Levels of measurement

Transcription

1 Levels of measurement What numerical data actually means and what we can do with it depends on what the numbers represent. Numbers can be grouped into 4 types or levels: nominal, ordinal, interval, and ratio. Nominal is the most simple, and ratio the most sophisticated. Each level possesses the characteristics of the preceding level, plus an additional quality. 1. Nominal Nominal is hardly measurement. It refers to quality more than quantity. A nominal level of measurement is simply a matter of distinguishing by name, e.g., 1 = male, 2 = female. Even though we are using the numbers 1 and 2, they do not denote quantity. The binary category of 0 and 1 used for computers is a nominal level of measurement. They are categories or classifications. The categories are established by the researcher and an item is counted when it falls into this category. The most significant point about nominal scales is that they do not imply any ordering among the response. For example, when classifying people according to their favorite color, there is no sense in which green is placed ahead of blue. Nominal levels of measurement is the least precise form of measurement. 1. MEAL PREFERENCE: Breakfast, Lunch, Dinner 2. RELIGIOUS PREFERENCE: 1 = Buddhist, 2 = Muslim, 3 = Christian, 4 = Jewish, 5 = Other 3. POLITICAL ORIENTATION: Republican, Democratic, Libertarian, Green 4. NUMBER of males or females 5. NUMBER of individuals who fall under the category of introvert or extrovert 6. HEIGHT the number of tall, medium or short people in a group 7. COUNTING the number of participants who did or did not experience anxiety Nominal category of the day - categories; no additional information 2. Ordinal Ordinal refers to order in measurement. An ordinal scale indicates direction, in addition to providing nominal information. Low/Medium/High; or Faster/Slower are examples of ordinal levels of measurement. Ranking an experience as a "nine" on a scale of 1 to 10 tells us that it was higher than an experience ranked as a "six." Many psychological scales or inventories are at the ordinal level of measurement. Unlike nominal levels of measurement, ordinal measurement allow comparisons of the degree to which two subjects possess the dependent variable. For example, placing feelings as being very unsatisfied satisfied, or very satisfied makes it meaningful to assert that one person is more satisfied than another with their microwave ovens. Such an assertion reflects the first persons use of a verbal label that comes later in the list than the label chosen by the second person. However, ordinal data fail to capture the precise difference between the data. In particular, it cannot be assumed that differences between tow levels of ordinal data are the same as the differences between tow other levels. For instance, it cannot be assumed that the difference between very unsatisfied and satisfied is the same as the difference between satisfied and very satisfied. In the same way, it cannot be assumed that if rank a group of people from tallest to shortest that the difference between the tallest person in the group and second tallest person in the group is the same amount of difference between the 4 th and 5 th tallest people in the group. In other words, ordinal level data lacks a degree of specific information. a. RANK: 1st place, 2nd place,... last place b. LEVEL OF AGREEMENT: No, Maybe, Yes c. POLITICAL ORIENTATION: Left, Center, Right d. RATING of ATTRACTIVENESS on a scale of 1 to 10 e. RACE RESULTS which racers came in 1 st, 2 nd, 3 rd, etc (actual times or intervals may be widely different) f. HEIGHT: Group of people in order from Shortest to Tallest g. T I Night Dawn Morning Noon Afternoon Evening Ordinal period of the day - indicates direction or order of occurrence; spacing between is uneven

