Joe Schumueller teaches a way of dealing with conditional probability called Bayesian Probability. It’s based on a theorem for finding the conditional probability that A occurs given that B has occurred if you know the probability that B occurs given that A has occurred, along with some additional probabilities.
 [Voiceover] Let's explore a special way, of dealing with conditional probability. It's called Bayesian Probability, and it's based on a theorem of refining the probability of A given B, if you know the probability of B given A, and some other probabilities. This is Baye's Theorem. The probability of A given B, is equal to the probability of B given A, times the probability of A, divided by the probability of B given A, times the probability of A, plus the probability of B given not A, times the probability of not A.
That's what those bars represent, not. How do we apply this? Here's an example. A multinational corporation gathers data on a new aptitude test for hiring applicants for trainee positions. They start by hiring all the applicants and giving them the test. They find that 70% of the applicants are successful in the position. Of the successful applicants, 90% passed the test. Of the unsuccessful applicants, 40% passed the test.
So, what the corporation wants to know is, what is probability of a applicant who passed the test, being successful in the position? This is an important question, if the corporation decides to only hire applicants, who successfully pass the test. So, let's set it up. A will equal successful applicant. An applicant who's successful in a position. B is an applicant who passes the test. So what we're looking for, is the probability of A given B.
The probability that applicant is successful, given that they've passed the test. Now, from the given information, what we know is that the probability, that an applicant is successful in the position is .70. We'll call that the probability of A. What this tells us, is the probability that the applicant is not successful, is .30. That's the probability of not A. Notice that .70 and .30, the probability of A and the probability of not A, add up to 1.00, more given information.
The probability that the applicant passed the test, given that the applicant is successful is .90. That's the probability of B given A. What this tells us, is that the probability that the applicant did not pass the test, given that the applicant is successful is .10. That's the probability of not B, given A. Notice that they add up to 1.00 also. And, the probability that the applicant passed the test, given that the applicant is not successful is .40. That's the probability of B given not A.
That tells us, that the probability that the applicant did not pass the test, given that the applicant is not successful is .60. And that's the probability of not B, given not A. So, all that combines together in Baye's Theorem in this way. The probability of B given A, times the probability of A, divided by the probability of B given A, times of probability of A, plus the probability of B, given not A, times the probability of not A.
In plugging in all the numbers that we have, and the numbers that we're able to figure out, it's .90, times .70, divided by .90, times .70, plus .40 times .30, which is equal to .84, for the probability of A given B. And this is a direct application of Baye's Theorem.
Author
Joseph SchmullerUpdated
7/6/2016Released
1/31/2016He explains how to organize and present data and how to draw conclusions from data using Excel's functions, calculations, and charts, as well as the free and powerful Excel Analysis ToolPak. The objective is for the learner to fully understand and apply statistical concepts—not to just blindly use a specific statistical test for a particular type of data set. Joseph uses Excel as a teaching tool to illustrate the concepts and increase understanding, but all you need is a basic understanding of algebra to follow along.
 Understanding data types and variables
 Calculating probability
 Understanding mean, median, and mode
 Calculating variability
 Organizing and graphing distributions
 Sampling distributions
 Making estimations
 Testing hypothesis: mean testing, z and ttesting, and more
 Analyzing variance
 Performing repeated measure testing
 Understanding correlation and regression
Skill Level Appropriate for all
Duration
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Introduction

Welcome1m 13s


1. Excel Statistics Essentials

Excel functions5m 25s

Excel statistical functions5m 55s

Excel graphics4m 37s

Excel Analysis ToolPak2m 22s


2. Understanding Data

Types of data4m 31s


3. Probability

Probability definitions2m 15s

Calculating probability7m 22s

Conditional probability2m 27s

Bayesian probability3m 36s


4. Central Tendency

Mean and its properties3m 2s

Median2m 38s

Mode2m 47s


5. Variability

Variance5m 51s

Standard deviation2m 46s


6. Distributions

Graph frequency polygons2m 11s

Properties of distributions5m 14s

Probability distributions4m 10s

7. Normal Distributions

Normal distribution graph2m 12s

8. Sampling Distributions

Central limit theorem3m 53s

Meet the tdistribution2m 24s

9. Estimation

Confidence in estimation4m 45s


10. Hypothesis Testing

11. Mean Hypothesis Testing

The ztest and the ttest4m 51s

12. Variance Hypothesis Testing

Chisquare distribution3m 54s


13. Z and T Hypothesis Testing

14. Matched Sample Hypothesis Testing

Matched samples2m 35s


15. FTest Hypothesis Testing

Ftest overview3m 55s


16. Analysis of Variance

More than two parameters6m 22s

ANOVA3m 22s

Applying ANOVA2m 17s


17. After the Analysis of Variance

18. Repeated Measures Testing

What is repeated measures?5m 48s


19. Hypothesis Testing with Two Factors

Statistical interactions5m 4s

Twofactor ANOVA5m 21s

Perform twofactor ANOVA2m 33s


20. Regression

Regression line overview5m 59s

Multiple regression analysis3m 24s


21. Correlation

Correlation overview2m 13s

Correlation coefficient2m 30s

Correlation and regression2m 45s


Conclusion

Up next54s

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Video: Bayesian probability