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For more information, please see full course syllabus of Statistics
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Lecture Comments (12)

0 answers

Post by Saadman Elman on August 31, 2014

It was very helpful! She clarified it very nicely.

0 answers

Post by Oliver Barry on May 2, 2014

Is there anywhere where we can get more examples to work through?

0 answers

Post by Ryan Hughes on February 10, 2014

Where does one ask questions from their class work that they would like help answering?

0 answers

Post by Abdihakim Mohamed on November 25, 2013

This is not specific, I feel like I am lost. I understand early part but the examples don't make sense. I mean basically I am lost in the examples.

0 answers

Post by Manoj Joseph on June 27, 2013

what do you mean by measured conclusions?

1 answer

Last reply by: Gayatri Arumugam
Tue Jan 8, 2013 11:48 PM

Post by Jameelah Hegazy on October 22, 2012

Great lecture.

Is it possible for members to save your lecture slides?

0 answers

Post by Matthew Manning on September 17, 2012

Just to make sure I'm understanding this correctly, Descriptive Statistics is basically exact information (the type of information that we desire from a population, but are unable to obtain. Inferential statistics is the information that we gain from samples, and we then use that info in order to come to conclusions.

0 answers

Post by Matthew Manning on September 16, 2012

What specific areas of Math on Educator.Com should I brush up on in order be successful at Statistics, I have obtained an override to bypass lower level classes. But I need to know specifically what I need to review in order to do well. Please be very specific, Thanks

0 answers

Post by Daniel Goff on April 18, 2012

great lecture...very informative

0 answers

Post by M Holland on December 1, 2010

Extra example 2 has errors in the finding the probability of the first item

0 answers

Post by Abraham Hsu on February 11, 2010

***Column "Yes" total =/= 279, but 379, therefore 178/379

Descriptive Statistics vs. Inferential Statistics

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Transcription: Descriptive Statistics vs. Inferential Statistics

Hi welcome to the first lesson in www.educator.com statistics course.0000

Today we are going to talk about descriptive statistics versus inferential statistics.0005

Here is the road map for today, first we need to distinguish how statistics is different from other mathematics.0012

We will talk about how descriptive and inferential statistics separate.0018

Finally we are going to talk about populations versus samples and then we are going to put all of those ideas together 0024

and look at how population, samples, descriptive, and inferential statistics all fit together.0030

First things first, how is statistics different from other specializations in mathematics such as trigonometry, geometry, calculus, linear algebra.0037

Statistics is different because it is the science of classifying, organizing, and interpreting or analyzing data.0048

You might be thinking to yourself - "Hey science? I thought this was mathematics." Right?0055

Its link implies much of science and because of that it is important in mathematics.0063

Let me explain that link to you in just one second.0069

First I want to step back and think about high school science firmament. 0073

A lot of high school science is concerned with measurement, we go around measuring things and measuring how fast people run 0077

and how fast things are dropped and how much things grow and how much things way.0084

How big things are and we are gathering a lot of data on measurement.0089

Then we find patterns within those measurements and that is basically the fundamentals behind high school science.0095

Those patterns can often be described as mathematical formulas.0104

I do not know if you have this experience that some of you may have had the experience of trying to derive the gravitational constant.0110

To some of you this equation might look familiar, D= ½ gt2.0117

(D) stands for distance, (g) stands for the gravitational constant and (t) stands for time.0126

Some of you may have had the experience of dropping things off a building and timing them 0138

and putting in these numbers to try and figure out what (g) is.0143

(g) theoretically is supposed to be 9.8 m/sec2.0149

But rarely do you calculate exactly 9.8 when you put in distance and time into this equation.0159

Often, science students think I'm terrible at science, I’m not getting the right answer 0167

but it is because all of these measurements are inherently a little bit sloppy.0173

Granted that high school students might be sloppier scientists than other scientists but in actuality all science experiments 0178

have measurement error and there is variance that comes with measurement.0186

There is always a little bit of jiggle in that data and often we do not pinpoint the exact right data even when you look at something 0191

like measuring someone's height, you might have 10 people measure the same person's height and come up with slightly different answers.0199

It is not because they are trying to cheat but that person might that a deep breath or slouch a little bit 0207

or maybe they read the tape measure at their hairline instead at their actual height. 0213

There are always different reasons for measurement error.0222

All science is fought with measurement error.0225

While because all experiments, even the good ones at SERV, MIT and Caltech, all experiments will have a little bit sloppiness.0230

That is because we are dealing with measuring the physical world.0242

It is not bad which we are looking at terrible scientist or just real messy 0250

it is just that inherently in measuring the world we are going to have a little bit of sloppiness.0256

Now because of that sloppiness, even the best experiment will produce a scatter of numbers.0262

Even best experiment as well as the worst experiments they will produce a scatter of values or measurements.0269

That is where the problem is right?0289

You will not get just one number like nice 9.8 gravitational constant, you will instead get this scatter of numbers.0290

How do we deal with that scatter and that is where statistics come in.0299

Statistics is the math of distributions then you could see how the math part and the science part fit together.0305

Statistics is invented because we want to do better in science.0311

We even have a special name for the scatter of measurements and that is called a distribution.0317

Not only that but we are going to look and see how we can go from frequencies of these values 0330

in order to get probability distributions of these values.0337

Those are also going to be called probability distributions.0341

One thing that should come to your mind is that when you have a scatter of values or a whole bunch of different probabilities 0360

predicting different values then you are not going to have just one number, you are going to have a whole set of numbers.0366

Because of that we are going to have to deal with the mathematics a little bit differently.0373

We are not just computing one number at a time and looking at one number and adding things to it, subtracting things to it, doing things to it.0378

Instead we are looking at entire distributions.0385

How do we treat these distributions?0389

How do we interpret them?0390

That is the question behind statistics.0392

You might think working with whole distributions that sounds problematic.0395

Sometimes it might seem like it.0400

It might seem like these equations are pretty complicated because we have to deal with the whole distribution.0403

Also you will get some great stuff out of working with distributions.0408

One reason is because distributions are often much more predictable than individual values.0412

Distributions are more predictable than individual values.0419

Models of distributions or theories of distributions can often predict the mathematical nature of randomness.0435

Is it not great?0444

They are predicting randomness.0445

That is what statistics is a little bit about, it is dealing with that randomness and teaming it.0448

How is statistics different from other specializations in mathematics?0456

It is born out of the science of classifying, organizing, and interpreting data, distributions of data to be more precise.0460

And because of that statistics is the mathematics of distributions.0469

Statistics is fundamental in all science in both natural and social sciences.0474

I’m a social science professor, a psychology professor by trade but even in the natural sciences all these discoveries that you have heard of 0480

they only come about through rigorous applications of statistics in physics, biology, economics, psychology,0490

you name it statistics have left its math there.0497

There are two skills that you need to know when to enter into statistics.0502

The first is the skill of data description or what you can think of that as exploration.0506

Often you could think of it as just an open-ended examination of the data.0512

Let us look and see what is there.0516

We are looking for patterns and often it is helpful to make a graph or to look at averages 0518

and standard deviations that are called summary values when you are looking for patterns.0524

These are tools that help us see patterns better.0535

The problem with just exploring or describing data is that you are not able to come to any conclusions.0540

You have to rain yourself from making conclusions when you are just doing descriptive statistics that is inferential statistics will come in.0548

When you make inferences in statistics you are doing a much more strict examination of the data according to set rules.0557

Then you will judge whether these patterns that you find through description are likely or not according to theories 0566

and different models that you may have set up.0575

At the end of inferential statistics you should be able to make measured conclusions.0579

Often in science we do not say statistics has proven this theory or completely disproven this theory.0585

Instead we make much more measured and qualified conclusions.0593

Those skills of description and inference applied directly to descriptive statistics and inferential statistics.0601

This thing that is different now is you want to think about those skills and how they apply to distributions.0611

Here is how descriptive statistics applies to distributions.0619

These are the concepts and tools that you need in order to analyze sample distributions.0624

Use to describe or explore sample distributions.0637

We just have taken the same concepts of what describing data means and we have applied it to sample distributions.0653

Distributions that we have plucked out and a set of data that we plucked out.0660

In inferential statistics what we need to do is then apply inference to distribution.0666

Here it is the concepts and tools to reason from sample distribution.0674

To make some inference to reason from a sample distribution to a larger population distribution.0694

In inferential statistics what we are doing is using those skills of inference to go from sample distributions 0715

but not only just to understand the sample but to make some inferences about a greater larger population.0721

