Section 2: Levels of measurement
From Research Methods in Psychology
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[edit] WHAT ARE YOU STUDYING?
IN THIS SECTION WE WILL EXAMINE THE FOUR DIFFERENT LEVELS OF MEASUREMENT THAT ARE USED IN PSYCHOLOGICAL RESEARCH. UNDERSTANDING THESE LEVELS OF MEASUREMENT IS CRUCIAL TO UNDERSTANDING THE MEASUREMENT PROCESS.
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Crucial Concept: The level of measurement of a variable informs us about the meaning of the relationships between numbers on a scale. |
Since experiments in psychology are concerned with the collection of data, and data are the result of measurements, it is important to have an understanding of the types of scales that we use for the type of data we collect. The choice of measuring scale will determine the type of statistical tests that we can perform on the data. A very important series of articles by Stevens (1946, 1951) introduced the idea that there are four categories of scales or levels of measurement that are used in psychology experiments. These are: nominal scales, ordinal scales, interval scales and ratio scales. If we don’t know the level of measurement, we don’t know what the numbers are telling us. (This sounds like a rather difficult, abstract idea, but it should make sense if you read on.)
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Crucial Tip: A good way of remembering these is to take the initial letters from each word to form the word NOIR (French for black). |
Outliers are easy to spot, but deciding what to do with them can be much trickier. If you have an outlier, you need to do some checking, to decide what you should do about it. First, you should see if you have made an error in entering your data. Data entry errors are the most common cause of outliers. Look for numbers that should not be there. If the maximum score on a test is 10, and someone has scored 66, then you have made an error. If you don't find an entry error, look for a measurement error. You should now check that any measurement that you took was done correctly. Did a piece of equipment malfunction? Obviously, if you find an error, you correct it if you can. If you cannot find an error, you must conclude that the data point is a ‘real’ data point. If it was a measure of reaction time, did the participant sneeze or yawn? Did they understand the instructions? Is there something unusual about them that means that they should not have been measured? If any of these are the case, you should try to correct the error in some way, and enter the correct value – if you can. If you cannot find the correct value, you should delete the data point. This may seem like cheating – you are throwing away a valid data point. You need to think about the underlying psychological process that generated the data point. If the participant who generated that reaction time did it because they sneezed, the psychological process was not the same, and you should not be interested in that process.
If you cannot eliminate any of these errors, and are convinced that you have a genuine measurement, then you have a dilemma. Your first option is to eliminate the point, and carry on with your analysis. If you eliminate the point, you will analyse your data well, but you will not analyse all of your data. Alternatively, you can keep the data point and analyse all of your data, but, as we will see in the next chapters, keeping the outlier in means that your distribution will not be normal and therefore the analysis you do will not be correct – and therefore you will analyse your data badly. Not much of a choice. (Sorry.)
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Section Summary When exploring your data, the first thing you should look at is the distribution of the data. This is done most easily using a histogram (frequency plot) or a box and whisker plot. The histogram will show you if the data are normally distributed. If they are not normally distributed, they may be non-normal because the data form the wrong shape, or because a small number of outliers. If the data form the wrong shaped distribution, the shape of the distribution may be skewed (non-symmetrical), or kurtosed (too flat, or too peaked). Skew is more serious than kurtosis. (The shape of the data may be changed using transformations.) Outliers might be errors. If they are errors, they should be fixed; if they are not errors, they should probably be removed. |
[edit] Nominal Scales
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Crucial Concept: Nominal data are data that record categories. |
The nominal level of measurement is often also known as categorical data. With this type of data observations are sorted into discrete, mutually exclusive categories. For example, keeping a record of the sex of each participant in an experiment is recording data at the nominal level. Males could be put into Category 1 and females into Category 2. Equally, you could do the reverse and put females into Category 1. The numbers 1 and 2 have no consequence except as labels. This nominal scale ranges from 1 to 3. As you can see, the actual numbers under which people or observations are classified are quite arbitrary. That is, the nominal number 2 in this example isn’t greater or better than 1, it is merely different. As this is the case, calculating the mean or arithmetical average (the sum of the scores divided by the number of scores) would, since the scores are only names or labels, be meaningless. Categorising people according to favourite food, eye colour and postal district are other examples of the use of nominal scales.
