If you are tracking the exact same subjects across two different points in time—like a patient’s blood pressure before and after a new medication—you typically use a Paired T-Test. But just like the standard t-test, the paired t-test assumes your…
You made it to the end. You now know how to look at a dataset, find its center, measure its spread, map its probability, and prove whether a change is statistically significant. You have learned the exact mathematical frameworks that…
So far in this module, we have been testing numbers. T-Tests and ANOVA are designed for continuous, quantitative data—things you can measure, like test scores, weight loss, or revenue. But what happens when your data isn’t a number at all?…
If you have 4 different landing pages (A, B, C, and D), your first instinct might be to just run a bunch of separate T-Tests. Never do this. Running multiple T-tests destroys your Alpha level. Remember that an Alpha of…
In the first lesson of this module, we established the rules of proof: set a Null Hypothesis, demand overwhelming evidence (Alpha), and calculate a P-Value. But how do you actually get that P-Value? If you are trying to compare two…
Imagine you want to know the average age of a customer buying your software. You obviously cannot track down every single user in the world to ask them. Instead, you pull a random sample of 500 customers and find their…
Imagine you are the Lead Data Scientist for a major e-commerce company. The design team just launched a new, bright orange checkout button. After one week, the data rolls in: sales with the orange button are 2% higher than the…
The easiest way to understand the difference between permutations and combinations is to realize that the inventor of the “combination lock” named it completely wrong. If your gym locker code is 1-2-3, entering 3-2-1 won’t open it. The order of…
When you want to compare the averages of two independent groups (like test scores from Class A vs. Class B), the standard go-to tool is the independent t-test. However, the t-test has a strict rule: your data must be roughly…
If you look at the monthly sales of a ski resort, the number of daily passengers on a commuter train, or the hourly temperature of a city, the data won’t look like a straight line. It will look like a…