Measurement scale, or
A common misconception about some of these examples has to do with "no true zero" versus "no zero possible." If we are measuring height and weight, for example, we will never get a measurement of zero ("no zero possible"), but the measurement scale still has a true zero on it. If we did get a measurement of zero (use your imagination!), it would mean the person being measured has no height or weight (absence of height or weight), whereas a measurement of zero degrees fahrenheit does NOT indicate the absence of temperature (or heat), and year zero on the Gregorian calendar was not the beginning of time. (In fact, there was no year zero on the Gregorian calendar.) The important discussion centers around the role of measurment scales in statistics. My opinion on this (which is, of course, correct) is that if you have numbers, you can do anything you want with them. I.e., you can do a t-test on ordinal data as long as the data are in numerical form and you've met the assumptions of the t-test. The difficulty comes with the meaning or interpretation of the result. For our purposes, we will differentiate between numerical data (interval or ratio measurement), ranked data (ordinal measurement), and categorical data (nominal measurement) for the purposes of deciding upon a statistical procedure. We will have to take some care with the interpretation of the result of that procedure, but then don't we always? If group one has a mean IQ score of 110, and group two has a mean IQ score of 95, and the two means are significantly different by t-test, does that indicate that people in group one are, on the average, more "intelligent" than people in group two? Similarly, if two instructors are rated on a Likert-type rating scale by 30 students each, and then means are taken of those 30 ratings for each instructor, is the instructor with the higher mean necessarily the better instructor? (NO!) | ||||||||||||||||||||

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