ISACA COBIT 5 – Measure (BOK V) Part 3

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• January 26, 2023
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5. Types of Data (BOK V.B.1)

In measurement phase of DMAC, which is M in DMAC. We are concerned about collecting data and when we are collecting data, we need to understand what are the types of data we have. Because if we know the type of data, we can use appropriate tool, we can use appropriate analysis for that. So, broadly classifying, we have two types of data. One is qualitative and another is quantitative. So if you hear the word correctly, qualitative is something related with quality and quantitative data is something which is related to the quantity. So the first one which is here is qualitative data. So qualitative data is description or the quality. For example, if I tell you look at this slide and tell me what all colors are on this slide, and then you can say that there is a bit of black, some blue, some white, some gray, these are the colors on this slide. So this is qualitative data.

On the other hand, quantitative data is something which is related to numbers. So if I ask you what is the length of this topic, how much time it takes to complete this particular video, that is a number, maybe five minute 35 seconds. Let’s say for example, that’s a number that is quantitative data and how does it differ what tool we use? Going back, for example, if I tell what is the average value of colors on this slide, that thing will not make a sense. You know that this slide has a blue color, this slide has a red color, a little bit of this slide has a black color and a white color.

You cannot find an average or the mean value of this. What you can find on the other hand is which is the most prominent color on this slide? So if I ask you that, then probably you can say yes, the white is the most prominent color on this slide. Coming to quantitative Data so we talked about one example as the length of this specific video. That’s something which is let’s say five minutes, some few seconds or something. But then if I ask you what is the average length of videos in this particular course, you can add all the times of all the videos and divide that by number of videos.

So you can find the average time for each video which you couldn’t find when I asked you the average value of the color on the slide, because that was not making sense. So if you know the type of data, then you can use the appropriate tool or the appropriate measurement for that. Another few examples of quantitative data could be the weight, weight of a piece being manufactured, the speed, the length, the time, the volume, temperature, humidity, all these things are measurements. So these all will fall under the category of quantitative data. So let’s put it here. The example of qualitative data could be color, this could be the appearance, this could be the rating on scale of one to five, whether you liked or did not like or you very much like that, or let’s say good, better, best, let’s say on the scale of three. If we have to find that. On the other hand, going to quantitative data, these are, let’s say the weight, the length, time, temperature, et cetera, et cetera.

Just like we looked at qualitative versus quantitative data on the previous slide. Let us look at another differentiation or another category of data which is continuous. And discrete data could be continuous or data could be discrete. So what is continuous? Continuous is something which can take any number of value in between two steps. For example, if you are looking at weight, weight of a person, the weight of one person could be 56 kg. If we go a little bit more into that, this could be 56. 1 or this could be 56. 13. Or you can go to any number of terms, digits in that this is what a continuous data will be like that there are no steps between 56, there are infinite number of values which this particular data can have. And the example which we took was the weight of a person. On the other hand, discrete data is something which is in the form of steps.

Steps such as the number of students. So you can have either number of students as 56 or 57. You cannot have number of students in a class as 56. 1. Same way if you are tossing a coin, if you toss a coin, you can get a head or tail. Then you can get only the round number of heads or tails. If you flip the coins, let’s say ten times. So you can have five times, you can have a head or six times you can have a head, but you cannot have a head for 5. 5 times out of ten. And this is what a discrete data is. So the example of continuous data is length, height, time. Whereas discrete data would be most of the time. This will be a count number of people, number of times, number of accidents, number of defective pieces. Going back to continuous data, continuous data gives more information with less samples. So here let’s assume that you are a quality control inspector and you have a plate which you need to inspect. And this has a hole in that and the whole diameter is, let’s say 10 mm.

That is the nominal value. That hole has to be of ten millimeter. But what is acceptable? The acceptable is anything between 9. 5 to 10. 5 is acceptable. So there are two ways you can take this measurement. One is you keep on picking piece by piece few samples you pick and in each sample you note down this diameter of the hole. So you pick the first piece and you find out that the diameter of this hole was 9. 7 mm. Pick the second piece, you find out this was 10. 1. You pick the third piece, this was 10. 3 and so on. This data which you are collecting is a continuous data because this can take any value. On the other hand, if your intent was to pass or fail anything, pass anything which is between this diameter 9. 5 to 10. 5, everything passes, and anything which is above or below this fails. Then what you can have is you can have a Go No Go plug gauge. So what? Go no go.