Just to go beyond our actual data.0728

In descriptive statistics we just stay with our sample.0731

We do not make any inferences beyond what we have.0735

It behooves us to figure out what is the difference between the population and the sample distribution?0743

Here it might be helpful to just think of the population a sort of like the truth.0751

This is where we are interested in.0756

Is it the truth? This is the truth.0759

This is the thing that we want to get at.0765

If you think about the gravitational constant, this is that magical value that is out there in the world.0767

The sample is not the truth, it is like a little bit of that truth.0775

When we drop our objects from the top of the building and measure how fast they come down, we are getting samples.0781

From those samples we are trying to get at the truth.0791

The sample is not the whole truth but the sample does provide a window to the truth.0794

It is important to realize that the sample is not the actual truth itself.0803

This is not what we want to know about.0808

We want to know about the population but we are using the sample in order to know about the population.0812

Some pros and cons.0819

Some pros of the population is this because it is the truth if you happen to have all the information 0822

about the real population it will be absolutely 100% accurate.0828

However here is the con, it is almost impossible to get.0836

It is almost impossible to get the truth, the real population true.0847

For instance let us say you just want to know what the real average height of every person in the United States is.0853

In order to do that you would have to get measurements from every single person in the United States.0861

All of those measurements would have to be 100% accurate.0868

Let us say I will give that to you, you will even do that.0872

By the time you are finish recording all of those measurements, some people would have died and new people will have been born.0874

All of a sudden your measurements would not be accurate anymore.0881

It is almost impossible to get the entire population.0885

Often in statistics, they will pick a small population like they will say consider all the people who attend your school 0890

and to shrink down the population that you could think about it without feeling like your mind is being blown.0897

In the real world it is basically impossible to get the real truth.0905

On the other hand, the sample has the pro of being convenient.0910

It is easy to get data from just a sample of the population. 0917

You do not have to get the whole population, you just have to get a sample of it and it is convenient and easy to get. 0923

Here is the big con that you need to worry about.0929

The con is that the sample might be what is called biased.0933

By biased they do not necessarily mean like the sample like racists or prejudiced in some way, 0938

I just mean that the sample may not be representative of the population.0944

The problem with that is when we look at our sample we are going to use our sample to try to get on the truth.0960

If our sample is different from the truth then it might lead us astray and that is called being biased.0965

When we describe the population in terms of numbers and we get some summary values for the population, 0975

those descriptive values are going to be called parameters.0982

A friend of mine who teaches statistics with a help of the population parameter.0988

On the other hand, for samples you would use what is called statistics.0996

This word for statistics is the same word as the word for the class.1006

But statistics covers all of statistics, descriptive, inferential, population, sample, all that stuff.1010

This is the sort of smaller use of that word.1018

Population and parameter, specific sample for statistics.1024

Now let us put all those ideas together.1033

How do we put together descriptive and inferential statistics with populations and samples?1036

It helps us to ground ourselves by starting off with the idea that what we are interested in, in knowing about is the entire population.1042

We want to know about the real population.1052

Let us deal with one population at a time for now.1056

Often we do not have the population's entire data in front of us, we only have a sample of that data. 1060

This is our wish to go from sample to the population but remember the sample can be biased, that is problematic.1069

Here is where statistics comes in.1080

From samples we compute statistics and from populations we could know the parameters.1083

But we often do not have this link either because we do not know anything about the actual population.1097

Here is where we are, what inferential statistics will help us do is make this link.1106

How do we go from statistics of the sample to population parameters?1114

This jump, this inferential jump is going to be made through inferential statistics.1119

However in order to go from the sample to statistics we will use descriptive statistics.1134

This is how it all fits together.1147

Let us try some examples. 1150

Here is example 1, a pollster asks a group of voters how they intend to vote in the upcoming election for governor.1153

In this example is the individual pollster primarily using descriptive statistics or inferential statistics.1161

What he or she computes parameters or samples.1171

Here the pollster is just asking a group of voters how they intend to vote.1175

A poll is often just a sample of the entire set of voters so I would say the pollster is probably going to compute some sample statistics.1180

We should say statistics not samples.1194

I would say the pollster is probably calculating statistics.1202

If the pollster just got an answer such as this sample of voters is going to vote for the governor 75% of them are going to vote for the governor 1208

and only 25% are not that would be counted as descriptive statistics.1219

Once this pollster actually uses that information to then make some inferences and predicts and then I predict the governor will win, 1225

that would be inferential statistics.1236

But so far, it does not say that.1238

It seems that only descriptive statistics is being used here.1242

Example 2, a teacher organizes his classes test grades into distribution from best to worst and compares it to the test grades of the entire school.1248

In this example is the individual primarily using descriptive statistics or inferential statistics.1259

First he is definitely using descriptive statistics in order to organize his classes data.1265

He is using this but then he is comparing it to the test grades that the entire school.1273

He is getting his sample, his class and looking at how they are relative to the entire school.1279

That leap is going to be inferential statistics.1290

I would say he is using both descriptive and inferential.1294

A statistician is interested in the choices of majors of this year’s entering freshmen at a university 10% of randomly sampled.1302

What is the population? what is the sample? What is the parameter? What is the statistic?1311

The population seems to be all freshmen at the University, right? but the sample is this 10%.1317

That is the population and the sample so what is the parameter?1337

The parameter is what are the real major choices of all the students.1342

Maybe he will look at it as you know maybe 50% are engineering and 20% are science and 30% are humanities.1355

Majors picked by freshmen.1374

What is the actual statistic?1383

The statistic that is going to be made up of the majors picked by the sample.1386

In order to go from this to this, you will need to use inferential statistics.1401

Example 4, a group of pediatricians are trying to estimate the rate of increase in obesity in young children in their city.1410

They begin a research project for every four years a group of 8 year-old children are randomly sampled from the city and weighed.1418

What is the population? What is the sample? what is the parameter? what is the statistic?1425

The population looks like young children in the city, whichever city this happens to be.1431

The sample is the group of 8 year-old children, group of selected to be in this study.1446

What is the parameter? 1469

The parameter would really be the actual rate of increasing obesity and they do not know what that is, they can not get that data.1474

By looking at the different groups of 8 year-old children every four years they could look at the rate between the samples.1490

The statistic would be the rate among the sample, the samples every four years.1503

