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| Levels of Measurement: The Difference in Numbers |
| Columns - Research to Practice | ||||||||
| Friday, 30 November 2001 | ||||||||
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This particular column covers how we measure data or numbers. All forms of measurement you will ever encounter can only sort, order, or count. To the average counselor, all numbers may look the same, but they do not mean the same thing. If we have a single number, like 27, we can only know what that means in terms of a measuring scale (Hayes, 2000). Twenty-seven could be someone's age, or the number of drinks your client had last weekend. Big difference.Imagine that numbers are trying to tell a story (Tal, 2001). These stories are similar to what clients tell you everyday. When you listen to those stories, you know there is some essence to each. They will have meaning and lie at the heart of the person. Numbers and statistics are just another way to tell a story. Granted, they are not very stirring, but they have vital information. Yet, too much information will confuse, and too little gives an incomplete picture. Good numbers, like a good story, keep to the essence. The different types of assessment Four different levels or scales of assessment (numbers) exist in statistics: nominal, ordinal, interval, and ratio. These scales of assessment deal with tabulating information. This is step-wise process. Understand the method of tabulation and that will help you understand the different types of statistical formulas that are used to calculate data. Each measurement scale can best be used with certain equations, which in turn, will give you different information. Nominal scales The first measurement scale is called the nominal scale (also known as a categorical scale) (Hayes, 2000; Vogt, 1999; Jaeger, 1993). This is the weakest and lowest level of measurement. It classifies (sorts) people or objects into two or more categories. In whatever classification system you wish to use, the person or object under investigation will have at least a common set of characteristics. For example, people can be female or male, have a certain eye color, or a particular age. The best we can do with this simple type of information is to assign numbers to the categories like female = 1 and male = 2, or blue eyes =1, brown eyes = 2, green eyes = 3, and just give the age as it is. In and of itself, there is not much meaning here. For example, we can't say female is Ômore' than male, or green eyes are Ôlower' than brown, or one age is Ôbetter' than another. (Some might argue with these comparisons, but that means bringing other variables into the mix.) The point is that nominal numbers alone do not say much. They really have no order and no value. Statistical formulas such as chi-square and multiple regression use nominal scales. These types of formulas try to compare characteristics in two or more groups and examine the relationship between two or more variables. Ordinal scales Moving up the scale, the next measurement is called ordinal (Hayes, 2000; Vogt, 1999; Jaeger, 1993). These types of scales put things in order in the sense that higher numbers represent higher values. With this scale, we can classify people or objects by ranking them on some characteristic of interest. This measurement really adds to the nominal measurement. Yet, a drawback of the ordinal scale is that the intervals between the numbers are not necessarily equal, and there is no zero point. For example, on a five-point rating scale (5 high, 1 low) that could measure the loss of control in addiction, the difference between a 2 and a 3 may not represent the same difference as that of 4 to 5. Plus, who could say one version of 2 to 3 would be exactly the same for somebody else's version? Obviously, no such scale exists, and even if it did, ordinal measures do not work that way. This can have dire clinical consequences, because one practitioner's version of 2 to 3 could be very different from another practitioner's version. Using only this scale, staff meetings could really become confusing, because no one would be speaking the same language. If this type of measure is all you have, then you still can compare characteristics in two or more groups, and examine the relationship between the two variables. In this case, the statistical formulas Spearmen rho is the appropriate statistical formula. Interval scale The interval scale is the third level of measurement (Hayes, 2000; Vogt, 1999; Jaeger, 1993). Essentially, it counts. It has all the properties of the nominal and ordinal scales, but is based upon predetermined equal intervals. This means one unit of scale represents the same magnitude across the whole range of the scale that is being used. Temperature is a prime example. The Fahrenheit scale has equal units between each number all across the length of its scale. The interval scale, however, does not have a true zero point. So this means that you cannot make statements about how many times one score is higher from another. The true interval measurement is fairly rare in the behavioral field, let alone for substance dependency. For example, if there was an interval type test that noted the intensity of alcoholism on a scale of 1 to 10 (1 low and 10 high), a score of 10 would not mean that is twice as much as a score of 5. Why? Because there is no zero reference. No scale such as the above example exists in the substance use disorder field. Ratio scale The last measurement is called a ratio scale (Hayes, 2000; Vogt, 1999; Jaeger, 1993). It also counts, and is considered to be the strongest and more precise level of measurement. It possesses all of the characteristics of each previous scale, but this one has a true zero point. So, this scale cannot have negative numbers. In our daily life, we deal with this level of measure most often. Think about measures such as height, weight, distance, and speed. At the clinical level, using this form of measure can cause the least amount of confusion, because of the equal interval and zero point. This way all people who use it are speaking the same language. Some medical test results are an example. Here you can say that one liver function test may be twice as high as a previous one. A number of 12-step groups that give tokens based on non-using days are using the ratio measurement. Because of the ratio scale's strength, it can be used in the most powerful statistical formulas available. A summary diagram of all we have discussed is provided (see Figure 1). If you Ôgot' the difference between these levels of measurement, you will most certainly have an easier time from now on. You will see how we put this measurement material to work when central tendency and variance is covered in the next column. Michael J. Taleff, PhD, CAC, MAC, is the Coordinator of the Alcohol and Drug Education Program at the University of Hawaii at Manoa. References Jaeger, R.M. (1993). Statistics: A spectator sport (2nd ed.). Thousand Oaks, CA: Sage. Hayes, N. (2000). Doing psychological research. Buckingham, England: Open University Press. Tal, J. (2001). Reading between the numbers. New York: McGraw-Hill. Vogt, W.P. (1999). Dictionary of statistics and methodology: A nontechnical guide for social sciences (2nd ed.). Thousand Oaks, CA: Sage.
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