Source: All graphs created by Dan Laub;Image of horse, PD, http://bit.ly/1JomSxu; Image of blue eye, PD, http://bit.ly/1UWiAEr; Image of green eye, PD, http://bit.ly/1YrmScs; Image of brown eye, PD, http://bit.ly/1OiJcQL; Image of hazel eye, PD, http://bit.ly/1mw4P3D; Image of iPhone, PD, http://bit.ly/1OiJrv4; Image of school, PD, http://bit.ly/1kctUPr; Image of scale, PD, http://bit.ly/1ISw0Q8; Image of ice cream, PD, http://bit.ly/1YkTbEu; Image of graduate, PD, http://bit.ly/1QUsPsl; Image of jogger, PD, http://bit.ly/1Joowze
Hi. Dan Laub here. And today I want to talk about how data comes in different types. What exactly do we mean by that? Well, let's first start with some objectives for this lesson. The first one is to understand what scales of measurement are in terms of the four different kinds we're going to discuss today. We have nominal, ordinal, interval, and ratio. And the second objective is to know how to recognize different types of situations in which each of these types of data can be used.
So let's get started. Remember that there are two types of variables-- explanatory variables and response variables. They can represent a quantity that is being changed or measured. And so with the steps of the experimental method, while there are 8 steps, let's focus on steps 5 through 8 for a moment.
Step 5, we're analyzing the results to determine what they tell us about the cause and effect relationship. Step 6, we're concluding whether or not the test showed us if our prediction was correct or not. Step 7, if we need to make revisions if the prediction happened to be wrong, we go back to step 2.
Or if it looks like the prediction is relatively plausible, we test it again to verify the results beginning with step 4. In step 8, if we're satisfied, we can report the findings so others can review or test themselves. And so the idea here behind analyzing the data is determining what types of data we can actually look at. And that's what this lesson is going to entail.
One of the first things that must be done in analyzing the reporting findings is to know what type of data is present and how to classify that data. Classifying data allows researchers to identify different types of information. So let's use an example as a horse race. We're going to see numbers all throughout a horse race. We're going to see the numbers on the horse in terms of which number they're representing. So it could be number 1, 2, so on and so forth.
We could see the order in which the horses finish the race-- first, second, third, fourth, and so on. We could see whether or not, if looking at the racing form, whether or not a horse is a male or female. Those are all different types of information. And what can we tell from that? Well, first of all, we know that the order that they place in is going to be something called ordinal measurement. In other words, first, second, or third-- it comes in order.
We also know that whether the gender is male or female doesn't really tell us anything numerically. And that's going to be something called a nominal measurement. And so there are going to a variety of different kinds of measurements we can look at simply from looking at a simple example like a horse race. Using the horse race is an example, let's compare the winnings of different horses. And one way to do that is to use a visual representation. In this case, it would be a bar graph.
So as you see here, we have a graph that represents four hypothetical horses. And just for the sake of simplicity, we'll call them Horse A, Horse B, Horse C, and Horse D. Notice how we can visually see the different types of data here. And that's relatively important, because it allows us to make a visual comparison of the winnings of the horses, and it's relatively easy to tell which horse has won more money than the other.
Let's look at a histogram, which is a different kind of representation. In this particular instance, we're looking at the ranges of the age of the jockeys of the horses. And so for example, at the low end we have 18. So the histogram tells us there are 11 jockeys between the ages of 18 and 22. And in the next range, there's 19 between the age of 22 and 26. And so on, all the way up to five jockeys over the age of 34.
And the nice part about graphs is it allows us to visually represent the data. When representing data, it often matters how that data is classified. And types of classification that we would get into more detail about as we continue this lesson. If a variable has a nominal scale, all it does is provide categories. Categories allow researchers to separate data based on characteristics that they might have. Such a variable is called a nominal variable.
Nominal scales do not show the direction or magnitude. Direction means that data can be ordered, and magnitude means that one thing can be considered larger or smaller than another. When something does not have magnitude, then this comparison can't be made. And when something does not have direction, then the order it's presented in does not matter. And so a nominal variable has neither.
