Combining X & Y Components Into Resultant Vector
This video explains how to solve for the magnitude and direction (ϴ) of a vector from its components. A very important part of most kinematics problems, and force problems too!
Author Archives: hangtime
Breaking Vectors Into X & Y Components
Something you have to do to vectors all the time is break them into their components. This video explains how to do that the easiest way possible, including some handy-dandy formulas in case you're not a super-fan of trig or SohCahToa.
Calculating The Magnitude of Vectors
The magnitude of a vector is its "length" (in quotes because often vectors represent things that don't have physical length, like forces, velocity and acceleration). This video explains how to calculate the magnitude of a vector from its coordinates or components.
Displacement Vectors vs Position Vectors
Just a quick video to explain what displacement and position vectors are, and explain the subtle differences between them.
Scalar vs Vector Quantities (Speed vs Velocity)
This video explains the difference between scalar vector quantities, including some examples and explanations that will help you on your next quiz!
Overview of Vectors In Physics
This specially-formulated video gives you an overview of vectors in a way genetically engineered to not freak you out if you're prone to vector anxiety.
This chapter covers how to do everything you need to do with vectors in physics, but especially the stuff you do constantly: breaking force and velocity vectors into their X & Y components, combining vector components back into a "resultant vector", and combining multiple vectors into one (like to find the net force vector) by breaking each into its components.
Two-Way Chi-Square Goodness-of-Fit Tests (on your CALCULATOR)
In this video, we'll see how to do "two-way" Chi-Square tests on a TI-84 calculator. Unfortunately, for these problems you have to input the "expected values" matrix, so that means you basically have to work half the problem by hand anyways. But at least your calculator will do the tedious big summation at the end for you, and spit out a P-value, so that's better than nothing.
"Two-Way" Chi-Square Goodness-of-Fit Contingency Table Test
These are called "two-way" tests because they involve two-way frequency tables (a.k.a. contingency tables), which are the type of frequency table that have a grid of numbers. The hard part of these is coming up with the "expected" values for the table, but once you get the hang of the formula for E, you can really plug-and-chug through them fast.
One-Way Chi-Square Goodness-of-Fit Test (by hand and on calculator)
The "one-way" in the title of this video refers to the fact that this more basic type of Chi-Square test involves tests on one-way frequency tables, which are the ones where you have only one list of numbers. This video covers both common types of one-way problems: testing for uniform distribution, and testing for a predicted pattern (i.e. weekends being busier than weekdays).
Goodness-of-fit problems are all about asking yourself the question: "Does the data in this frequency table match a pattern I'm expecting?" It's yet another type of hypothesis test. In the "one-way" versions of these problems, there's basically just one column of numbers. In the "two-way" versions you're dealing with a contingency table ("two-way" table) with two or more columns of data, plus a bunch of rows, so things get trickier, but the key is to try not to think too much and instead put your faith in the plug-and-chug.
ANOVA on Calculator
ANOVA, or "analysis of variance", is a fun way to compare the means of three or more samples. Since you've been doing hypothesis testing of means for a while now, this video is pretty quick. First I walk you through the null and alternative hypotheses for this type of problem, then I show you how easy it is to crank out on your calculator.
For a while now we've been doing hypothesis tests, usually comparing just two samples. The only thing that's new with ANOVA, or Analysis of Variance, is that it allows you to compare the means of as many samples as you want. And you want to compare lots of samples, right?
Coefficient of Determination (r2): Explained vs Unexplained Variation
This video gets pretty mathy, so feel free to bail if you get in over your head. The diagram covered in this video tends to get discussed by most profs in class, but it doesn't have much use other than in proving stuff or laying the groundwork for advanced stats classes. So while it's a good concept to understand for intro to stats students, ask your teacher if it's going to be on the test before you go beating yourself up over it.
Residuals In Linear Regression (a.k.a. Unexplained Variation)
This video explains what residuals are, how to calculate them on your calculator, and also how to plot the "residuals plot" on your calculator.
Extrapolation vs Prediction vs Interpolation
If you have one of those stats teachers who goes on the occasional rant about extrapolation, or you're just curious what extrapolation is all about, this video is for you. Don't let anyone accuse you of extrapolating your data!
Prediction Intervals Using Linear Regression
These aren't covered by all classes, and mostly you'll be creating them using your stats package (calculators don't do them), so this video is aimed at explaining what they are and the formulas involved so that you can understand what your computer is spitting out.
Standard Error of Linear Regression
This video explains "standard error", a.k.a. σest or sest: what it means, the formula, and how to calculate it on your calculator. It's pretty messy. (Free tip: it's NOT the "s" value that gets spit out when you do a LinRegTTest(), so don't make that mistake!)
Linear Regressions On Your Calculator
This video covers the nuts and bolts (and button presses) you'll need to do everything about linear regressions on your TI-84: entering data, graphing the scatter plot, calculating the regression line coefficients, graphing the regression line, and making "predictions" using the regression line you just calculated. Fun!
Method of Least Squares Explained
This is just a quick explanation of what is meant by "least squares", and why they're squaring everything.