Scales of Measurement - Nominal, Ordinal, Interval, Ratio (Part 2) - Introductory Statistics

This video reviews the scales of measurement covered in introductory statistics: nominal, ordinal, interval, and ratio (Part 2 of 2).

Scales of Measurement
Nominal, Ordinal, Interval, Ratio

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Video Transcript:
meaningful just like interval but it also has ratios that are meaningful and there is also a true zero point and by true zero point what we mean there is that zero means what we think of as zero typically or the absence of the property like 0 inches there is no length or what have you. OK so an example would be weight in pounds and here 10 pounds is twice as much as five pounds or other words 10 / 5 is 2 or 2 times as much. So that's a meaningful ratio and in addition to this zero pounds means no weight or an absence of weight so there's a true zero point. So if something is zero pounds that means it has no weight whatsoever. OK so now let's compare the scales and I think this is where you really can start to see some of the differences between these four scales more clearly as we really start to differentiate between them through examples. So interval vs ordinal we'll start there. Recall that our interval example was temperature and in that example a one degree difference is the same at all points of the scale that was our example of interval and then for ordinal we have the place in the race first, second, and third the difference in finishing between first and second now for ordinal is not necessarily and probably is not the same as the difference between second and third. Now you might say we'll wait a second the difference between first and second is 1 and the difference between second and third is 1 so that should be the same as interval. But what we need to think about here is to ask yourself let's say we're sitting there at the finish line and the person finishes in first and second those two let's say are neck and neck and the first place person just barely wins at the end and then along comes third place person much later so we have first the second neck and neck and then third comes along later let's say a minute later or something like that. So in this race the difference between first and second was very small but the difference between second and third was very large so those aren't equal intervals among the adjacent categories and that's why it's ordinal. So for this example it's ordinal because we know there's order to it 1st is better than 2nd, 2nd than 3rd but we can't say that those adjacent categories are equal. OK next interval versus ratio. Now the two qualities of ratio recall is that the ratios are meaningful and there's a true zero point, where zero means the absence of the property. Well think of temperature. Zero degrees how is it outside if you thought of zero degrees you wouldn't say there's an absence of coldness or heat outside you would say it's really cold, right? Zero degrees Fahrenheit it's 32 degrees below the freezing point so it's really cold. So zero does not indicate an absence of the property there and then in terms of the ratios if we think back to our ratio example with the weight of objects if I had a five-pound object and I had another five pound object and I put both those on the scale that would give me 10 pounds right total weight. But if I have a 40-degree day and I have another 40-degree day so a cold day and a cold day and I put both of those together I don't get suddenly a warm day 80 degrees. A 40-degree day and a 40-degree day is still a 40-degree day it doesn't suddenly equal an 80 degree day. So the ratio isn't meaningful there for temperature. So this is why temperature is interval and weight is ratio. OK and then finally let's take a look at nominal vs ordinal, interval, and ratio. So recall with our example of baseball uniform numbers the numbers only serve to differentiate between players. There is no order to them 25 isn't necessarily better than 23. There's no meaningful differences; I can't subtract 25-23 get a two and then my next number up let's say is 30 and 35 subtract 35 and 30 and get a 5 that doesn't make any sense. We wouldn't subtract uniform numbers and expect to get any meaning out of that and then ratios are not meaningful there's no true zero point. Think of someone who chose the number zero in baseball. That doesn't mean there's an absence of a baseball player there right zero means nothing that would just be a player with the number zero. So that's why baseball wouldn't be ordinal, interval, or ratio. Alright that's it for scales of measurement. Thanks for watching.