In that way they will try to use this rate in order to estimate this rate.1521

That is the end of lesson one for www.educator.com.1527

Thanks so much for watching.1530

I. Introduction
  Descriptive Statistics vs. Inferential Statistics 25:31
   Intro 0:00 
   Roadmap 0:10 
    Roadmap 0:11 
   Statistics 0:35 
    Statistics 0:36 
   Let's Think About High School Science 1:12 
    Measurement and Find Patterns (Mathematical Formula) 1:13 
   Statistics = Math of Distributions 4:58 
    Distributions 4:59 
    Problematic… but also GREAT 5:58 
   Statistics 7:33 
    How is It Different from Other Specializations in Mathematics? 7:34 
    Statistics is Fundamental in Natural and Social Sciences 7:53 
   Two Skills of Statistics 8:20 
    Description (Exploration) 8:21 
    Inference 9:13 
   Descriptive Statistics vs. Inferential Statistics: Apply to Distributions 9:58 
    Descriptive Statistics 9:59 
    Inferential Statistics 11:05 
   Populations vs. Samples 12:19 
    Populations vs. Samples: Is it the Truth? 12:20 
    Populations vs. Samples: Pros & Cons 13:36 
    Populations vs. Samples: Descriptive Values 16:12 
   Putting Together Descriptive/Inferential Stats & Populations/Samples 17:10 
    Putting Together Descriptive/Inferential Stats & Populations/Samples 17:11 
   Example 1: Descriptive Statistics vs. Inferential Statistics 19:09 
   Example 2: Descriptive Statistics vs. Inferential Statistics 20:47 
   Example 3: Sample, Parameter, Population, and Statistic 21:40 
   Example 4: Sample, Parameter, Population, and Statistic 23:28 
II. About Samples: Cases, Variables, Measurements
  About Samples: Cases, Variables, Measurements 32:14
   Intro 0:00 
   Data 0:09 
    Data, Cases, Variables, and Values 0:10 
    Rows, Columns, and Cells 2:03 
    Example: Aircrafts 3:52 
   How Do We Get Data? 5:38 
    Research: Question and Hypothesis 5:39 
    Research Design 7:11 
    Measurement 7:29 
    Research Analysis 8:33 
    Research Conclusion 9:30 
   Types of Variables 10:03 
    Discrete Variables 10:04 
    Continuous Variables 12:07 
   Types of Measurements 14:17 
    Types of Measurements 14:18 
   Types of Measurements (Scales) 17:22 
    Nominal 17:23 
    Ordinal 19:11 
    Interval 21:33 
    Ratio 24:24 
   Example 1: Cases, Variables, Measurements 25:20 
   Example 2: Which Scale of Measurement is Used? 26:55 
   Example 3: What Kind of a Scale of Measurement is This? 27:26 
   Example 4: Discrete vs. Continuous Variables. 30:31 
III. Visualizing Distributions
  Introduction to Excel 8:09
   Intro 0:00 
   Before Visualizing Distribution 0:10 
    Excel 0:11 
   Excel: Organization 0:45 
    Workbook 0:46 
    Column x Rows 1:50 
    Tools: Menu Bar, Standard Toolbar, and Formula Bar 3:00 
   Excel + Data 6:07 
    Exce and Data 6:08 
  Frequency Distributions in Excel 39:10
   Intro 0:00 
   Roadmap 0:08 
    Data in Excel and Frequency Distributions 0:09 
   Raw Data to Frequency Tables 0:42 
    Raw Data to Frequency Tables 0:43 
    Frequency Tables: Using Formulas and Pivot Tables 1:28 
   Example 1: Number of Births 7:17 
   Example 2: Age Distribution 20:41 
   Example 3: Height Distribution 27:45 
   Example 4: Height Distribution of Males 32:19 
  Frequency Distributions and Features 25:29
   Intro 0:00 
   Roadmap 0:10 
    Data in Excel, Frequency Distributions, and Features of Frequency Distributions 0:11 
   Example #1 1:35 
    Uniform 1:36 
   Example #2 2:58 
    Unimodal, Skewed Right, and Asymmetric 2:59 
   Example #3 6:29 
    Bimodal 6:30 
   Example #4a 8:29 
    Symmetric, Unimodal, and Normal 8:30 
    Point of Inflection and Standard Deviation 11:13 
   Example #4b 12:43 
    Normal Distribution 12:44 
   Summary 13:56 
    Uniform, Skewed, Bimodal, and Normal 13:57 
   Sketch Problem 1: Driver's License 17:34 
   Sketch Problem 2: Life Expectancy 20:01 
   Sketch Problem 3: Telephone Numbers 22:01 
   Sketch Problem 4: Length of Time Used to Complete a Final Exam 23:43 
  Dotplots and Histograms in Excel 42:42
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Previously 1:02 
    Data, Frequency Table, and visualization 1:03 
   Dotplots 1:22 
    Dotplots Excel Example 1:23 
   Dotplots: Pros and Cons 7:22 
    Pros and Cons of Dotplots 7:23 
    Dotplots Excel Example Cont. 9:07 
   Histograms 12:47 
    Histograms Overview 12:48 
    Example of Histograms 15:29 
   Histograms: Pros and Cons 31:39 
    Pros 31:40 
    Cons 32:31 
   Frequency vs. Relative Frequency 32:53 
    Frequency 32:54 
    Relative Frequency 33:36 
   Example 1: Dotplots vs. Histograms 34:36 
   Example 2: Age of Pennies Dotplot 36:21 
   Example 3: Histogram of Mammal Speeds 38:27 
   Example 4: Histogram of Life Expectancy 40:30 
  Stemplots 12:23
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   What Sets Stemplots Apart? 0:46 
    Data Sets, Dotplots, Histograms, and Stemplots 0:47 
   Example 1: What Do Stemplots Look Like? 1:58 
   Example 2: Back-to-Back Stemplots 5:00 
   Example 3: Quiz Grade Stemplot 7:46 
   Example 4: Quiz Grade & Afterschool Tutoring Stemplot 9:56 
  Bar Graphs 22:49
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:08 
   Review of Frequency Distributions 0:44 
    Y-axis and X-axis 0:45 
    Types of Frequency Visualizations Covered so Far 2:16 
    Introduction to Bar Graphs 4:07 
   Example 1: Bar Graph 5:32 
    Example 1: Bar Graph 5:33 
   Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs? 11:07 
    Do Shapes, Center, and Spread of Distributions Apply to Bar Graphs? 11:08 
   Example 2: Create a Frequency Visualization for Gender 14:02 
   Example 3: Cases, Variables, and Frequency Visualization 16:34 
   Example 4: What Kind of Graphs are Shown Below? 19:29 
IV. Summarizing Distributions
  Central Tendency: Mean, Median, Mode 38:50
   Intro 0:00 
   Roadmap 0:07 
    Roadmap 0:08 
   Central Tendency 1 0:56 
    Way to Summarize a Distribution of Scores 0:57 
    Mode 1:32 
    Median 2:02 
    Mean 2:36 
   Central Tendency 2 3:47 
    Mode 3:48 
    Median 4:20 
    Mean 5:25 
   Summation Symbol 6:11 
    Summation Symbol 6:12 
   Population vs. Sample 10:46 
    Population vs. Sample 10:47 
   Excel Examples 15:08 
    Finding Mode, Median, and Mean in Excel 15:09 
   Median vs. Mean 21:45 
    Effect of Outliers 21:46 
    Relationship Between Parameter and Statistic 22:44 
    Type of Measurements 24:00 
    Which Distributions to Use With 24:55 
   Example 1: Mean 25:30 
   Example 2: Using Summation Symbol 29:50 
   Example 3: Average Calorie Count 32:50 
   Example 4: Creating an Example Set 35:46 
  Variability 42:40
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Variability (or Spread) 0:45 
    Variability (or Spread) 0:46 
   Things to Think About 5:45 
    Things to Think About 5:46 
   Range, Quartiles and Interquartile Range 6:37 
    Range 6:38 
    Interquartile Range 8:42 
   Interquartile Range Example 10:58 
    Interquartile Range Example 10:59 
   Variance and Standard Deviation 12:27 
    Deviations 12:28 
    Sum of Squares 14:35 
    Variance 16:55 
    Standard Deviation 17:44 
   Sum of Squares (SS) 18:34 
    Sum of Squares (SS) 18:35 
   Population vs. Sample SD 22:00 
    Population vs. Sample SD 22:01 
   Population vs. Sample 23:20 
    Mean 23:21 
    SD 23:51 
   Example 1: Find the Mean and Standard Deviation of the Variable Friends in the Excel File 27:21 
   Example 2: Find the Mean and Standard Deviation of the Tagged Photos in the Excel File 35:25 
   Example 3: Sum of Squares 38:58 
   Example 4: Standard Deviation 41:48 
  Five Number Summary & Boxplots 57:15
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Summarizing Distributions 0:37 
    Shape, Center, and Spread 0:38 
    5 Number Summary 1:14 