[edit] Ordinal Scales
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Crucial Concept: Ordinal data record information about the rank order of scores. |
If we put objects or individuals are put into a rank order, we are using an ordinal scale. Data sorted in this way are sometimes also referred to as ordered categorical data. For example, an experimenter might ask you to rank your five favourite TV programmes into an order of preference - so that 1 signifies your most favourite and 5 signifies you least favourite. The data collected would be measure at the ordinal level. The ordinal scale in this example ranges from 1 to 5. You cannot assume that the differences in preference between TV programmes are always equal. That is, you might like your second favourite almost as much as you like your favourite, whereas you might prefer your third a long way ahead of your fourth favourite. Another example of ordinal data could be a list of the first, second and third order runners in a race to cross the finish line. The runner who crosses the line first could be a long way ahead of the runner who crosses the line second, whilst the second position could be only just ahead of the third. In other words, ordinal scales do not have equal intervals. As with nominal scales, therefore, you usually should not add values from an ordinal scale or perform other mathematical operations on those data.
[edit] Interval Scales
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Crucial Concept: Interval scales tell us about the order of data points, and the size of the intervals in between data points. |
Interval data represents a much higher level of measurement than ordinal data. When data are measured on an interval scale, we know about the rank order (as with ordinal data), but we also know about the intervals - that is the differences. When we measured data on an ordinal scale we did not know anything about the distance between a score of 1 and a score of 2 - we did not know the size of the interval. When we measure numbers on an interval scale, we know that the distance - the interval - between the scores 1 and 2 is the same as the distance between 2 and 3.
The centigrade scale of temperature measurement is an example of an interval scale. The intervals between adjacent values in the centigrade scale are equal: it is reasonable to add and subtract the numbers on the centigrade scale. For example a temperature change of 10* from 10* to 20* is exactly the same size as a temperature change of 10* from 30* to 40*. We can also say that the difference in temperature between 40* and 20* is twice as much as the difference in temperature between 60* and 50*. However, interval scales do not have an absolute zero point. For example, 0* centigrade does not mean that the thermometer is measuring s no heat at all: the 0 mark is simply a point on the scale.
[edit] Ratio Scales
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Crucial Concept: a ratio scale is an interval scale with a true zero point. |
The ratio scale has all the properties of the interval scale - equal intervals that can be added and subtracted. The important difference is that the ratio scale, unlike the interval scale, does have a true zero point. The implication of having a true zero point is that numbers on the scale, as well as being added and subtracted, can be multiplied and divided - you can say that one measurement was twice as big as another. You can’t do this with a scale which doesn’t have a true zero - 20* is not twice as hot as 10*C (if you aren’t convinced that this is true, tell me what twice as hot [or cold] as 0*C). As an example of a ratio scale, consider the measurement of response times in a psychology experiment. The ratio scale has an absolute zero (e.g., a clock starts ticking at 0 seconds) we can determine the ratios of values. For example, a participant in an experiment who took 10 seconds to respond to a stimulus can be said to have taken twice as long as a participant who took 5 seconds to respond (a ratio of 2 to 1). The distinction in psychology between interval and ration measures is usually unimportant – ratio scales are treated as if they were interval.
The table below contains a summary of the levels of measurement (adapted from Stevens, 1951).
| Scale | What do we know | What does it tell us | Examples |
| Nominal | Equal versus not equal | The same, or not the same | Shoe colour |
| Ordinal | Order | Above or below | Order in a race |
| Interval | Equality of intervals | The amount above or a certain amount below | Temperature (Celsius) |
| Ratio | Equality of ratios | The amount, and the proportion, above and below | Time (seconds) |
Interval and ratio data are sometimes grouped together and referred to as cardinal data, or continuous data. It is possible to convert data from one level of measurement to another, but only in one direction. If you have data measured on a ratio scale you can convert them to interval data, by ignoring the zero. If you have data that are measured on a ratio scale you can convert them to ordinal data, by converting them to ranks. If you have data that are measured on an ordinal scale, you can convert them to nominal data, by grouping them into ‘high’ or ‘low’ categories. However, this is normally a bad thing to do – you can convert in one direction, but you cannot convert in the other direction, because the conversions that I have described involve discarding information, which cannot be retrieved.
[edit] Section Summary
This section has examined the four levels of measurement: nominal, interval, ordinal and ratio, and given examples of their use.
