduct controlled experiments. However, small sample sizes might not provide reliable results due to factors like randomness and sample bias, which is why a larger sample size is usually needed.

What is the role of sample size in hypothesis testing?

Sample size is crucial because a small sample might not represent the larger population accurately. Larger sample sizes reduce the impact of random variations and allow for more confident conclusions about the validity of the hypothesis.

What is the null hypothesis and why do we start with it?

The null hypothesis (H₀) represents the established belief or default assumption—such as 'Drug A is as effective as Drug B.' We start with the null hypothesis because it's important to approach any claim skeptically and test whether the new idea can provide strong evidence to reject the status quo.

What is the alternative hypothesis (Ha) in hypothesis testing?

The alternative hypothesis (Ha) is the claim or theory being tested. It represents what we are trying to prove, such as 'Drug B is more effective than Drug A.' The goal is to collect data that can either support or reject the null hypothesis in favor of the alternative hypothesis.

Why is it important to play 'devil’s advocate' in hypothesis testing?

Playing devil’s advocate, or starting with skepticism about the new hypothesis, helps ensure that any claims are thoroughly tested and not just accepted without evidence. This approach ensures the validity and reliability of the results.

How does hypothesis testing relate to real-world decision-making?

Hypothesis testing helps to make decisions based on data rather than assumptions or intuition. It provides a systematic approach to testing claims, whether in drug efficacy, product recommendations, or other areas where evidence is crucial for making informed choices.

Can you explain the concept of randomness in hypothesis testing with the coin-flipping example?

In the coin-flipping example, getting heads several times in a row may seem unusual, but it's a result of randomness. Hypothesis testing helps us distinguish between true patterns and random occurrences, so we don’t mistakenly attribute randomness to an underlying cause.

What does rejecting the null hypothesis prove in hypothesis testing?

Rejecting the null hypothesis means that the evidence collected supports the alternative hypothesis. In our case, rejecting the null hypothesis (that Drug B is not more effective than Drug A) would indicate that Drug B is indeed more effective, based on the data.

How are historical beliefs about the sun and Earth used as an example in hypothesis testing?

The historical belief that the sun rotated around the Earth was the null hypothesis. When Copernicus proposed that the Earth revolves around the sun, his theory had to be tested. Rejecting the null hypothesis in this case led to the acceptance of a new scientific truth about our solar system.