   Boxplot: Visualizing 5 Number Summary 3:37 
    Boxplot: Visualizing 5 Number Summary 3:38 
   Boxplots on Excel 9:01 
    Using 'Stocks' and Using Stacked Columns 9:02 
    Boxplots on Excel Example 10:14 
   When are Boxplots Useful? 32:14 
    Pros 32:15 
    Cons 32:59 
   How to Determine Outlier Status 33:24 
    Rule of Thumb: Upper Limit 33:25 
    Rule of Thumb: Lower Limit 34:16 
    Signal Outliers in an Excel Data File Using Conditional Formatting 34:52 
   Modified Boxplot 48:38 
    Modified Boxplot 48:39 
   Example 1: Percentage Values & Lower and Upper Whisker 49:10 
   Example 2: Boxplot 50:10 
   Example 3: Estimating IQR From Boxplot 53:46 
   Example 4: Boxplot and Missing Whisker 54:35 
  Shape: Calculating Skewness & Kurtosis 41:51
   Intro 0:00 
   Roadmap 0:16 
    Roadmap 0:17 
   Skewness Concept 1:09 
    Skewness Concept 1:10 
   Calculating Skewness 3:26 
    Calculating Skewness 3:27 
   Interpreting Skewness 7:36 
    Interpreting Skewness 7:37 
    Excel Example 8:49 
   Kurtosis Concept 20:29 
    Kurtosis Concept 20:30 
   Calculating Kurtosis 24:17 
    Calculating Kurtosis 24:18 
   Interpreting Kurtosis 29:01 
    Leptokurtic 29:35 
    Mesokurtic 30:10 
    Platykurtic 31:06 
    Excel Example 32:04 
   Example 1: Shape of Distribution 38:28 
   Example 2: Shape of Distribution 39:29 
   Example 3: Shape of Distribution 40:14 
   Example 4: Kurtosis 41:10 
  Normal Distribution 34:33
   Intro 0:00 
   Roadmap 0:13 
    Roadmap 0:14 
   What is a Normal Distribution 0:44 
    The Normal Distribution As a Theoretical Model 0:45 
   Possible Range of Probabilities 3:05 
    Possible Range of Probabilities 3:06 
   What is a Normal Distribution 5:07 
    Can Be Described By 5:08 
    Properties 5:49 
   'Same' Shape: Illusion of Different Shape! 7:35 
    'Same' Shape: Illusion of Different Shape! 7:36 
   Types of Problems 13:45 
    Example: Distribution of SAT Scores 13:46 
   Shape Analogy 19:48 
    Shape Analogy 19:49 
   Example 1: The Standard Normal Distribution and Z-Scores 22:34 
   Example 2: The Standard Normal Distribution and Z-Scores 25:54 
   Example 3: Sketching and Normal Distribution 28:55 
   Example 4: Sketching and Normal Distribution 32:32 
  Standard Normal Distributions & Z-Scores 41:44
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   A Family of Distributions 0:28 
    Infinite Set of Distributions 0:29 
    Transforming Normal Distributions to 'Standard' Normal Distribution 1:04 
   Normal Distribution vs. Standard Normal Distribution 2:58 
    Normal Distribution vs. Standard Normal Distribution 2:59 
   Z-Score, Raw Score, Mean, & SD 4:08 
    Z-Score, Raw Score, Mean, & SD 4:09 
   Weird Z-Scores 9:40 
    Weird Z-Scores 9:41 
   Excel 16:45 
    For Normal Distributions 16:46 
    For Standard Normal Distributions 19:11 
    Excel Example 20:24 
   Types of Problems 25:18 
    Percentage Problem: P(x) 25:19 
    Raw Score and Z-Score Problems 26:28 
    Standard Deviation Problems 27:01 
   Shape Analogy 27:44 
    Shape Analogy 27:45 
   Example 1: Deaths Due to Heart Disease vs. Deaths Due to Cancer 28:24 
   Example 2: Heights of Male College Students 33:15 
   Example 3: Mean and Standard Deviation 37:14 
   Example 4: Finding Percentage of Values in a Standard Normal Distribution 37:49 
  Normal Distribution: PDF vs. CDF 55:44
   Intro 0:00 
   Roadmap 0:15 
    Roadmap 0:16 
   Frequency vs. Cumulative Frequency 0:56 
    Frequency vs. Cumulative Frequency 0:57 
   Frequency vs. Cumulative Frequency 4:32 
    Frequency vs. Cumulative Frequency Cont. 4:33 
   Calculus in Brief 6:21 
    Derivative-Integral Continuum 6:22 
   PDF 10:08 
    PDF for Standard Normal Distribution 10:09 
    PDF for Normal Distribution 14:32 
   Integral of PDF = CDF 21:27 
    Integral of PDF = CDF 21:28 
   Example 1: Cumulative Frequency Graph 23:31 
   Example 2: Mean, Standard Deviation, and Probability 24:43 
   Example 3: Mean and Standard Deviation 35:50 
   Example 4: Age of Cars 49:32 
V. Linear Regression
  Scatterplots 47:19
   Intro 0:00 
   Roadmap 0:04 
    Roadmap 0:05 
   Previous Visualizations 0:30 
    Frequency Distributions 0:31 
   Compare & Contrast 2:26 
    Frequency Distributions Vs. Scatterplots 2:27 
   Summary Values 4:53 
    Shape 4:54 
    Center & Trend 6:41 
    Spread & Strength 8:22 
    Univariate & Bivariate 10:25 
   Example Scatterplot 10:48 
    Shape, Trend, and Strength 10:49 
   Positive and Negative Association 14:05 
    Positive and Negative Association 14:06 
   Linearity, Strength, and Consistency 18:30 
    Linearity 18:31 
    Strength 19:14 
    Consistency 20:40 
   Summarizing a Scatterplot 22:58 
    Summarizing a Scatterplot 22:59 
   Example 1: Gapminder.org, Income x Life Expectancy 26:32 
   Example 2: Gapminder.org, Income x Infant Mortality 36:12 
   Example 3: Trend and Strength of Variables 40:14 
   Example 4: Trend, Strength and Shape for Scatterplots 43:27 
  Regression 32:02
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Linear Equations 0:34 
    Linear Equations: y = mx + b 0:35 
   Rough Line 5:16 
    Rough Line 5:17 
   Regression - A 'Center' Line 7:41 
    Reasons for Summarizing with a Regression Line 7:42 
    Predictor and Response Variable 10:04 
   Goal of Regression 12:29 
    Goal of Regression 12:30 
   Prediction 14:50 
    Example: Servings of Mile Per Year Shown By Age 14:51 
    Intrapolation 17:06 
    Extrapolation 17:58 
   Error in Prediction 20:34 
    Prediction Error 20:35 
    Residual 21:40 
   Example 1: Residual 23:34 
   Example 2: Large and Negative Residual 26:30 
   Example 3: Positive Residual 28:13 
   Example 4: Interpret Regression Line & Extrapolate 29:40 
  Least Squares Regression 56:36
   Intro 0:00 
   Roadmap 0:13 
    Roadmap 0:14 
   Best Fit 0:47 
    Best Fit 0:48 
   Sum of Squared Errors (SSE) 1:50 
    Sum of Squared Errors (SSE) 1:51 
   Why Squared? 3:38 
    Why Squared? 3:39 
   Quantitative Properties of Regression Line 4:51 
    Quantitative Properties of Regression Line 4:52 
   So How do we Find Such a Line? 6:49 
    SSEs of Different Line Equations & Lowest SSE 6:50 
    Carl Gauss' Method 8:01 
   How Do We Find Slope (b1) 11:00 
    How Do We Find Slope (b1) 11:01 
   Hoe Do We Find Intercept 15:11 
    Hoe Do We Find Intercept 15:12 
   Example 1: Which of These Equations Fit the Above Data Best? 17:18 
   Example 2: Find the Regression Line for These Data Points and Interpret It 26:31 
   Example 3: Summarize the Scatterplot and Find the Regression Line. 34:31 
   Example 4: Examine the Mean of Residuals 43:52 
  Correlation 43:58
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Summarizing a Scatterplot Quantitatively 0:47 
    Shape 0:48 
    Trend 1:11 
    Strength: Correlation ® 1:45 
   Correlation Coefficient ( r ) 2:30 
    Correlation Coefficient ( r ) 2:31 
   Trees vs. Forest 11:59 
    Trees vs. Forest 12:00 
   Calculating r 15:07 
    Average Product of z-scores for x and y 15:08 
   Relationship between Correlation and Slope 21:10 
    Relationship between Correlation and Slope 21:11 
   Example 1: Find the Correlation between Grams of Fat and Cost 24:11 
   Example 2: Relationship between r and b1 30:24 
   Example 3: Find the Regression Line 33:35 
   Example 4: Find the Correlation Coefficient for this Set of Data 37:37 
  Correlation: r vs. r-squared 52:52
   Intro 0:00 
   Roadmap 0:07 
    Roadmap 0:08 
   R-squared 0:44 
    What is the Meaning of It? Why Squared? 0:45 
   Parsing Sum of Squared (Parsing Variability) 2:25 
    SST = SSR + SSE 2:26 
   What is SST and SSE? 7:46 
    What is SST and SSE? 7:47 
   r-squared 18:33 
    Coefficient of Determination 18:34 
   If the Correlation is Strong… 20:25 
