Free videos to help you learn and understand concepts in Statistics.

A set of notes to help you understand the Binomial Setting and how to set up binomial proportions. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

OVERSEAS

Introduction of Sample Proportions

I introduce the structure of scatterplots and explain what characteristics you will need to use to intrepret them.  I discuss how lurking variables can help to form the patterns that we see.  I also go over the two type of outliers we may see in scatterplots.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Scatter Plot Intro and Lurking Variables defined

I introduce log transformations and show how to make curved exponential data linear so that we can analyze the data with a linear regression line.  Part 2 is transforming data that follows a power function.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Log Transformation Part 1

I finish my log transformation introduction by introducing notes for Power Functions.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Log Transformations Part 2

I work through a 1 sample mean z-test.  I include the required checks for working with means, preview how to make a hypothesis statement, and compare how a z-score with means compares to a z-score test with a single piece of data.

After attending a recent AP Statistics training I have added some annotations to my examples.  
Defining Mu
Mu is the mean stopping distance
Checking Conditions
3) With n=30 the Central Limit Theorem will ensure the sampling distribution of the sample means will be approximately Normal.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

1 Sample Mean Z-Test Example

I explain the differences of finding Power of a t-Test compared to Power of a z-Test. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Power of a T Test 1 Sample Mean

A review of the shapes of distributions and the relationships between the three measures of center.  Also included is an intro to the Ogive graph and Time Plots.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Distribution Shapes, Ogive Graphs, and Time Plots

An AP Statistics lecture introducing probabilities, randomness, Law of Large Numbers, Probability Model, Tree Diagram, 5 Rules of Probability,etc. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Intro to Probabilities Part 2

I introduce the Central Limit theorem and explain how it helps to set up the distribution of sample means.  This video only discusses setting up the distribution of a one sample mean when given the population standard deviation.  I hint of the upcoming topic of t-distributions

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Intro to Sample Mean Distribution and Central Limit Theorem

I work through an example of finding power of  a 1 sample proportion z test which is 2 sided.

I added some annotations to the language of my examples.
Defining the variable:
P: The population proportion of people that travel during the holidays.
Normality:
 With 350(.68)=238 and 350(1-.68)=112 being greater than or equal to 10, the sampling distribution of sample proportions will be approximately Normal. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Power 1 Sample Proportion z-Test (2 Sided)

An introduction to the benefits, construction, and interpretation of stem plots.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Stem Plots in Statistics

I define and compare the two types of Random Variables in AP Statistics...Discrete & Continuous. The formulas for finding the mean and standard deviation of a discrete random variables are introduced, and I also review the old mean and standard deviation formulas that the calculators does when you do 1 Var Stats. Many old concepts are reviewed in this video such as probability models, z-scores, normality, degrees of freedom, etc.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Discrete & Continuous Random Variables (Full Length)

An introduction to pie charts and bar graphs.  I talk about their construction and the pros and cons of each type of graph.  Please excuse my grammatical error on the third bullet under pie charts...category's relation.  My apologies for misspelling categorical in the video!!!

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Categorical Graphs in Statistics

I introduce the Linear Regression t test and confidence intervals for the slope of a regression line. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Linear Regression t test and Confidence Interval Corrected

I continue to introduce sampling techniques.  In this video I go over Stratified Random Samples, Stratified Random Sample, Cluster Samples, and Multistage Samples.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Sampling Techniques Part 2

I go over the General Addition and Multiplication Rules in Statistics. I show how a Venn diagram can help with the General Addition Rule. I also explain how we started to learn conditional probabilities when we did row and column percents in 2 way tables.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

General Probability Rules (Full Length)

I introduce the Chi Square Goodness of Fit test and finish with two examples.  EXAMPLES AT 5:10 15:55

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Chi Square Goodness of Fit Test

Intro to Probabilities Part 3

In part 2 of my lecture about the Binomial Setting, I show how to set up a probability distribution function for a binomial variable when x is defined as the number of successes.  I then introduce how to find probabilities of binomial events through Normal Approximation and compare this process with the exact values we get with binompdf and binomcdf from a calculator.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Binomial Setting & Binomial Distribution in Statistics Pt 2

