Sign In | Subscribe

Enter your Sign on user name and password.

Forgot password?
  • Follow us on:
Start learning today, and be successful in your academic & professional career. Start Today!
Loading video...
This is a quick preview of the lesson. For full access, please Log In or Sign up.
For more information, please see full course syllabus of Statistics
  • Discussion

  • Download Lecture Slides

  • Table of Contents

  • Transcription

  • Related Books

Lecture Comments (4)

0 answers

Post by Saadman Elman on September 3, 2014

I Found this lecture very beneficial. Thanks Dr. Ji Son.

0 answers

Post by paula G on January 31, 2014

me too is this a technical fault?

0 answers

Post by Manoj Joseph on April 26, 2013

I am finding it difficult to access the last portion of the lecture specifically the example portion at the end. Is it because of accessibility restrictions on my basic subscription?

About Samples: Cases, Variables, Measurements

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.

  • Intro 0:00
  • Data 0:09
    • Data, Cases, Variables, and Values
    • Rows, Columns, and Cells
    • Example: Aircrafts
  • How Do We Get Data? 5:38
    • Research: Question and Hypothesis
    • Research Design
    • Measurement
    • Research Analysis
    • Research Conclusion
  • Types of Variables 10:03
    • Discrete Variables
    • Continuous Variables
  • Types of Measurements 14:17
    • Types of Measurements
  • Types of Measurements (Scales) 17:22
    • Nominal
    • Ordinal
    • Interval
    • Ratio
  • 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

Transcription: About Samples: Cases, Variables, Measurements

Welcome to

Today we are going to talk about samples and about cases, variables, and measurement within samples.0002

We need to talk about samples because statistics is all about data and data is made up of cases, right?0012

Each individual that is part of that data set is called the case, and cases are actually made up of variables.0019

You could think of variables as different characteristics within a case and a variable can take on different values.0028

Just to give you an example here is the data set that is simple and we have three cases, 3 shapes and they have different variables.0037

You can think of these as dimension.0048

Dimensions of shape, color, area, right?0051

These variables right up here, these can actually have different values.0056

For instance, triangle is the value for this case, for this variable of shape.0068

For this case, square is the value for the variable of shape and circle is the value for the variable shape for this case.0076

A variable can take on different values and because of that it is called a variable because it could vary.0091

It does not have to vary for instance take a look at color right here.0099

This is a variable that has all of the same values, teal.0103

Although they do not have to, in a variable the values do not have to vary, they can.0110

We could put a red case in there and it is okay.0119

One thing to note is that regardless of data sets oftentimes you will see cases listed in rows.0127

Often each row is the case.0134

Also often each column is the variable and you will learn about different kinds of variables as we go on.0136

When you look at columns you see variables.0144

When you look at entire rows you see cases.0147

Not only that but when you look at a cell, a cell is a combination of a particular row and a particular column.0151

When you look at a cell, that cell often contains a value.0159

The next two cases, variables, and values, as a small note about where they might be in space you might say usually in rows.0164

This one is usually in columns and values are usually in cell.0178

Does it always have to be the case but usually by convention many data sets are organized like this.0186

We can look here.0194

Here the cases seem to be made up of individuals.0195

Here the individuals are taken from

The variables are things like gender, friends, siblings, and number of tagged photos.0204

Tagged photos by itself is the variable, it could vary.0213

There are lots of different values that it could hold.0217

For instance 24, 42, and 21.0220

These are different values that could be sort of sitting in the place of the variable tagged photo.0224

Just to give you one more example, here is an example of aircrafts.0236

These cases are aircrafts and on each row there is information for this particular aircraft on that row.0241

The different variables here are number of seats, the cargo that it can carry in tens, and let us say average flying speed.0250

Here we could see that the B747 has 410 seats as the value for the variable number of seats.0262

Once again it is organized, rows being cases, columns being variable and cells being values.0272

I want to introduce one other idea.0285

Remember I said that variables can have different values, they do not have to differ but they can.0288

There are some characteristics that will not vary though because of a particular design of the study.0296

For instance, maybe a study would like to look at a pregnant women0301

and how much prenatal exercise they do and whether that predicts the health of their baby.0306

Because of the design of this study, the variable gender is actually not going to be a variable0316

because there are very few of them doing prenatal exercises because they are pregnant.0324

Instead this is what it is going to be called a constant because the values are all the same by design, are defined.0329

The question is great we know how to organize the data once we get it but how do we actually get that data?0340

The process of getting new data is called research and often research is taught with the five scientific steps and asking a question,0348

coming up with the hypothesis, coming up with the design, research analysis, and coming up with the conclusion.0359

