For more information, please see full course syllabus of Statistics

For more information, please see full course syllabus of Statistics

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### 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

### General Statistics Online Course

### Transcription: About Samples: Cases, Variables, Measurements

*Welcome to www.educator.com.*0000

*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 www.facebook.com.*0200

*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 women*0301

*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 variable*0316

*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 statistics*0369

*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 variables*0607

*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 variable*0734

*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 that*0810

*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 2*0988

*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 2*1229

*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 scale*1425

*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 so*1784

*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 difficulty*1802

*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 continuous*1918

*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 www.educator.com.*1931

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?