Statistics About Samples: Cases, Variables, Measurements

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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 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