Author Archives: hangtime

Linear Regression Explained (Vocab)

If you're confused by this whole linear regression thing and only have time to watch one linear regression video, this is the one. Instead of walking through all the minutia of doing these on a calculator, I take a step back and explain what it is we're trying to do with regressions, how to use them, and what some of the vocab means. Armed with that info, you'll understand how all the other linear regression videos fit together.

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What Is A Statistical Model

On a deep-down level -- sometimes on a surface level as well -- stats teachers are Math People. And Math People love to bandy around abstract terms like "statistical model" when they could have just said "equation of a line that kind of goes through the middle of that scatter plot of data." But hey, that's what I'm here for, to use words that actually make sense to normal people!

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Linear Regression: What Is A Statistical Model
Linear Regression Explained (Vocab)
Linear Regressions On Your Calculator
Standard Error of Linear Regression
Prediction Intervals Using Linear Regression
Extrapolation vs Prediction vs Interpolation
Residuals In Linear Regression (a.k.a. Unexplained Variation)
Coefficient of Determination (r2): Explained vs Unexplained Variation
Method of Least Squares Explained

This 9-video section covers everything you could ever need to know about linear regression analysis... In "non-math terms", what is a statistical Model? What the heck is a linear regression? What is the "method of least squares"? Using your calculator to do linear regressions, graph the equations, and make predictions for specific values of x. How to calculate standard error on your calculator. Prediction intervals using linear regression. What is the difference between "prediction" and "extrapolation", and why is my teacher always accusing people of extrapolating? What are residuals, a.k.a. "unexplained variation", and what's that crazy diagram with the lines and triangles that my teacher keeps drawing? What is the coefficient of determination? So much to cover, let's get to it!

Part of the course(s): Statistics

"If p is low, the null must go"

This is a silly saying that I only discovered lately but which allegedly helps some students remember whether P is supposed to be big or small in a hypothesis test. To me it just sounds like a made up quote from Jackie Chiles on Seinfeld (a character based on O.J.'s lawyer, Johnny Cochran), but hey, that doesn't make it wrong.

This video appears on the page: Hypothesis Testing Explained

Linear Correlation Test On Your Calculator

Rather than plug r into a formula to get a t-value, you can instead do a full hypothesis test of your data without even touching paper. Pretty sweet!

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Correlation Coefficient Hypothesis Tests

This video explains how to test whether your data has statistically significant linear correlation, by using yet another t-value formula to generate a t-value based on r, which you can then test against critical values.

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Linear Correlation Coefficients On Your Calculator

WARNING: before your calculator will spit out values for r and r2, you have to turn on "diagnostic mode". It's a setting deep in your calculator. This video explains how to do that, then once you do r is a piece of cake.

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How To Interpret A Linear Correlation Coefficient

Linear correlation is the basis for a lot of chapters coming up, so before we jump in, it's really important to get a good grounding of what the heck r is, why it goes from -1 to 1, and the unexpected situations that may result in a value of 0.

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Correlation (r):
How To Interpret A Linear Correlation Coefficient (Pearson Coefficient or "r")
Linear Correlation Coefficients On Your Calculator
Correlation Coefficient Hypothesis Tests
Linear Correlation Test On Your Calculator

These videos cover the Pearson Coefficient of Linear Correlation, or r-value, which basically tells you if your scatter plot (or plots) of data pairs lies along a line or not. Also covered are hypothesis testing of linear correlation, and calculating r on your calculator.

Part of the course(s): Statistics

Comparing Standard Deviations of Two Samples

This type of problem isn't covered by many stats classes, because let's face it, standard deviation isn't something people go around hypothesizing about unless they have a lot of time on their hands (or they're running a high-precision factory). Nonetheless, we do have to cover it, so I cooked up a couple of silly examples to get us there.

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The F-Distribution Table

Yet another distribution! F-values are pretty similar to chi-square, except they're so crazy that you actually need two different degrees of freedom, and therefore the table takes up like 10 pages at the back of your textbook. Kinda nuts, so expect to be doing these mostly on your calculator.

This video appears on the page: Hypothesis Tests Comparing Standard Deviations of Two Samples

Hypothesis Tests Comparing Standard Deviations of Two Samples:
F-distributions, F-value table

At this point we've been at this hypothesis testing thing for a while, so you know what's coming: more formulas, more plug-and-chug, yet another table of critical values, and some predictable null and alternative hypotheses!

Part of the course(s): Statistics

Hypothesis Testing Two Proportions on your Calculator

Let's face it: to do almost any hypothesis test, you're going to need a calculator just to get through all the crazy square root formulas. But this video shows you how to use your calculator so you don't even have to touch paper in order to test a hypothesis about the proportions of two samples.

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Confidence Intervals of Two Sample Proportions

This video covers a very specific type of problem: you're given proportion data (a percentage) for two different samples, and you're asked to provide a confidence interval estimating the difference between the populations represented by the two samples.

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Hypothesis Tests Comparing Two Proportions

This video covers all the formulas you'll need to know to test hypotheses regarding proportions of two samples. For example, comparing polling data from ten years ago to a new sample taken recently, or comparing the opinions of different groups.

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Hypothesis Tests Comparing Two Proportions
Hypothesis Tests Comparing Two Proportions
Confidence Intervals of Two Sample Proportions
Hypothesis Testing Two Proportions on your Calculator

These videos cover the very specific type of question where you are testing proportions of samples (such as percentage who like pizza) to see if one sample has a significantly different proportion than the other. As usual with proportions, you'll be seeing a lot of p's, q's, and n's!

Part of the course(s): Statistics

Mean Comparisons On Your Calculator

There are so many types of sample mean hypothesis tests, it's hard to keep track! I put the calculator how-to's in the previous videos about each type of problem, but in this video I just jump through them real quick and show you the menu picks for each of the types of problems, so you can review them quickly before a test. Add this to your playlist!

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Confidence Intervals Comparing Means of Two Samples

This video shows you how to create a confidence interval comparing two sample means, based on looking at the formulas for hypothesis testing two means.

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Comparing Sample Means with Matched Pairs (Dependent)

Yet another type of Student t-Test, this is a fun type of hypothesis test because it's what you see all the time in real life, especially in before-and-after infomercials! It's also good for stats students because: 1) the formulas are a lot simpler than the crazy ones comparing other types of means; and 2) the problems are pretty easy to spot. Also included: doing these on your calculator.

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Means of Independent Samples-Sigmas Unknown But Assumed Equal (Pooled Variance)

Stay with me: When you compare two samples, you're trying to figure out something about the populations from which those samples were drawn, right? In this particular type of hypothesis test, even though you don't know the standard deviations of those two populations, we will nonetheless assume that the two standard deviations are equal so that we can "pool" their variances. Why? The reasons are subtle, but they have to do with getting to use more degrees of freedom.

This video appears on the page: Hypothesis Tests Comparing Two Means