Monthly Archives: February 2016

The Chi-Square Distribution

This video introduces a few aspects of the Chi-Square distribution that you're supposed to know off the top of your head, either for the test or because it will help you get what's going on with the problems that use this funky distribution.

This video appears on the page: The Chi-Square Distribution

Minimum Sample Size for Proportion Estimates

As you know, bigger samples lead to smaller margins of error. This video covers the type of problem where they give you the margin of error, then ask you to calculate the minimum sample size you'd have to take in order to accomplish that margin of error.

This video appears on the page: Confidence Intervals for Proportions

Confidence Intervals For Proportions

This video covers problems where you are given a proportion or percentage of a sample which has come quality (p), and you are asked to estimate a confidence interval for the population proportion with that same characteristic. Since you're working with p and q, as usual this only works for larger sample sizes.

This video appears on the page: Confidence Intervals for Proportions

Confidence Intervals for Proportions:
Confidence Intervals For Proportions
Minimum Sample Size for Proportion Estimates

These videos cover problems where you are given a proportion or percentage of a sample which has come quality (p), and you are asked to estimate a confidence interval for the population proportion with that same characteristic.

Part of the course(s): Statistics

The Chi-Square Distribution:
The Chi-Square Distribution
Chi-Square Critical Values

This chapter covers the basics of the Chi-Square Distribution (X2). Chi-Square gets a lot of play throughout stats, so this chapter just covers the basics of the distribution, its properties, the (X2)table and what happens for larger degrees of freedom.

Part of the course(s): Statistics

Confidence Intervals of Means -- Sigma NOT Known

This video covers the type of confidence interval problem where they give you the stats of the sample -- mean and standard deviation -- but you do NOT know sigma (standard deviation of the population), so you have to use the Student t-distribution to calculate your margin of error and confidence interval.

This video appears on the page: Confidence Intervals of Means — Sigma NOT Known

Confidence Intervals for Mean (when sigma is NOT known)

This chapter covers the type of confidence interval problem where they give you the stats of the sample -- mean and standard deviation -- but you do not know sigma (standard deviation of the population), so you have to use the Student t-distribution to calculate your margin of error and confidence interval.

Part of the course(s): Statistics

t-Values On Your Calculator

Just like with z-values, your calculator has a few different functions that can replace looking up values in a table. But these ones don't quite do the work for you the way the normal distribution functions do.

This video appears on the page: The Student t-Distribution

Student t-Distribution Table

This video explains how to look up critical t-values on the t-distribution table. You'd think it would be crazy because the numbers are all different depending on degrees of freedom (df), but unlike z-values, the t-value table only covers the most common values you would need for various levels of confidence -- 90%, 95%, 99%, etc -- so it ends up being pretty manageable.

This video appears on the page: The Student t-Distribution

Student t-Distribution

This video explains a few of the things you're supposed to know about the Student t-Distribution, including the strange fact that it has a different shape depending on your sample size (a.k.a. "degrees of freedom", a.k.a. "df").

This video appears on the page: The Student t-Distribution

The Student t-Distribution:
Student t-Distribution
Student t-Distribution Table
t-Values On Your Calculator

This chapter introduces "Student's t-Distribution", which is kind of like the normal distribution, except it's got t-values instead of z-values. You'll be using t-values tons from here on out, for lots of different types of Student t-Tests, where you use t instead of z for smaller sample sizes and when you don't know the population standard deviation (i.e. real world applications).

Part of the course(s): Statistics

Minimum Sample Size When Sigma Is Known

This video covers a particular type of confidence interval problem where instead of giving you a sample size and asking for the confidence interval, they give you the intended margin of error and ask you to calculate the minimum sample size to attain that level of precision. This video's formulas only work when you know POPULATION standard deviation (not just for sample).

This video appears on the page: Confidence Intervals for Mean—Sigma Is Known

Confidence Intervals When Sigma Is Known

This video works a bunch of examples of how to plug-and-chug your way through confidence interval and margin of error problems where you are told the POPULATION standard deviation (sigma), yet somehow you can only estimate the population mean using the mean of a sample. Pretty contrived, but every prof uses these to introduce the concepts of confidence intervals.

This video appears on the page: Confidence Intervals for Mean—Sigma Is Known

Confidence Intervals for Mean (when Sigma Is Known):
Critical Z-Values In Confidence Intervals
Confidence Intervals When Sigma Is Known
Minimum Sample Size When Sigma Is Known

The next few chapters each cover a specific type of confidence interval problem. This chapter covers the first type that most books cover, the ones where they tell you the mean of a sample but sigma FOR THE ENTIRE POPULATION and ask you to calculate a confidence interval to estimate the mean of the population. How, you may ask, would you know the standard deviation of an entire population but not the mean? Exactly. These are just a non-realistic type of problems that books use to introduce the concept of confidence intervals.

Part of the course(s): Statistics

Critical Z-Values In Confidence Intervals

This video introduces the concept of a critical value, and then goes through some of the most common ones that you'll see again and again in confidence interval problems: z-values for 90%, 95%, and 99% confidence intervals.

This video appears on the page: Intro to Confidence Intervals ,Confidence Intervals for Mean—Sigma Is Known

What A Confidence Interval Does NOT Tell You

I normally steer clear of mathy topics, but this one seems to get hit by every teacher and book, so it's worth taking on. Specifically, what words are you allowed to use when describing confidence intervals, and what words will get you busted down to private.

This video appears on the page: Intro to Confidence Intervals

What Is A Confidence Interval?

This video gets the confidence ball rolling by explaining in normal English what the point of these crazy things is (hint: if you're majoring in anything besides math or physics, this is the most useful thing you've done in stats thus far). Also covered are the concept of margin of error, and how to spot a confidence interval problem.

This video appears on the page: Intro to Confidence Intervals

Intro to Confidence Intervals:
What Is A Confidence Interval?
What A Confidence Interval Does NOT Tell You
Critical Z-Values In Confidence Intervals

This chapter introduces the concept of confidence intervals, along with the most important concepts you're supposed to understand for multiple choice type questions. Also very importantly, it explains the definition of confidence intervals -- and what they are NOT -- because for some reason every Stats teacher and book seems to make a really big deal about the exact words you use to describe what a confidence interval tells you. Sticklers!

Part of the course(s): Statistics

Normal Approximation of Binomial Distributions

Not all classes cover this topic. The basic idea is that some binomial distribution problems -- for example, finding the probability that if you flip a coin 8 times you'll get 5 or more heads -- get really time-consuming for larger numbers of flips (trials). It's the "or more" that gets you. Using z-values makes this type of problem a lot faster and easier!

Part of the course(s): Statistics

Normal Approximation of Binomial Distributions

The basic idea is that some binomial distribution problems -- for example, finding the probability that if you flip a coin 8 times you'll get 5 or more heads -- get really time-consuming for larger numbers of flips (trials). It's the "or more" that gets you. Using z-values makes this type of problem a lot faster and easier!

This video appears on the page: Normal Approximation of Binomial Distributions