Plug gauge looks like. So there will be a plug gauge like this. And this will have two ends. One end will be 9. 5 diameter, this diameter, and another end of this plug will be 10. 5. So what Inspector can do is take this plug and insert this plug into hole 9. 5. Side should pass through that and 10. 5 should not pass through that hole. So if 9. 5 side passes through that, that shows that the hole is bigger than 9. 5. And if 10. 5 doesn’t pass through that, that means that hole is less than 10. 5. So the Inspector will pass this. So this end becomes Go end and this end becomes no Go end. And based on that, Inspector can pass or fail a piece. So Inspector takes ten pieces and find out that out of ten, eight pieces passes this. What sort of data this Inspector is getting here is discrete data.

Because Inspector is not measuring the diameter of this hole. Inspector is just looking at pass and fail, just counting the number. So this will be a discrete data. As you can very well understand at this time, discrete data doesn’t give you much information. This just tells you pass and fail. This doesn’t tell you that most of your holes are for example, between ten to 10. 5. That sort of information, that sort of a knowledge can only come from continuous data. And that is the reason I tell that continuous data gives more information with less samples. It’s more sensitive that we have seen that it gives more information, it’s more sensitive and it provides more information when you have a continuous data. But as you would have seen, continuous data takes time to collect. So there is a value related to that, there is effort and money related to that.

So you put more money, more effort in taking data, because you want to take continuous data, but in return that is going to give you more information, more insight into the issue as well. But this is expensive as compared to discrete data. So this is the difference between continuous data and discrete data. Why we are looking at this here? Because as we go further into this course, we will be talking about distributions, we will be talking about normal distribution, binomial distribution. And that time we will say that continuous data, you can use a normal distribution for that. If your data is normally distributed, the appropriate distribution for discrete data would be binomial.

We will be talking about these distributions later. But just to tell you that there is a sense in knowing whether the data which you are collecting is a continuous data or discrete data. And both of these have their own advantage and disadvantage. So if you have a less time, you want quick results. Discrete data is helpful, but it is less sensitive. This gives less information compared to the continuous data. So this completes our discussion on continuous versus discrete type of data.

6. Measurement Scales (BOK V.B.2)

Previously we talked about data and we talked about continuous versus discrete, qualitative versus quantitative data. Here we go a bit more into details of this classification of data. So data can be classified into four categories, nominal ordinal interval and ratio. So nominal ordinal interval and ratio. So just to remember, you can remember the term noir. Noir. These are the scales of data. Let’s look at each of these starting with nominal type of data. So here the example of nominal data is color, the color such as blue, green, red. So that’s the example of nominal. That’s what we have here. When we talk of nominal ordinal interval and ratio, we will be talking about three main things. One thing is, is there an order? And when we say order, can we put sequence to this? The blue, the green, the red, there’s no order to that. For example, if I say number 1234, I can say that there is an order in that. But here in this example of nominal, blue, green, red, there is no order. So there is no order in the nominal data. Second thing which we will be discussing here is difference. So that’s a difference. Is there any meaningful difference between these items and probably that will make sense once you have order. So if there is no order, then there is no question of having difference. But what difference would I mean is like between one and two, there is a difference of one. Between two and three, there is a difference of one. Between three and four there is a difference of one.

So there is difference which makes sense here. But when you look at the difference between blue and green, green and red, that doesn’t make any meaningful sense. And since there is no order, so definitely difference will not make any sense. Nominal, we don’t have order, we don’t have difference. And third thing which you will be looking here is absolute zero. So third thing is absolute zero. Is there an absolute zero here? An absolute zero is absence of something. So when we see talk of colors, blue, green, red, is there anything which we could say that absence of color? No, there is nothing such thing that there is an absence of color. So that doesn’t make sense. So in nominal form of data, there is no order, there is no meaningful difference and there is no absolute zero. So let’s move on to the next level of data. And when I say next level of data, the next level of data is higher and more meaningful than nominal data and that is ordinal data.

So let’s move on to the next slide and look at the ordinal data. So here we have example of ordinal data, ordinary data example is things like pass fail, things like good, bad, worst. So now here you can see that there is some sort of order here, good, bad, worst. So there is a flow here good is better than bad and bad is better than worst. So there is a order here. So as we talked in nominal three things, let’s look at these three things here. Is there an order here in nominal? Yes, there is an order. So order is there is there a meaningful difference between two values? No, there is no meaningful difference between two values. So the difference between good and bad and the difference between bad and worst doesn’t make any sense. These are just the levels. There is an order here but there is no meaningful difference between two items. So order is yes, difference is no.