    If the Correlation is Strong… 20:26 
   If the Correlation is Weak… 22:36 
    If the Correlation is Weak… 22:37 
   Example 1: Find r-squared for this Set of Data 23:56 
   Example 2: What Does it Mean that the Simple Linear Regression is a 'Model' of Variance? 33:54 
   Example 3: Why Does r-squared Only Range from 0 to 1 37:29 
   Example 4: Find the r-squared for This Set of Data 39:55 
  Transformations of Data 27:08
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Why Transform? 0:26 
    Why Transform? 0:27 
   Shape-preserving vs. Shape-changing Transformations 5:14 
    Shape-preserving = Linear Transformations 5:15 
    Shape-changing Transformations = Non-linear Transformations 6:20 
   Common Shape-Preserving Transformations 7:08 
    Common Shape-Preserving Transformations 7:09 
   Common Shape-Changing Transformations 8:59 
    Powers 9:00 
    Logarithms 9:39 
   Change Just One Variable? Both? 10:38 
    Log-log Transformations 10:39 
    Log Transformations 14:38 
   Example 1: Create, Graph, and Transform the Data Set 15:19 
   Example 2: Create, Graph, and Transform the Data Set 20:08 
   Example 3: What Kind of Model would You Choose for this Data? 22:44 
   Example 4: Transformation of Data 25:46 
VI. Collecting Data in an Experiment
  Sampling & Bias 54:44
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Descriptive vs. Inferential Statistics 1:04 
    Descriptive Statistics: Data Exploration 1:05 
    Example 2:03 
   To tackle Generalization… 4:31 
    Generalization 4:32 
    Sampling 6:06 
    'Good' Sample 6:40 
   Defining Samples and Populations 8:55 
    Population 8:56 
    Sample 11:16 
   Why Use Sampling? 13:09 
    Why Use Sampling? 13:10 
   Goal of Sampling: Avoiding Bias 15:04 
    What is Bias? 15:05 
    Where does Bias Come from: Sampling Bias 17:53 
    Where does Bias Come from: Response Bias 18:27 
   Sampling Bias: Bias from Bas Sampling Methods 19:34 
    Size Bias 19:35 
    Voluntary Response Bias 21:13 
    Convenience Sample 22:22 
    Judgment Sample 23:58 
    Inadequate Sample Frame 25:40 
   Response Bias: Bias from 'Bad' Data Collection Methods 28:00 
    Nonresponse Bias 29:31 
    Questionnaire Bias 31:10 
    Incorrect Response or Measurement Bias 37:32 
   Example 1: What Kind of Biases? 40:29 
   Example 2: What Biases Might Arise? 44:46 
   Example 3: What Kind of Biases? 48:34 
   Example 4: What Kind of Biases? 51:43 
  Sampling Methods 14:25
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Biased vs. Unbiased Sampling Methods 0:32 
    Biased Sampling 0:33 
    Unbiased Sampling 1:13 
   Probability Sampling Methods 2:31 
    Simple Random 2:54 
    Stratified Random Sampling 4:06 
    Cluster Sampling 5:24 
    Two-staged Sampling 6:22 
    Systematic Sampling 7:25 
   Example 1: Which Type(s) of Sampling was this? 8:33 
   Example 2: Describe How to Take a Two-Stage Sample from this Book 10:16 
   Example 3: Sampling Methods 11:58 
   Example 4: Cluster Sample Plan 12:48 
  Research Design 53:54
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Descriptive vs. Inferential Statistics 0:51 
    Descriptive Statistics: Data Exploration 0:52 
    Inferential Statistics 1:02 
   Variables and Relationships 1:44 
    Variables 1:45 
    Relationships 2:49 
   Not Every Type of Study is an Experiment… 4:16 
    Category I - Descriptive Study 4:54 
    Category II - Correlational Study 5:50 
    Category III - Experimental, Quasi-experimental, Non-experimental 6:33 
   Category III 7:42 
    Experimental, Quasi-experimental, and Non-experimental 7:43 
   Why CAN'T the Other Strategies Determine Causation? 10:18 
    Third-variable Problem 10:19 
    Directionality Problem 15:49 
   What Makes Experiments Special? 17:54 
    Manipulation 17:55 
    Control (and Comparison) 21:58 
   Methods of Control 26:38 
    Holding Constant 26:39 
    Matching 29:11 
    Random Assignment 31:48 
   Experiment Terminology 34:09 
    'true' Experiment vs. Study 34:10 
    Independent Variable (IV) 35:16 
    Dependent Variable (DV) 35:45 
    Factors 36:07 
    Treatment Conditions 36:23 
    Levels 37:43 
    Confounds or Extraneous Variables 38:04 
   Blind 38:38 
    Blind Experiments 38:39 
    Double-blind Experiments 39:29 
   How Categories Relate to Statistics 41:35 
    Category I - Descriptive Study 41:36 
    Category II - Correlational Study 42:05 
    Category III - Experimental, Quasi-experimental, Non-experimental 42:43 
   Example 1: Research Design 43:50 
   Example 2: Research Design 47:37 
   Example 3: Research Design 50:12 
   Example 4: Research Design 52:00 
  Between and Within Treatment Variability 41:31
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Experimental Designs 0:51 
    Experimental Designs: Manipulation & Control 0:52 
   Two Types of Variability 2:09 
    Between Treatment Variability 2:10 
    Within Treatment Variability 3:31 
   Updated Goal of Experimental Design 5:47 
    Updated Goal of Experimental Design 5:48 
   Example: Drugs and Driving 6:56 
    Example: Drugs and Driving 6:57 
   Different Types of Random Assignment 11:27 
    All Experiments 11:28 
    Completely Random Design 12:02 
    Randomized Block Design 13:19 
   Randomized Block Design 15:48 
    Matched Pairs Design 15:49 
    Repeated Measures Design 19:47 
   Between-subject Variable vs. Within-subject Variable 22:43 
    Completely Randomized Design 22:44 
    Repeated Measures Design 25:03 
   Example 1: Design a Completely Random, Matched Pair, and Repeated Measures Experiment 26:16 
   Example 2: Block Design 31:41 
   Example 3: Completely Randomized Designs 35:11 
   Example 4: Completely Random, Matched Pairs, or Repeated Measures Experiments? 39:01 
VII. Review of Probability Axioms
  Sample Spaces 37:52
   Intro 0:00 
   Roadmap 0:07 
    Roadmap 0:08 
   Why is Probability Involved in Statistics 0:48 
    Probability 0:49 
    Can People Tell the Difference between Cheap and Gourmet Coffee? 2:08 
   Taste Test with Coffee Drinkers 3:37 
    If No One can Actually Taste the Difference 3:38 
    If Everyone can Actually Taste the Difference 5:36 
   Creating a Probability Model 7:09 
    Creating a Probability Model 7:10 
   D'Alembert vs. Necker 9:41 
    D'Alembert vs. Necker 9:42 
   Problem with D'Alembert's Model 13:29 
    Problem with D'Alembert's Model 13:30 
   Covering Entire Sample Space 15:08 
    Fundamental Principle of Counting 15:09 
   Where Do Probabilities Come From? 22:54 
    Observed Data, Symmetry, and Subjective Estimates 22:55 
   Checking whether Model Matches Real World 24:27 
    Law of Large Numbers 24:28 
   Example 1: Law of Large Numbers 27:46 
   Example 2: Possible Outcomes 30:43 
   Example 3: Brands of Coffee and Taste 33:25 
   Example 4: How Many Different Treatments are there? 35:33 
  Addition Rule for Disjoint Events 20:29
   Intro 0:00 
   Roadmap 0:08 
    Roadmap 0:09 
   Disjoint Events 0:41 
    Disjoint Events 0:42 
   Meaning of 'or' 2:39 
    In Regular Life 2:40 
    In Math/Statistics/Computer Science 3:10 
   Addition Rule for Disjoin Events 3:55 
    If A and B are Disjoint: P (A and B) 3:56 
    If A and B are Disjoint: P (A or B) 5:15 
   General Addition Rule 5:41 
    General Addition Rule 5:42 
   Generalized Addition Rule 8:31 
    If A and B are not Disjoint: P (A or B) 8:32 
   Example 1: Which of These are Mutually Exclusive? 10:50 
   Example 2: What is the Probability that You will Have a Combination of One Heads and Two Tails? 12:57 
   Example 3: Engagement Party 15:17 
   Example 4: Home Owner's Insurance 18:30 
  Conditional Probability 57:19
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   'or' vs. 'and' vs. Conditional Probability 1:07 