I introduce how to compare 2 sample proportions through the use of z-tests and confidence intervals.  I finish with a 2 Sample Pooled z-test.  EXAMPLES AT 11:09 21:28
I have added annotations to improve some of the language of my example.
Defining the variables
Pm: Population proportion of men snacking
Pw: Population proportion of women snacking
Conditions:
SRS is stated
Since 380(.608)=231.04, 380(1-.608)=148.96, 370(.53)=196.1, 370(1-.53)=173.9 are all greater than or equal to 5 the sampling distribution of the difference of sample proportions will be approximately Normal.
Independence:  It is reasonable to assume each population of men and women are greater than ten times each sample size 10(380)=3800 and 10(370)=3700.
Conclusion:  The observed difference of .078 or 7.8% or one more extreme has a p value of .03 which is less than our level of significance of .05 so we reject Ho.  There is not enough evidence to conclude there is a difference in the snacking habits of men and women.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

2 Proportions Pooled Hypothesis z-test & Confidence Intervals

I define what Type 1 and Type 2 errors and do an example.  I then introduce power and work through and example of finding the power of a 1 sample mean z-test and the probability of a Type 2 error. The x's in the first half of my Power example should have bars on top of them to represent sample means.
Power of a T-test for Sample Means
   • Power of a T Test 1 Sample Mean  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Type 1 Error Type 2 Error Power 1 Sample Mean Hypothesis z-Test

An AP Statistics lecture introducing probabilities, randomness, Law of Large Numbers, Probability Model, Tree Diagram, 5 Rules of Probability,etc.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Intro to Probabilities Part 1

I show you how to calculate Z-scores and find areas under the bell curve...p-values.  I will also show you how to find statistics from areas under the curve...such as quartiles.  
Updated version of this lesson which includes calculator usage: 
Z score Calculations and Calculator Normcdf InvNorm Probabilities
   • Z score Calculations and Calculator N...  

You can find p-values with a calculator as well.  This is what it looks like on a TI-NSPIRE
TI-NSPIRE Z score to Pval & Pval to Zscore NormCDF invNorm 
   • TI-NSPIRE Z score to Pval & Pval to Z...  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

z-score Calculations & Percentiles in a Normal Distribution

I defined causation, review the two types of lurking variables, and I go over the 5 checks for evidence of causation. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Causation Defined & 5 Key Checks for Signs of Causattion

I define density curves.  I also define Normality through the Empirical Rule.  We then introduce the Z-score formula, which is a linear transformation, and show how is allows us to use the Standard Normal Distribution to find p-values.  DENSITY CURVES 0:04 EMPERICAL RULE 3:48 Z-SCORE INTRO 6:50 EXAMPLE 11:01
I have no idea what happened to the end of my lesson.  If you need help finding area under a bell curve you can check out    • z-score Calculations & Percentiles in...  

Thank you very much Summer Rae Newhouse for providing the Closed Captions for this lesson.  Your help is greatly appreciated!!!

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Density Curves, Empirical Rule & Normality, Z-score Intro

I finish my lecture on Experimental Design with an introduction to Block Design, Matched Pairs Design, and Double Blind Experiments.

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Experimental Design Part 2

An introdution to Standard Deviation, it's properties, and the  linear transformation process.  LINEAR TRANSFORMATION AT 9:01

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Standard Deviation and Linear Transformations

I define and discuss the differences of observational studies and experiments.  I then discuss the difference between a sample and a census, then introduce two types of sampling techniques that yield biased results...Voluntary Response and Convenience Sampling.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Sampling Techniques Part 1

I explain the relationship between 2-sided significance tests and confidence intervals.
I have included some annotation corrections to improve some of the wording of my example.
DEFINING THE VARIABLE
Mu equals the mean amount of product.
CONCLUSION
Since our p value is between .05 and .10 which is greater than the level of significance of .05 we fail to reject Ho.  There is not enough evidence to conclude the companies product does not contain 16oz.  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

2 Sided Hypothesis Tests & Confidence Intervals Please Read Description

I work through a Chi Square test on a 2 way table without much aid from a calculator.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Chi Square Calculation by Hand

I do multiple examples of Normal Approximation calculations of sample proportions.  I also compare this process to using the binomcdf(n,p,k) commands in you calculator.
PLEASE NOTE: The Independence check should read:  Independence:  It is reasonable to assume the population of all people that travel is at least 10 times larger than 350 or 3500 people. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Example of 1 Sample Proportion Z-test

I overview the definition of standard deviaiton and introduce the IQR test in statistics.