That sort of addresses that question.0366

In order to reframe the 5 steps of science so that it relates more to statistics0369

I’m going to talk about these things in terms of cases because that is what is involved in statistics.0379

Research will be about how to get the sample.0388

Already we are putting in our statistics terms, how to get the sample.0400

The research question is often a proposed relationship among variables.0404

A hypothesis often goes with that so it is says yes I do think this is the relationship or I think there is another relationship.0419

These often go together.0430

The research design is the procedure that we use for actually collecting the data.0432

Measurement is actually the process for gathering quantitative information that represents some variable or variables.0451

Let us say the quantitative values just to use the same words.0470

Values that represents or variables.0475

Here we are talking about how to actually get the sample.0493

We are looking at proposed relationships among variables within those cases.0496

Research design is all about the procedure for collecting that data.0502

Measurement is about gathering quantitative values that represents some variables.0507

Research analysis is what we often think of when we think of statistical analysis so I put statistics right here.0514

Here in statistics, there statistical analysis is going to have its own statistical question and hypothesis.0522

It is also going to have statistical procedures.0533

You are going to be able to come up with statistical conclusion.0540

Often this little mini set is often called hypothesis testing.0547

We will get to that when we talk about inferential statistics towards the middle and latter end of the course.0563

Finally the research conclusion is going to be different than the statistical conclusion.0572

Here in the research conclusion we step out again and go back to how this analysis relates to this overall research question.0577

This is the general conclusion.0588

This general conclusion is created from the statistical conclusion as well as in considering all that came ahead of you.0594

What kinds of variables are there if our research question and our hypotheses are all going to be made up of variables0607

we better try to figure out what kind of variables could there be?0614

There are a couple of different variables that you need to know.0619

When we already covered this one is not a variable it is right outside the border in variable but it is related.0622

A constant is the characteristic that cannot vary in the data set.0630

For whatever reason it cannot vary but other than that they are two kinds of variables you need to know.0633

One is discrete variables and when we talk about discreteness, we are talking about things that have very particular values.0639

When you think about a number line there are only certain places that can contribute a value to a discrete variable.0650

These are the only values sort of allowed in a discrete variable.0665

Example might be something like number of siblings, you may wish you had only one and a half sibling but that is actually not possible.0670

Number of siblings is what we think of as a discrete variable.0680

You either have 1 or 2, you rarely have 1.65 or 1.82 number of siblings.0686

Also another example might be number of gold medals won in the Olympics.0695

Often people do not win just half a medal or 1/8 of a medal, or 5 2/6 of the medal.0706

Instead they win whole medals.0715

There is only particular place on the number line that can contribute values to these variables.0717

These are examples of discrete variables.0725

Continuous variables are exactly the opposite.0728

We might have these in a whole numbers like 1, 2, 3, 4 but when you have a continuous variable0734

you could have this be the value or you could have this be the value or one right next to it as the value or over here as the value.0740

Any of these values can contribute to the variable.0748

One way you might want to think of this is that there are no gaps on the scale.0753

Any value can contribute, can be part of this variable.0763

In discrete variables only certain values can take part in this variable.0769

Examples of continuous variables are things like length, weight, these are values that can have any number.0777

It does not have to be 100 or 101, it could be 100.1 or 100.001, or 100.0001.0794

There is an infinite even between 0 and 1, there is an infinite number of values that0810

could contribute to a continuous variables such as length or weight.0816

Other possibilities are more abstract, things like anxiety level or knowledge of history.0822

Somebody could be maybe right here in terms of anxiety level but someone else could be very close but just less anxious in them.0833

These are what I thought of as continuous variables because any value is actually possible.0847

Here is the thing, we cannot actually quite get variables in the world.0858

We cannot get the batch true, instead we have to measure it and often measurements are almost all discrete.0864

When you actually measure something we often round, for instance when we measure height we do not measure it to the .0001 inch or centimeter,0873

instead we often round it to the nearest whole unit.0885

Often people do not say I’m 5’6 and 375 of an inch.0891

Often people do not say that and because of that most measurements are actual scale of getting values of the variables.0901

Those end up turning all variables into discrete variables.0912

But underlying the variable, it does not have to be discrete just because we measure it in that way.0918

When a variable is measured you will end up with a particular set of numerical values.0925

That is often what we think of as our sample distribution, our scatter of numbers.0930

It often helps to ask ourselves what kind of scale is it on.0937

It is all going to be discrete but there are different levels of in formativeness that measurement scales can give us.0943