    'or' vs. 'and' vs. Conditional Probability 1:08 
   'and' vs. Conditional Probability 5:57 
    P (M or L) 5:58 
    P (M and L) 8:41 
    P (M|L) 11:04 
    P (L|M) 12:24 
   Tree Diagram 15:02 
    Tree Diagram 15:03 
   Defining Conditional Probability 22:42 
    Defining Conditional Probability 22:43 
   Common Contexts for Conditional Probability 30:56 
    Medical Testing: Positive Predictive Value 30:57 
    Medical Testing: Sensitivity 33:03 
    Statistical Tests 34:27 
   Example 1: Drug and Disease 36:41 
   Example 2: Marbles and Conditional Probability 40:04 
   Example 3: Cards and Conditional Probability 45:59 
   Example 4: Votes and Conditional Probability 50:21 
  Independent Events 24:27
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Independent Events & Conditional Probability 0:26 
    Non-independent Events 0:27 
    Independent Events 2:00 
   Non-independent and Independent Events 3:08 
    Non-independent and Independent Events 3:09 
   Defining Independent Events 5:52 
    Defining Independent Events 5:53 
   Multiplication Rule 7:29 
    Previously… 7:30 
    But with Independent Evens 8:53 
   Example 1: Which of These Pairs of Events are Independent? 11:12 
   Example 2: Health Insurance and Probability 15:12 
   Example 3: Independent Events 17:42 
   Example 4: Independent Events 20:03 
VIII. Probability Distributions
  Introduction to Probability Distributions 56:45
   Intro 0:00 
   Roadmap 0:08 
    Roadmap 0:09 
   Sampling vs. Probability 0:57 
    Sampling 0:58 
    Missing 1:30 
    What is Missing? 3:06 
   Insight: Probability Distributions 5:26 
    Insight: Probability Distributions 5:27 
    What is a Probability Distribution? 7:29 
   From Sample Spaces to Probability Distributions 8:44 
    Sample Space 8:45 
    Probability Distribution of the Sum of Two Die 11:16 
   The Random Variable 17:43 
    The Random Variable 17:44 
   Expected Value 21:52 
    Expected Value 21:53 
   Example 1: Probability Distributions 28:45 
   Example 2: Probability Distributions 35:30 
   Example 3: Probability Distributions 43:37 
   Example 4: Probability Distributions 47:20 
  Expected Value & Variance of Probability Distributions 53:41
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Discrete vs. Continuous Random Variables 1:04 
    Discrete vs. Continuous Random Variables 1:05 
   Mean and Variance Review 4:44 
    Mean: Sample, Population, and Probability Distribution 4:45 
    Variance: Sample, Population, and Probability Distribution 9:12 
   Example Situation 14:10 
    Example Situation 14:11 
   Some Special Cases… 16:13 
    Some Special Cases… 16:14 
   Linear Transformations 19:22 
    Linear Transformations 19:23 
    What Happens to Mean and Variance of the Probability Distribution? 20:12 
   n Independent Values of X 25:38 
    n Independent Values of X 25:39 
   Compare These Two Situations 30:56 
    Compare These Two Situations 30:57 
   Two Random Variables, X and Y 32:02 
    Two Random Variables, X and Y 32:03 
   Example 1: Expected Value & Variance of Probability Distributions 35:35 
   Example 2: Expected Values & Standard Deviation 44:17 
   Example 3: Expected Winnings and Standard Deviation 48:18 
  Binomial Distribution 55:15
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Discrete Probability Distributions 1:42 
    Discrete Probability Distributions 1:43 
   Binomial Distribution 2:36 
    Binomial Distribution 2:37 
   Multiplicative Rule Review 6:54 
    Multiplicative Rule Review 6:55 
   How Many Outcomes with k 'Successes' 10:23 
    Adults and Bachelor's Degree: Manual List of Outcomes 10:24 
   P (X=k) 19:37 
    Putting Together # of Outcomes with the Multiplicative Rule 19:38 
   Expected Value and Standard Deviation in a Binomial Distribution 25:22 
    Expected Value and Standard Deviation in a Binomial Distribution 25:23 
   Example 1: Coin Toss 33:42 
   Example 2: College Graduates 38:03 
   Example 3: Types of Blood and Probability 45:39 
   Example 4: Expected Number and Standard Deviation 51:11 
IX. Sampling Distributions of Statistics
  Introduction to Sampling Distributions 48:17
   Intro 0:00 
   Roadmap 0:08 
    Roadmap 0:09 
   Probability Distributions vs. Sampling Distributions 0:55 
    Probability Distributions vs. Sampling Distributions 0:56 
   Same Logic 3:55 
    Logic of Probability Distribution 3:56 
    Example: Rolling Two Die 6:56 
   Simulating Samples 9:53 
    To Come Up with Probability Distributions 9:54 
    In Sampling Distributions 11:12 
   Connecting Sampling and Research Methods with Sampling Distributions 12:11 
    Connecting Sampling and Research Methods with Sampling Distributions 12:12 
   Simulating a Sampling Distribution 14:14 
    Experimental Design: Regular Sleep vs. Less Sleep 14:15 
   Logic of Sampling Distributions 23:08 
    Logic of Sampling Distributions 23:09 
   General Method of Simulating Sampling Distributions 25:38 
    General Method of Simulating Sampling Distributions 25:39 
   Questions that Remain 28:45 
    Questions that Remain 28:46 
   Example 1: Mean and Standard Error of Sampling Distribution 30:57 
   Example 2: What is the Best Way to Describe Sampling Distributions? 37:12 
   Example 3: Matching Sampling Distributions 38:21 
   Example 4: Mean and Standard Error of Sampling Distribution 41:51 
  Sampling Distribution of the Mean 1:08:48
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Special Case of General Method for Simulating a Sampling Distribution 1:53 
    Special Case of General Method for Simulating a Sampling Distribution 1:54 
    Computer Simulation 3:43 
   Using Simulations to See Principles behind Shape of SDoM 15:50 
    Using Simulations to See Principles behind Shape of SDoM 15:51 
    Conditions 17:38 
   Using Simulations to See Principles behind Center (Mean) of SDoM 20:15 
    Using Simulations to See Principles behind Center (Mean) of SDoM 20:16 
    Conditions: Does n Matter? 21:31 
    Conditions: Does Number of Simulation Matter? 24:37 
   Using Simulations to See Principles behind Standard Deviation of SDoM 27:13 
    Using Simulations to See Principles behind Standard Deviation of SDoM 27:14 
    Conditions: Does n Matter? 34:45 
    Conditions: Does Number of Simulation Matter? 36:24 
   Central Limit Theorem 37:13 
    SHAPE 38:08 
    CENTER 39:34 
    SPREAD 39:52 
   Comparing Population, Sample, and SDoM 43:10 
    Comparing Population, Sample, and SDoM 43:11 
   Answering the 'Questions that Remain' 48:24 
    What Happens When We Don't Know What the Population Looks Like? 48:25 
    Can We Have Sampling Distributions for Summary Statistics Other than the Mean? 49:42 
    How Do We Know whether a Sample is Sufficiently Unlikely? 53:36 
    Do We Always Have to Simulate a Large Number of Samples in Order to get a Sampling Distribution? 54:40 
   Example 1: Mean Batting Average 55:25 
   Example 2: Mean Sampling Distribution and Standard Error 59:07 
   Example 3: Sampling Distribution of the Mean 61:04 
  Sampling Distribution of Sample Proportions 54:37
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Intro to Sampling Distribution of Sample Proportions (SDoSP) 0:51 
    Categorical Data (Examples) 0:52 
    Wish to Estimate Proportion of Population from Sample… 2:00 
   Notation 3:34 
    Population Proportion and Sample Proportion Notations 3:35 
   What's the Difference? 9:19 
    SDoM vs. SDoSP: Type of Data 9:20 
    SDoM vs. SDoSP: Shape 11:24 
    SDoM vs. SDoSP: Center 12:30 
    SDoM vs. SDoSP: Spread 15:34 
   Binomial Distribution vs. Sampling Distribution of Sample Proportions 19:14 
    Binomial Distribution vs. SDoSP: Type of Data 19:17 
    Binomial Distribution vs. SDoSP: Shape 21:07 
    Binomial Distribution vs. SDoSP: Center 21:43 