For example, let's consider eye color. So if you were at the department of motor vehicles getting a new driver's license and you're filling out the form and they ask you what your eye color is because they're going to put it on your driver's license, and you're asked to pick from four different choices. And let's say those choices are blue, brown, green, and hazel-- common eye colors.
These choices don't have magnitude, because they can't be compared to one another. Blue eyes aren't necessarily bigger or better than brown eyes. Nor do they have a direction. The order they're presented in doesn't matter. They can be alphabetical order, which is probably what they would be. Nominal variables can also have categories that are numbers.
As an example, dial a telephone number. It's going to have an area code. The area code is going to be example of a nominal variable that consists of a number. All numbers within that area code would start with the same three digits. And the area code could vary from one region to the next.
Now, a variable has an ordinal scale if it provides categories, but only if the categories can be put in a meaningful order. What this means is that for each category, one can decide which is better or which is worse than others, or simply which item comes before another. Type of variable like this is called an ordinal variable. While ordinal scales do show direction, they do not show magnitude, because direction refers to the position of categories or numbers.
So for example, let's look at the different classes that might exist in a high school or college. We have freshman, sophomore, junior, and senior, and those are very common categories that are used to separate students based on how long they have attended the school. The class categories don't have magnitude, although you might say, well, gee, a senior might be better than a freshman or a junior. But nonetheless, they don't have magnitude.
However, they do have direction, since freshmen come first, sophomore come second, junior third and senior fourth. There are some scales of measurement for which we need to consider the difference between variables on the scale. And those types of variables will lead us to the next topic of this lesson. A variable has an interval scale if it provides numbers, so that the difference between two values can be measured. And the difference between any two values can always be determined the same way.
For example, let's consider SAT scores. The difference between a 1500 score and a 1700 score has the same meaning as the difference between a 1250 score and a 1450 score. This type of variable is called an interval variable.
With an interval variable, the number 0 does not mean that something does not exist. Meaning that somebody took the SAT and got a 0. Doesn't mean that they didn't take the exam. It simply means that they obviously didn't answer any questions correctly. And the fourth scale I want to talk about today is the ratio scale.
A variable has a ratio scale if it is an interval variable where the only difference is that a value of 0 does mean that something does not exist. This is called a ratio variable, and they occur in most types of physical measurements such as length and width and weight as well. Variables that provide a count are also ratio variables, such as, say, the number of apps you have on your phone. Weight is a great example of a ratio scale that we can see used in everyday life.
For instance, ordering a double scoop of ice cream would indicate that the cone contains twice as much by weight as a mere single scoop. This is different than an interval scale, however, because we are suggesting that there is multiple more of something, so two times as much, for instance, rather than simply saying, well, the second scoop of ice cream has 10 ounces more ice cream.
So the four types of data we've discussed can be separated the two major areas-- categorical data and quantitative data. Categorical data related to nominal and ordinal variables, while quantitative data are related to interval and ratio variables. For example, let's think about a group of people who are divided into two categories-- college graduates and non-college graduates. This will be considered a categorical variable as well as a nominal variable, as there is no direction or magnitude associated with it.
Another example would be the numbers on runners in a marathon. These numbers are considered categorical and could be ordinal if they were issued in the order in which the runners registered for the race. So for instance, the first runner that registered got number 1. The second one got number 2, and so on. However, just because they are numbers does not necessarily mean that they are quantitative variables.
So let's go over the objectives once again for this particular lesson. The first objective was understanding the scales of measurement in terms of nominal-- which we covered-- ordinal, interval, and ratio. And we went over all four of those and provided different examples for each one of them.
The second objective was to know how to recognize different situations in which this type of data is used. And we went over some examples of different situations that apply to each one of those types, both categorical as well as quantitative. So again, my name is Dan Laub, and hopefully, you got some value from this lesson.
A scale that provides numbers, and the difference of two numbers is a measure of the magnitude of their difference.
A scale that only provides categories.
A scale that provides categories, but the categories can be put in a meaningful order.
An interval scale, and additionally the number zero means the absence of a given quantity.