Let me give you some examples.0953

One reason that it might be helpful to think about what kind of measurement scale a piece of data is on is because it helps us compare pieces of data.0958

For instance could we look at number of friends and compare that to ranking in class.0968

Those numbers actually stand for very different ideas and that is what we mean by measurement scale.0975

What does the number mean?0983

What kind of information does it give us?0985

When we think of something like gender, here we are using a number 1 and 20988

but are we saying that somehow 2 males if you add them together you get a female?0994

Is that what we really think? Not really.1001

These numbers are just stand ins for other ideas.1004

When we are talking about number of friends, if we had somebody who has 48 friends,1009

we do mean they have approximately 1/4 of the friends that the second person has.1015

Can we compare ranking in class?1021

Is this person somehow too better than this person? How do we compare?1025

It often helps to know what kind of measurement scale we are working with.1034

There are four different kinds of measurement scales you need to know.1039

Here they are nominal, ordinal, interval, and ratio and I have listed them in an order where they become progressively more informative.1044

There is more and more information as we sort of go down.1054

These are the types of skills you might run into.1057

Nominal scales are often referred to as dummy codes because nominal scales are just numbers that stands for names.1061

The look on the surface like numbers but they are just names and the numbers do not actually have any meaning.1071

There is no meaning in the number, they just stand in like a dummy for a name or category.1079

Right so nominal scales stands for the idea name.1086

You can think of this is a qualitative scale, there is no order.1094

Some examples might be things like color of eyes, there is no order.1109

It is not that blue has to go before brown, or green has to come after brown.1113

There is no particular order to it.1117

Another idea that nominal scale is political affiliation or type of major.1121

These are nominal scales because it is not that there is any inherent order.1129

Even if we assign numbers to it, the numbers are just arbitrary, they do not actually mean anything.1132

Things like types of cheese, state that you come from, what language you speak, those are all examples of nominal measurements.1140

The second level we can think of measurement, it has a little bit more information.1152

It is no longer just a stand in, here we now have an order.1160

The numbers actually tell you about order but they may have uneven intervals.1166

1 and 2 are not the same distance apart as 2 and 3.1174

A good example of this is Olympic gold medal, silver medal, and bronze medal.1186

When we think of gold medal, silver medal, and bronze medal, and let us think of this is how the long jump.1192

The gold medal may have jumped this far.1206

The silver medal may have been very close.1210

But the bronze medal may have been far off.1213

But when they actually get their medals you cannot tell how far off each one was.1217

You do not know whether the intervals are the same or different.1223

Here we preserve order.1227

Now when we know the number 1 and 2 we know that number 1 definitely comes before number 21229

but we do not actually know the interval distance between them.1235

Other examples of ordinal scales are things like your rank in law school,1240

that ranking number does not actually tell you how much better someone is than someone else.1246

They might be very close but their numbers might say they are one apart.1253

Often examples of things that are ordinal are often rank ordered.1261

Whenever you hear the word rank, that is often our ordinal scales.1266

Things like having a Masters degree, PhD or bachelors degree, those have ordinal scales.1272

They have order in terms of how much schooling you had to do but they do not necessarily have the same distance between them.1281

Now we get to interval scales and remember I said it is more and more informative as we go down,1296

now we have order as well but also even intervals.1300

The distance between 1 and 2 is the same as the distance between 2 and 3.1307

When we have interval scales you might think that is like a regular number of line.1313

There is one thing that this scale is missing, although it has order and an even intervals there is no meaningful 0.1321

Here is what this means usually when we have a meaningful 0 then that would mean that when we say there is 0 of this,1331

then there is literally none of whatever it is.1342

In an interval scale it is relative.1347

It does not matter whether you start marking out 1 or whether you start marking at 0, or whether you start marking at 125.1350

Let me give you an example that is commonly used especially in the social sciences.1359

Often when people are asked about their opinion in self report, they are asked to rate something.1363

How happy do you feel on a scale of 1 to 5, 5 being very happy and 1 being not happy.1370

Would have it mattered if they had set the scale from 0 to 4 instead?1379

1, 2, 3, 4, 5 versus 0, 1, 2, 3, 4.1385

You could see that if someone marks the 5 on the scale and some of them marks a 4 on the scale.1393

It is not that this person is less happy, there are the ones who are maximally happy, right?1398

It is just that they had a different scale that they were using.1404

These are examples of interval scales where the 0 actually does not mean 0 of happiness,1409

it is just whatever it is relative to the scale that you are using.1416

That is what we mean by no meaningful 0, you can often test for yourself whether something is a interval scale1425

by moving the scale a little bit and seeing if it is still okay.1432

If it is okay then you know you have an interval scale.1439

Let us say you get something like another survey question that says how satisfied are you with your job?1440