    Binomial Distribution vs. SDoSP: Spread 24:08 
   Example 1: Sampling Distribution of Sample Proportions 26:07 
   Example 2: Sampling Distribution of Sample Proportions 37:58 
   Example 3: Sampling Distribution of Sample Proportions 44:42 
   Example 4: Sampling Distribution of Sample Proportions 45:57 
X. Inferential Statistics
  Introduction to Confidence Intervals 42:53
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Inferential Statistics 0:50 
    Inferential Statistics 0:51 
   Two Problems with This Picture… 3:20 
    Two Problems with This Picture… 3:21 
    Solution: Confidence Intervals (CI) 4:59 
    Solution: Hypotheiss Testing (HT) 5:49 
   Which Parameters are Known? 6:45 
    Which Parameters are Known? 6:46 
   Confidence Interval - Goal 7:56 
    When We Don't Know m but know s 7:57 
   When We Don't Know 18:27 
    When We Don't Know m nor s 18:28 
   Example 1: Confidence Intervals 26:18 
   Example 2: Confidence Intervals 29:46 
   Example 3: Confidence Intervals 32:18 
   Example 4: Confidence Intervals 38:31 
  t Distributions 1:02:06
   Intro 0:00 
   Roadmap 0:04 
    Roadmap 0:05 
   When to Use z vs. t? 1:07 
    When to Use z vs. t? 1:08 
   What is z and t? 3:02 
     z-score and t-score: Commonality 3:03 
    z-score and t-score: Formulas 3:34 
    z-score and t-score: Difference 5:22 
   Why not z? (Why t?) 7:24 
    Why not z? (Why t?) 7:25 
   But Don't Worry! 15:13 
    Gossett and t-distributions 15:14 
   Rules of t Distributions 17:05 
    t-distributions are More Normal as n Gets Bigger 17:06 
    t-distributions are a Family of Distributions 18:55 
   Degrees of Freedom (df) 20:02 
    Degrees of Freedom (df) 20:03 
   t Family of Distributions 24:07 
    t Family of Distributions : df = 2 , 4, and 60 24:08 
    df = 60 29:16 
    df = 2 29:59 
   How to Find It? 31:01 
    'Student's t-distribution' or 't-distribution' 31:02 
    Excel Example 33:06 
   Example 1: Which Distribution Do You Use? Z or t? 45:26 
   Example 2: Friends on Facebook 47:41 
   Example 3: t Distributions 52:15 
   Example 4: t Distributions , confidence interval, and mean 55:59 
  Introduction to Hypothesis Testing 1:06:33
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   Issues to Overcome in Inferential Statistics 1:35 
    Issues to Overcome in Inferential Statistics 1:36 
    What Happens When We Don't Know What the Population Looks Like? 2:57 
    How Do We Know whether a sample is Sufficiently Unlikely 3:43 
   Hypothesizing a Population 6:44 
    Hypothesizing a Population 6:45 
    Null Hypothesis 8:07 
    Alternative Hypothesis 8:56 
   Hypotheses 11:58 
    Hypotheses 11:59 
   Errors in Hypothesis Testing 14:22 
    Errors in Hypothesis Testing 14:23 
   Steps of Hypothesis Testing 21:15 
    Steps of Hypothesis Testing 21:16 
   Single Sample HT ( When Sigma Available) 26:08 
    Example: Average Facebook Friends 26:09 
    Step1 27:08 
    Step 2 27:58 
    Step 3 28:17 
    Step 4 32:18 
   Single Sample HT (When Sigma Not Available) 36:33 
    Example: Average Facebook Friends 36:34 
    Step1: Hypothesis Testing 36:58 
    Step 2: Significance Level 37:25 
    Step 3: Decision Stage 37:40 
    Step 4: Sample 41:36 
   Sigma and p-value 45:04 
    Sigma and p-value 45:05 
    On tailed vs. Two Tailed Hypotheses 45:51 
   Example 1: Hypothesis Testing 48:37 
   Example 2: Heights of Women in the US 57:43 
   Example 3: Select the Best Way to Complete This Sentence 63:23 
  Confidence Intervals for the Difference of Two Independent Means 55:14
   Intro 0:00 
   Roadmap 0:14 
    Roadmap 0:15 
   One Mean vs. Two Means 1:17 
    One Mean vs. Two Means 1:18 
   Notation 2:41 
    A Sample! A Set! 2:42 
    Mean of X, Mean of Y, and Difference of Two Means 3:56 
    SE of X 4:34 
    SE of Y 6:28 
   Sampling Distribution of the Difference between Two Means (SDoD) 7:48 
    Sampling Distribution of the Difference between Two Means (SDoD) 7:49 
   Rules of the SDoD (similar to CLT!) 15:00 
    Mean for the SDoD Null Hypothesis 15:01 
    Standard Error 17:39 
   When can We Construct a CI for the Difference between Two Means? 21:28 
    Three Conditions 21:29 
   Finding CI 23:56 
    One Mean CI 23:57 
    Two Means CI 25:45 
   Finding t 29:16 
    Finding t 29:17 
   Interpreting CI 30:25 
    Interpreting CI 30:26 
   Better Estimate of s (s pool) 34:15 
    Better Estimate of s (s pool) 34:16 
   Example 1: Confidence Intervals 42:32 
   Example 2: SE of the Difference 52:36 
  Hypothesis Testing for the Difference of Two Independent Means 50:00
   Intro 0:00 
   Roadmap 0:06 
    Roadmap 0:07 
   The Goal of Hypothesis Testing 0:56 
    One Sample and Two Samples 0:57 
   Sampling Distribution of the Difference between Two Means (SDoD) 3:42 
    Sampling Distribution of the Difference between Two Means (SDoD) 3:43 
   Rules of the SDoD (Similar to CLT!) 6:46 
    Shape 6:47 
    Mean for the Null Hypothesis 7:26 
    Standard Error for Independent Samples (When Variance is Homogenous) 8:18 
    Standard Error for Independent Samples (When Variance is not Homogenous) 9:25 
   Same Conditions for HT as for CI 10:08 
    Three Conditions 10:09 
   Steps of Hypothesis Testing 11:04 
    Steps of Hypothesis Testing 11:05 
   Formulas that Go with Steps of Hypothesis Testing 13:21 
    Step 1 13:25 
    Step 2 14:18 
    Step 3 15:00 
    Step 4 16:57 
   Example 1: Hypothesis Testing for the Difference of Two Independent Means 18:47 
   Example 2: Hypothesis Testing for the Difference of Two Independent Means 33:55 
   Example 3: Hypothesis Testing for the Difference of Two Independent Means 44:22 
  Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 1:14:11
   Intro 0:00 
   Roadmap 0:09 
    Roadmap 0:10 
   The Goal of Hypothesis Testing 1:27 
    One Sample and Two Samples 1:28 
   Independent Samples vs. Paired Samples 3:16 
    Independent Samples vs. Paired Samples 3:17 
    Which is Which? 5:20 
   Independent SAMPLES vs. Independent VARIABLES 7:43 
    independent SAMPLES vs. Independent VARIABLES 7:44 
   T-tests Always… 10:48 
    T-tests Always… 10:49 
   Notation for Paired Samples 12:59 
    Notation for Paired Samples 13:00 
   Steps of Hypothesis Testing for Paired Samples 16:13 
    Steps of Hypothesis Testing for Paired Samples 16:14 
   Rules of the SDoD (Adding on Paired Samples) 18:03 
    Shape 18:04 
    Mean for the Null Hypothesis 18:31 
    Standard Error for Independent Samples (When Variance is Homogenous) 19:25 
    Standard Error for Paired Samples 20:39 
   Formulas that go with Steps of Hypothesis Testing 22:59 
    Formulas that go with Steps of Hypothesis Testing 23:00 
   Confidence Intervals for Paired Samples 30:32 
    Confidence Intervals for Paired Samples 30:33 
   Example 1: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 32:28 
   Example 2: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 44:02 
   Example 3: Confidence Intervals & Hypothesis Testing for the Difference of Two Paired Means 52:23 
  Type I and Type II Errors 31:27
   Intro 0:00 
   Roadmap 0:18 
    Roadmap 0:19 
   Errors and Relationship to HT and the Sample Statistic? 1:11 
    Errors and Relationship to HT and the Sample Statistic? 1:12 
   Instead of a Box…Distributions! 7:00 
    One Sample t-test: Friends on Facebook 7:01 
    Two Sample t-test: Friends on Facebook 13:46 
   Usually, Lots of Overlap between Null and Alternative Distributions 16:59 
    Overlap between Null and Alternative Distributions 17:00 
   How Distributions and 'Box' Fit Together 22:45 
    How Distributions and 'Box' Fit Together 22:46 
   Example 1: Types of Errors 25:54 
   Example 2: Types of Errors 27:30 
   Example 3: What is the Danger of the Type I Error? 29:38 