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Standard Deviation Preview and IQR Test

In a two part video I introduce the Binomial Setting and Distribution where x is defined as the number of successes.  This lecture also includes the formulas and examples for of the Binomial Coefficient and the Binomial Probability Formula.  I also go over how to use the binompdf(n,p,k) and binomcdf(n,p,k) commands in a calculator.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Binomial Setting & Binomial Distribution in Statistics Pt 1

I help you identify left skewness, right skewness, and bell curves in an Ogive graph.  At 6:40 I said "this is left skewed"- that is incorrect. Skewness is determined by the direction of the tail. In the histogram, the tail tapers off to the right, so it is right skewed.﻿
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Determining Skewness In Ogive Graphs

I start going over 5 number summary of distributions, define resistance, and box plots.

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Resistance, Mean, Median, 5 Number Summary and BoxPlots

I introduce correlation and how it measures the strength and direction of a linear relationship.  I also discuss the many properties of correlation you must be familiar with.  Coefficient of Determination is also defined.

In the last example about MPG, r = -.8 and not positive .8 as written.

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Intro of Corellation "r" to measure linear strength

I introduce the concept of the Chi Square Test on 2 Way Tables.  I work through 2 examples.  1) Chi Square Test for Homogeneity of Populations 2) Chi Square Test for Independence  EXAMPLES AT 0:10 3:24 10:36

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Chi Square Test for Independence & Homogeneity

I introduce the basics of setting up a significance test, such as defining a null and alternative hypothesis, checking conditions, etc.  I finish by working through an example of a matched pairs t-test.  EXAMPLE AT 19:00  Please note these changes in wording of my example:  Normality:  With difference being fairly symmetric & unimodal, the CLT will ensure the sampling distribution of sample means will be approximately Normal.   Definition of Mu should be Mean of difference in Post Test and PreTest.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Significance Hypothesis Test Intro & Matched Pairs t-Test

I introduce how to do a 2 sample mean t test comparing 2 means in statistics.  I cover the goals of the comparison, the required conditions that need to be checked, robustness, how to combine means and variance, and give the formulas for z-test...t-test...and confidence intervals.  I finish with a few examples.  EXAMPLE begins at 22:48
I have added some annotations to refine the wording of my example:
DEFINING THE VARIABLES
Mu 1: Population mean improvement of test scores for traditional teaching.
Mu 2: Population mean improvement of test scores for teaching that incorporates technology.
NORMALITY CHECK
Normality: With N1+N2=20 which is between 15 and 30, the Central Limit Theorem ensures the sampling distribution of difference of means is approximately Normal since the box plots only show mild skewness.

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2 Sample t-test of Means & Confidence Interval PLEASE READ DESCRIPTION

Introducing the uses of histograms in statistics, how to construct them and interpret them.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Histograms in Statistics

The four key points are discussed when describing distributions in statistics...Shape, Center, Spread, and Outliers.  Please forgive the misspelling of DESCRIBED in the video.

TIP to identify Left & Right Skewness:  (Thanks LeBadman:)
Left: Mean is less than Median is less than Mode
Symmetrical: Mean, Median and Mode are approximately equal
Right: Mean is greater than Median is greater than Mode

You just take: Mean, Median, Mode
If it's left skewed, you will see the inequalities pointing to the left.
If it's right skewed, you will see the inequalities pointing to the right.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Describing Distributions in Statistics

In part one of this lecture I cover basic definitions related to experiments, the 3 Principles of Experimental Design, and define Statistical Significance.

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Experimental Design Part 1

I finish my three part introduction of Sample Surveys.  In this lecture I define Undercoverage, Non-Response, discuss causes of Biased Results, define Inference, and preview Sample Distributions. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Cautions about Sample Surveys, Causes of Bias, and Inference defined

I introduce the concept of confidence intervals and finish with an example of a one sample mean z interval.  A note about Margin of Error:  The Margin of Error accounts for random variability, NOT sampling errors, non-response, or undercoverage, etc.  EXAMPLE AT 16:50

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Intro to Confidence Intervals & 1 Sample Mean z Interval

I introduce the t-distribution and work through an example of a 1 Sample Mean t-Confidence Interval.  EXAMPLE AT 9:34
Some annotations are included:
Normality: With n greater than 30 the Central Limit Theorem ensures the sampling distribution of averages will be approximately Normal.  Make a connection between your problems n and standard size of 30.
In Example:
Normality: As long as the population distribution has no outliers and no strong skewness, the Central Limit Theorem should ensure the sampling distribution of sample means will be approximately Normal.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  