2 3. Interval Interval scales provide information about order, and also possess equal intervals. From the previous example, if we knew that the distance between 1 and 2 was the same as that between 7 and 8 on our 10- point rating scale, then we would have an interval scale. An example of an interval scale is temperature, either measured on a Fahrenheit or Celsius scale. A degree represents the same underlying amount of heat, regardless of where it occurs on the scale. Measured in Fahrenheit units, the difference between a temperature of 46 and 42 is the same as the difference between 72 and 68. Equal- interval scales of measurement can be devised for opinions and attitudes. However, constructing them involves an understanding of mathematical and statistical principles beyond those covered in this course. But it is important to understand the different levels of measurement when using and interpreting scales. a. TIME OF DAY on a 12- hour clock b. POLITICAL ORIENTATION: Score on standardized scale of political orientation c. OTHER scales constructed so as to possess equal intervals d. HEIGHT of a person(s) in centimeters or Inches e. TIME of day on a 12 hour clock Interval example is time of day - equal intervals; analog (12- hr.) clock, difference between 1 and 2 pm is same as difference between 11 and 12 am 4. Ratio The ratio scale of measurement is the most informative level of measurement. It really just an interval measurement with the additional property that its zero position indicates the absence of the quantity being measured. You can think of a ratio scale as the three earlier scales rolled up in one. Like a nominal scale, it provides a name or category for each object (the numbers serve as labels). Like an ordinal scale, the objects are ordered (in terms of the ordering of the numbers). Like an interval scale, the same difference at two places on the scale has the same meaning. And in addition, the same ratio at two places on the scale also carries the same meaning. In other words, In addition to possessing the qualities of nominal, ordinal, and interval scales, a ratio scale has an absolute zero (a point where none of the quality being measured exists). Using a ratio scale permits comparisons such as being twice as high, or one- half as much. Reaction time (how long it takes to respond to a signal of some sort) uses a ratio scale of measurement - - time. Although an individual's reaction time is always greater than zero, we conceptualize a zero point in time, and can state that a response of 24 milliseconds is twice as fast as a response time of 48 milliseconds. In memory experiments, the dependent variable is often the number of items correctly recalled. What scale of measurement is this? You could reasonably argue that it is a ratio scale. First, there is a true zero point: some subjects may get no items correct at all. Moreover, a difference of one represents a difference of one item recalled across the entire scale. It is certainly valid to say that someone who recalled 12 items recalled twice as many items as someone who recalled only 6 items. However, these words must be roughly the same level of difficulty. Other Examples a. RULER: inches or centimeters b. YEARS of work experience c. INCOME: Money earned last year d. MEMORY number of correctly remembered items from a LIST of words (if equal difficulty) e. GPA: Grade point average f. NUMBER of children a couple has Ratio A 24- hr. time format has an absolute 0 (midnight); 14 o'clock is twice as long from midnight as 7 o'clock

3 ADDITIONAL NOTES The level of measurement for a particular variable is defined by the highest category that it achieves. For example, categorizing someone as extroverted (outgoing) or introverted (shy) is nominal. If we categorize people 1 = shy, 2 = neither shy nor outgoing, 3 = outgoing, then we have an ordinal level of measurement. If we use a standardized measure of shyness (and there are such inventories), we would probably assume the shyness variable meets the standards of an interval level of measurement. As to whether or not we might have a ratio scale of shyness, although we might be able to measure zero shyness, it would be difficult to devise a scale where we would be comfortable talking about someone's being 3 times as shy as someone else. Measurement at the interval or ratio level is desirable because we can use the more powerful statistical procedures available for Means and Standard Deviations. To have this advantage, often ordinal data are treated as though they were interval; for example, subjective ratings scales (1 = terrible, 2= poor, 3 = fair, 4 = good, 5 = excellent). The scale probably does not meet the requirement of equal intervals - - we don't know that the difference between 2 (poor) and 3 (fair) is the same as the difference between 4 (good) and 5 (excellent). In order to take advantage of more powerful statistical techniques, researchers often assume that the intervals are equal.

4 Application Questions: State the highest appropriate level of measurement 1. Year in college: Freshman Sophomore Junior Senior 2. Number of student questions asked during class 3. Categories on a likert type scale 4. A person s position on the issue of Capital Punishment or Abortion 5. The types of bicycles in a shop e) Nominal f) Ordinal g) Interval h) Ratio 6. Military titles- - Lieutenant, Captain, Major, Colonel. 7. Kinds of clothing: hat, shirt, shoes, pants STRONGLY DISAGREE DISAGREE NEUTRAL AGREE STRONGLY AGREE Support Oppose Not Sure Mountain Touring Road Recumbent Hybrid Lieutenant Captain Major Colonel Hat Shirt Shoes Pants

5 8. A score on a 5- point quiz measuring knowledge of algebra is an example of a(n) 9. City of birth is an example of a(n) 10. Number of shapes remembered on a test of memory out of 10 possible