  Effect Size & Power 44:41
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Distance between Distributions: Sample t 0:49 
    Distance between Distributions: Sample t 0:50 
   Problem with Distance in Terms of Standard Error 2:56 
    Problem with Distance in Terms of Standard Error 2:57 
   Test Statistic (t) vs. Effect Size (d or g) 4:38 
    Test Statistic (t) vs. Effect Size (d or g) 4:39 
   Rules of Effect Size 6:09 
    Rules of Effect Size 6:10 
   Why Do We Need Effect Size? 8:21 
    Tells You the Practical Significance 8:22 
    HT can be Deceiving… 10:25 
    Important Note 10:42 
   What is Power? 11:20 
    What is Power? 11:21 
   Why Do We Need Power? 14:19 
    Conditional Probability and Power 14:20 
    Power is: 16:27 
   Can We Calculate Power? 19:00 
    Can We Calculate Power? 19:01 
   How Does Alpha Affect Power? 20:36 
    How Does Alpha Affect Power? 20:37 
   How Does Effect Size Affect Power? 25:38 
    How Does Effect Size Affect Power? 25:39 
   How Does Variability and Sample Size Affect Power? 27:56 
    How Does Variability and Sample Size Affect Power? 27:57 
   How Do We Increase Power? 32:47 
    Increasing Power 32:48 
   Example 1: Effect Size & Power 35:40 
   Example 2: Effect Size & Power 37:38 
   Example 3: Effect Size & Power 40:55 
XI. Analysis of Variance
  F-distributions 24:46
   Intro 0:00 
   Roadmap 0:04 
    Roadmap 0:05 
   Z- & T-statistic and Their Distribution 0:34 
    Z- & T-statistic and Their Distribution 0:35 
   F-statistic 4:55 
    The F Ration ( the Variance Ratio) 4:56 
   F-distribution 12:29 
    F-distribution 12:30 
   s and p-value 15:00 
    s and p-value 15:01 
   Example 1: Why Does F-distribution Stop At 0 But Go On Until Infinity? 18:33 
   Example 2: F-distributions 19:29 
   Example 3: F-distributions and Heights 21:29 
  ANOVA with Independent Samples 1:09:25
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   The Limitations of t-tests 1:12 
    The Limitations of t-tests 1:13 
   Two Major Limitations of Many t-tests 3:26 
    Two Major Limitations of Many t-tests 3:27 
   Ronald Fisher's Solution… F-test! New Null Hypothesis 4:43 
    Ronald Fisher's Solution… F-test! New Null Hypothesis (Omnibus Test - One Test to Rule Them All!) 4:44 
   Analysis of Variance (ANoVA) Notation 7:47 
    Analysis of Variance (ANoVA) Notation 7:48 
   Partitioning (Analyzing) Variance 9:58 
    Total Variance 9:59 
    Within-group Variation 14:00 
    Between-group Variation 16:22 
   Time out: Review Variance & SS 17:05 
    Time out: Review Variance & SS 17:06 
   F-statistic 19:22 
    The F Ratio (the Variance Ratio) 19:23 
   S²bet = SSbet / dfbet 22:13 
    What is This? 22:14 
    How Many Means? 23:20 
    So What is the dfbet? 23:38 
    So What is SSbet? 24:15 
   S²w = SSw / dfw 26:05 
    What is This? 26:06 
    How Many Means? 27:20 
    So What is the dfw? 27:36 
    So What is SSw? 28:18 
   Chart of Independent Samples ANOVA 29:25 
    Chart of Independent Samples ANOVA 29:26 
   Example 1: Who Uploads More Photos: Unknown Ethnicity, Latino, Asian, Black, or White Facebook Users? 35:52 
    Hypotheses 35:53 
    Significance Level 39:40 
    Decision Stage 40:05 
    Calculate Samples' Statistic and p-Value 44:10 
    Reject or Fail to Reject H0 55:54 
   Example 2: ANOVA with Independent Samples 58:21 
  Repeated Measures ANOVA 1:15:13
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   The Limitations of t-tests 0:36 
    Who Uploads more Pictures and Which Photo-Type is Most Frequently Used on Facebook? 0:37 
   ANOVA (F-test) to the Rescue! 5:49 
    Omnibus Hypothesis 5:50 
    Analyze Variance 7:27 
   Independent Samples vs. Repeated Measures 9:12 
    Same Start 9:13 
    Independent Samples ANOVA 10:43 
    Repeated Measures ANOVA 12:00 
   Independent Samples ANOVA 16:00 
    Same Start: All the Variance Around Grand Mean 16:01 
    Independent Samples 16:23 
   Repeated Measures ANOVA 18:18 
    Same Start: All the Variance Around Grand Mean 18:19 
    Repeated Measures 18:33 
   Repeated Measures F-statistic 21:22 
    The F Ratio (The Variance Ratio) 21:23 
   S²bet = SSbet / dfbet 23:07 
    What is This? 23:08 
    How Many Means? 23:39 
    So What is the dfbet? 23:54 
    So What is SSbet? 24:32 
   S² resid = SS resid / df resid 25:46 
    What is This? 25:47 
    So What is SS resid? 26:44 
    So What is the df resid? 27:36 
   SS subj and df subj 28:11 
    What is This? 28:12 
    How Many Subject Means? 29:43 
    So What is df subj? 30:01 
    So What is SS subj? 30:09 
   SS total and df total 31:42 
    What is This? 31:43 
    What is the Total Number of Data Points? 32:02 
    So What is df total? 32:34 
    so What is SS total? 32:47 
   Chart of Repeated Measures ANOVA 33:19 
    Chart of Repeated Measures ANOVA: F and Between-samples Variability 33:20 
    Chart of Repeated Measures ANOVA: Total Variability, Within-subject (case) Variability, Residual Variability 35:50 
   Example 1: Which is More Prevalent on Facebook: Tagged, Uploaded, Mobile, or Profile Photos? 40:25 
    Hypotheses 40:26 
    Significance Level 41:46 
    Decision Stage 42:09 
    Calculate Samples' Statistic and p-Value 46:18 
    Reject or Fail to Reject H0 57:55 
   Example 2: Repeated Measures ANOVA 58:57 
   Example 3: What's the Problem with a Bunch of Tiny t-tests? 73:59 
XII. Chi-square Test
  Chi-Square Goodness-of-Fit Test 58:23
   Intro 0:00 
   Roadmap 0:05 
    Roadmap 0:06 
   Where Does the Chi-Square Test Belong? 0:50 
    Where Does the Chi-Square Test Belong? 0:51 
   A New Twist on HT: Goodness-of-Fit 7:23 
    HT in General 7:24 
    Goodness-of-Fit HT 8:26 
   Hypotheses about Proportions 12:17 
    Null Hypothesis 12:18 
    Alternative Hypothesis 13:23 
    Example 14:38 
   Chi-Square Statistic 17:52 
    Chi-Square Statistic 17:53 
   Chi-Square Distributions 24:31 
    Chi-Square Distributions 24:32 
   Conditions for Chi-Square 28:58 
    Condition 1 28:59 
    Condition 2 30:20 
    Condition 3 30:32 
    Condition 4 31:47 
   Example 1: Chi-Square Goodness-of-Fit Test 32:23 
   Example 2: Chi-Square Goodness-of-Fit Test 44:34 
   Example 3: Which of These Statements Describe Properties of the Chi-Square Goodness-of-Fit Test? 56:06 
  Chi-Square Test of Homogeneity 51:36
   Intro 0:00 
   Roadmap 0:09 
    Roadmap 0:10 
   Goodness-of-Fit vs. Homogeneity 1:13 
    Goodness-of-Fit HT 1:14 
    Homogeneity 2:00 
    Analogy 2:38 
   Hypotheses About Proportions 5:00 
    Null Hypothesis 5:01 
    Alternative Hypothesis 6:11 
    Example 6:33 
   Chi-Square Statistic 10:12 
    Same as Goodness-of-Fit Test 10:13 
   Set Up Data 12:28 
    Setting Up Data Example 12:29 
   Expected Frequency 16:53 
    Expected Frequency 16:54 
   Chi-Square Distributions & df 19:26 
    Chi-Square Distributions & df 19:27 
   Conditions for Test of Homogeneity 20:54 
    Condition 1 20:55 
    Condition 2 21:39 
    Condition 3 22:05 
    Condition 4 22:23 
   Example 1: Chi-Square Test of Homogeneity 22:52 
   Example 2: Chi-Square Test of Homogeneity 32:10 
XIII. Overview of Statistics
  Overview of Statistics 18:11
   Intro 0:00 
   Roadmap 0:07 
    Roadmap 0:08 
   The Statistical Tests (HT) We've Covered 0:28 
    The Statistical Tests (HT) We've Covered 0:29 
   Organizing the Tests We've Covered… 1:08 
    One Sample: Continuous DV and Categorical DV 1:09 
    Two Samples: Continuous DV and Categorical DV 5:41 
    More Than Two Samples: Continuous DV and Categorical DV 8:21 
   The Following Data: OK Cupid 10:10 
    The Following Data: OK Cupid 10:11 
   Example 1: Weird-MySpace-Angle Profile Photo 10:38 
   Example 2: Geniuses 12:30 
   Example 3: Promiscuous iPhone Users 13:37 
   Example 4: Women, Aging, and Messaging 16:07