You will rate it on a scale of 0 to 100.1447

If it was on a scale of 100 to 200, would it make any big difference?1452

Not really.1460

That is how you know that it is an interval scale.1461

Finally we get to the crème de la crème, this is the highest level and if interval is missing a meaningful 0 I bet you can guess what ratio has.1467

Here we have order, we have even intervals, and we have a meaningful 0.1478

In case these are ratio scales are often things like height or weight where 0 means 0, none of something, none of some unit.1491

If you are 0 inches tall that means you are 0, that means 0.1505

That is the big difference between nominal, ordinal, interval, and ratio scales.1515

Let us look at some examples to exercise these concepts.1523

Here we have a preschool, elementary, junior high school, college and graduate school, form what kind of scale.1529

Let us see preschool, elementary school, junior high, senior high, college, graduate school, they have an order, check.1538

Is there even intervals?1549

The difference between preschool and elementary schools, preschool might take maybe 2 years and elementary school might take 6 years.1556

Even there along we could see they actually take different intervals.1564

Junior high might be 2 to 3 years, high school is 4 years, college 4 years, graduate school that could to be anywhere from 2 to 10 years right.1568

This definitely does not seem like they have even intervals.1581

And because of that even if we assign these things a number like 1, 2, 3, 4, 5, 6 it would not be that if we subtract that one it would be 0.1588

I would say there is no real 0 either .1603

Because it does have order, let us go with ordinal scale.1607

Example 2, in one state voters register as Republican, Democrat, or Independent, which scale of measurement is used?1617

Here is there an order to this like there was for the schooling?1625

Not really.1630

You may have a different opinion depending on your political leanings but these are just different categories of people.1631

I would say that this is a nominal scale.1639

Even if we assign numbers to it, they will be purely symbolic.1641

Example 3, a math professor gives students a 30 item test on the first day to ascertain his students basic math knowledge.1649

Bob got a 0, Joe got a 10, Carlos got 20 and Nate and Layla got a perfect score, what kind of a scale of measurement is this?1657

0 actually does sort of mean something if you think about it as how many items they got correctly.1668

And getting 1 item correct versus 2 item correct, this that ascertain their basic math knowledge?1677

Let us separate it out into first basic math knowledge.1688

Basic math knowledge is the actual variable that this professor is interested in.1696

Basic math knowledge is a continuous variable.1703

Somebody could have just a smidge more or just a smidge less than someone else so every value can be covered.1707

In order to get the values for this variable they used a certain kind of measurement.1717

He used a certain kind of measurement.1725

The measurement tool he used was this 30 item test.1729

The 30 item tests what kind of measurement scale is this on?1735

I would say it does have a true 0, 0 does mean something, you get 0 items correct.1742

It does have even intervals so when you are counting like how many questions correct and you know that 30 is better than 20 is better than 10.1752

It has order.1767

I would say that this is a ratio scale.1770

Just because it is a ratio scale does not mean that it actually measures basic math knowledge in a precise way.1774

After all someone who has a 0 on this test, it may not be that they do not know anything right so1784

how it actually matches that to the variable is still up for grabs as the question but in terms of the measurement scale it might be a ratio scale.1792

There is one way that it could not be a ratio scale and that is if the questions are differing levels of difficulty1802

so there are difficult questions and not difficult levels of questions, that could screw us up.1814

Let us just assume right now that all the items are sort of roughly similar levels of difficulty, if so then I would go with ratio scale.1823

Example 4, if the active measurement is disregarded which of the following variables are fundamentally discrete and which are continuous?1834

Temperature is probably continuous because you could be a little bit hotter, a little bit more hotter, a little bit hotter than that.1845

Every kind of value can we have on that scale, no gaps.1855

Time elapsed, this is also continuous because you could have every small increment of time accounted for.1864

In gender I would say this is discrete because there is not every single kind of variation in between.1874

Brands of orange juice, I would also say discrete this actually sounds nominal.1886

Size of family, this is also something that is discrete, again it is hard to have 2.75 people in the family.1894

Merit rating of employees so how much merit does an employee deserve?1904

Fundamentally that is continuous, one employee could be just a little bit better or worse than another employee.1909

They could be very close.1916

In the same way achievement score in mathematics that could also be continuous1918

because somebody might be able to achieve just a little bit more in math than someone else.1923

That is example 4, thanks for watching