And do we have absolute zero here? That was the third item which we wanted to look here in each level of data. So absolute zero, there is no absolute zero in Ordinal data. Let’s move on to the next higher level of data which is interval coming to interval, the example of interval is temperature in degrees Celsius. So that’s one example of that. This is different from ratio. So once we go to ratio we’ll be talking of height, weight, volume and many other things in ratio. But the only thing which we are considering here in interval is the temperature in Celsius. Let’s look at that. Is there an order here? Yes, there is an order when you look at the temperature in degrees Celsius. So if you look at ten degrees Celsius, 20 degrees Celsius, 30 degrees Celsius, there is an order here once you take temperature measurement so yes there is an order. Order is there is difference meaningful?

Yes, difference is meaningful here which was not the meaningful thing in ordinal in Ordinal, we were looking at good, bad, worst. So you couldn’t find a difference between two items here you can find a difference between two items. You can find difference between 20 degree Celsius and ten degree Celsius which is ten degrees Celsius and same thing between 30 and 20. Also there is ten degree Celsius difference and both these ten degree Celsius are the same thing. So difference of ten degree Celsius is the difference of ten degree Celsius only whether that is from 20 to ten or whether that is 30 to 20. So difference yes. And is there an absolute zero here? So absolute zero? No, there is no absolute zero when you look at temperature in degrees Celsius.

So at zero degrees Celsius when we look at zero degrees Celsius that doesn’t mean the absence of temperature, that is just one temperature at which the water freezes but that doesn’t mean that at zero degree Celsius temperature doesn’t exist. So there is no absolute zero when you are looking at the temperature and degree Celsius. Let’s move on to the next level of data which is ratio. So here in ratio, most of the measurements, most of the numbers value which you get all around you would be in ratio category, height of people, mass, weight, volume, depth, all these measurement, the current level, all these things are ratio. The only difference between interval and ratio is in ratio, you have an absolute zero which you didn’t have in interval. Looking at the same three things here, is there an order here? Yes, there is an order here. So when you look at height, 1 meter height, two meter height, three meter height, there is an order here.

So 1 meter, 2 meters, 3 meters, 3 meters is bigger than 2 meters. 2 meters is bigger than 1 meter. So there is an order here, there is meaningful difference between two values, 2 meters and 1 meter. The difference of that is 1 meter. Between three and 2 meters, there is a difference of 1 meter. So there is difference is meaningful here. So you have a meaningful difference between two values. And the third thing here was absolute zero, absolute zero, which we said in temperature degree Celsius that there was no absolute zero. But here, in this ratio type of measurements, we do have absolute zero. So when we say absolute zero height, that means there is no height, that something doesn’t exist, absolute mass, that something doesn’t exist.

So there is an absolute zero as well. So these were the four levels of data. So, as you would have guessed rightly, as we move from nominal to ordinal to interval to ratio, things gets more advanced, ratio is more advanced, ratio gives more information as compared to, let’s say nominal or ordinal. So with this discussion, let’s go to the next slide and look at the summary of the discussion which we had so far. So here on this table, I have all four levels of data which is nominal, nominal here, ordinal interval and ratio. As we already talked, in nominal, there is no order, there is no meaningful difference and then there is no meaningful zero and so on. So all these things, we have already talked about that, we already looked at the examples of each of these. Now, when it comes to finding out value, some descriptive statistics, some meaningful result out of this data, what could be used?

So we have an example of central tendency. And central tendency in a common language would be something like an average. So when you have a nominal data, can you find an average of that? You cannot find average because these are not numbers, these are some descriptions such as the color red, blue, you cannot have an average of that. So what you have here is the measurement of central tendency. Here would be mode. And mode is something which is the most occurring item. So mode is something which is the most occurring value in the group in the data which you have. That is something which you can find when your data is nominal. And if your data is ordinal to find the central tendency of that, either you can use mode or you can use median also. And median is something that when you arrange things in order, the central value that something is median. So you can find the mode or the median in case of ordinal data.

And once you reach to interval and ratio in these two types, and these are the highest level of data here, you can use any of the commonly used central tendency measurements, which are mode, median and mean. Now, looking at these four levels of data, how do these compare? When we talked about earlier qualitative and quantitative data, and you would have rightly guessed that the nominal and ordinal type of data, nominal or ordinal level of data is qualitative data, which is quality, which is the description in nominal. If you remember, we talked about things such as colors red, blue, green. In ordinal, we took an example of something like a good bad, worst pass fail.

Both of these nominal and ordinal were qualitative data. These were qualities, these were descriptions. And when you look at interval and ratio, these are quantitative data and quantitative, where there are numbers, where there are quantities. And that’s how these four levels of data, which is nominal ordinal interval ratio, are connected with qualitative or quantitative data.

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