This video reviews the scales of measurement covered in introductory statistics: nominal, ordinal, interval, and ratio (Part 1 of 2).
Scales of Measurement
Nominal, Ordinal, Interval, Ratio
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In this video we'll take a look at what are known as the scales of measurement. OK first of all measurement can be defined as the process of applying numbers to objects according to a set of rules. So when we measure something we apply numbers or we give numbers to something and this something is just generically an object or objects so we're assigning numbers to some thing or things and when we do that we follow some sort of rules. Now in terms of introductory statistics textbooks there are four scales of measurement nominal, ordinal, interval, and ratio. We'll take a look at each of these in turn and take a look at some examples as well, as the examples really help to differentiate between these four scales. First we'll take a look at nominal. Now in a nominal scale of measurement we assign numbers to objects where the different numbers indicate different objects. The numbers have no real meaning other than differentiating between objects. So as an example a very common variable in statistical analyses is gender where in this example all males get a 1 and all females get a 2. Now the reason why this is nominal is because we could have just as easily assigned females a 1 and males a 2 or we could have assigned females 500 and males 650. It doesn't matter what number we come up with as long as all males get the same number, 1 in this example, and all females get the same number, 2. It doesn't mean that because females have a higher number that they're better than males or males are worse than females or vice versa or anything like that. All it does is it differentiates between our two groups. And that's a classic nominal example. Another one is baseball uniform numbers. Now the number that a player has on their uniform in baseball it provides no insight into the player's position or anything like that it just simply differentiates between players. So if someone has the number 23 on their back and someone has the number 25 it doesn't mean that the person who has 25 is better, has a higher average, hits more home runs, or anything like that it just means they're not the same playeras number 23. So in this example its nominal once again because the number just simply differentiates between objects. Now just as a side note in all sports it's not the same like in football for example different sequences of numbers typically go towards different positions. Like linebackers will have numbers that are different than quarterbacks and so forth but that's not the case in baseball. So in baseball whatever the number is it provides typically no insight into what position he plays. OK next we have ordinal and for ordinal we assign numbers to objects just like nominal but here the numbers also have meaningful order. So for example the place someone finishes in a race first, second, third, and so on. If we know the place that they finished we know how they did relative to others. So for example the first place person did better than second, second did better than third, and so on of course right that's obvious but that number that they're assigned one, two, or three indicates how they finished in a race so it indicates order and same thing with the place finished in an election first, second, third, fourth we know exactly how they did in relation to the others the person who finished in third place did better than someone who finished in fifth let's say if there are that many people, first did better than third and so on. So the number for ordinal once again indicates placement or order so we can rank people with ordinal data. OK next we have interval. In interval numbers have order just like ordinal so you can see here how these scales of measurement build on one another but in addition to ordinal, interval also has equal intervals between adjacent categories and I'll show you what I mean here with an example. So if we take temperature in degrees Fahrenheit the difference between 78 degrees and 79 degrees or that one degree difference is the same as the difference between 45 degrees and 46 degrees. One degree difference once again. So anywhere along that scale up and down the Fahrenheit scale that one degree difference means the same thing all up and down that scale. OK so if we take eight degrees versus nine degrees the difference there is one degree once again. That's a classic interval scale right there with those differences are meaningful and we'll contrast this with ordinal in just a few moments but finally before we do let's take a look at ratio.