Hey internet student, welcome to the brief tutorial statistics. My name is Matthias Bertel, I'm professor for mathematics and statistics at the University of Applied Sciences in Offenburg and in this video I'm going to explain the scales of measure, also called levels of measurement. I hope you enjoy this video, if you do please give it a thumbs up and subscribe for more educational content. But now to the scales of measure.
One of the many advantages of statistics is that it works equally fine No matter whether your subject is medicine, criminology, economics or anything else. I could explain the levels of measurement using the stock market or I could just use an apple. I'm going with the apple because it's healthy and cost efficient. Now let's think about how we perceive and describe this apple. We do this by determining attributes that relate to the apple and then we measure the apple against these attributes.
If you aren't quite clear about what I mean by that, please watch my video about the basic statistical terms. The link is in the description and should also appear somewhere here on the screen. But now back to the apple. First I notice its color. This apple is red.
I also could weigh the apple and find that it is 5 ounces. Maybe not the most obvious but certainly also a characteristic of this apple is that it was harvested on September the 14th. And another essential feature in apples, at least for me, is their sweetness.
This one is... I would say medium. So that was the first apple but I'm prepared I've got more apples. This is a new apple and it is green. It tastes quite sour.
Very sour actually. It was harvested on September the 4th and it weighs 7 ounces. Last apple, obviously yellow, quite sweet, picked on October 4th and it is 6 ounces. So with that we collected some data very quickly. Now let's put that information into a table because that's what statisticians like doing.
Statistics is always about counting and comparing things. If we compare the apples based on the four attributes that we just collected data against, we notice the following. If we look to the very right to the weight, we see numbers. With these numbers we can do basically anything we know from mathematics.
We could for example calculate the difference in the weight of the second and the first apple and find that there is a difference of two ounces. Or we could add up the weight of all three apples, divide it by the number of apples and find that the average weight is six ounces per apple. Not a problem at all. However, if we look to the left, where I've noted the colors and the sweetness, we haven't got any numbers, so adding and dividing just won't work.
Obviously, although everything we have in this table are values, measured against attributes, there is a difference in what type of operations we can do with them. And that is what we call the level of measurement. Normally, one distinguishes four levels of measurement.
And for each of these levels, we have one example in this table. And now, I'm going to explain what these levels are. The first level of measurement, or scale of measure, is called nominal scale. The values on a nominal scale are characterized by the fact that with respect to them, we can only say whether two statistical units are the same or not. In our apple example, this applies to the attribute color.
So, these two are different, so are these two apples, but these two apples are the same. Therefore, we say that the attribute color is measured on a nominal scale. And this holds true for all attributes that allow only equal, not equal comparisons.
Another example would be state of residence. of equal brands. By the way, more generally speaking, a scale is the set of all possible values against a given attribute.
The second level of measurement is referred to as ordinal scale. Values on an ordinal scale can still be compared as to whether they are equal or not, but in addition we can also put them into an order. This is the case for the attribute sweetness.
All three apples were differently sweet. One was very sour, one was very sweet, and there was also one in between the two. So we can easily put the three apples into an order with respect to their sweetness.
In social sciences, to include business administration, this scale of measure is quite common for example when people are asked for their opinion in surveys. The third type of scale is called interval scale. In addition to the already known comparisons equal, unequal and order, values that are measured on an interval scale allow us to determine a distance between them. This is possible, for example, for the harvest dates of three apples.
Not only can we say that the dates are different, or put them into an order, The distance between the dates I'm going to use plus and minus to indicate the possibility of calculating that is 10 days for the green and the red apple and 20 days for the red and the yellow apple. So, dates are measured on an interval scale. The fourth and highest level of measurement, in addition to the three other types of comparison, also allows the calculation of ratios between the values. For example, it does make sense to say that the green apple is 1.4 times the weight of the red apple. Scales on which it does make sense to form ratios between their values we call ratio scales.
Most things that are measured in numbers form a ratio scale. Another example for a ratio scale is anything that is measured in terms of monetary value such as revenue, cost, profit, etc. Now let's recap.
Comparisons between characteristics were equal-unequal, order, distance and ratios. The scales of measure we called nominal scale, ordinal scale, interval scale and ratio scale. An example for a nominal scale is color and on a nominal scale we could only say whether two values are the same or not. That's the only meaningful comparison on nominal scale. On an ordinal scale, an example for that would be sweetness, we can determine whether two values are equal or unequal, and we can also arrange the apples, for example, in accordance to their sweetness.
Looking at the date, we can say that it was measured on an interval scale. As we can say whether two dates are the same or not, there is also an order in dates and there is also a distance between them. Ratios, on the other hand, don't make sense. It isn't meaningful to divide September 14th by September 4th. Because weight, our last characteristic we looked at, is measured on a ratio scale, all operations are possible.
And these are the four scales of measurement. So, why do we need to know about them? Scale theory is a very basic but also very important foundation of statistics.
In statistics there are a lot of methods. Some methods require us to sum up values. Others are based on forming ratios and others just work by putting values into order. Whether a given method, at least in principle, is applicable to a given dataset or not, therefore, obviously depends on whether the required mathematical operations are appropriate on the scale of measure that the dataset belongs to.
That is the case in every craft. If you want to put in a screw, you wouldn't use a hammer, and you wouldn't put in a nail using a screwdriver. And that's why we need to understand scales of measure.
so that we can always choose the method that suits the problem. So that was my explanation of the four different levels of measurement. If you enjoyed this video, don't forget to subscribe. Thank you for watching and hope to see you soon.