Since numbers involve counting, we must understand the nature of the measurement process before we can collect data and count. When we describe and analyze library or information problems, we inevitably use numbers and quantities. Normally, we do this by classifying and grouping to reduce the diversity of human thought and behavior into a manageable form. Note that words such as "usually," "often," "few," "several," and "many" refer to quantitative concepts. In our research, we will not use vague quantitative terms, but will substitute real number or a range of numbers.
Some aspects of human behavior are easier to measure than others. For example, it is easier to measure the income of a librarian than the happiness derived from spending it.
There is an important and strong relationship between the statistical measures used to analyze data and the nature of the numbers used to capture variables and values.
We measure variables through their values. For example, the sex variable has two values: male and female.
All values must be mutually exclusive.
Your computer and any software that you may use will not know if your variables and values use the appropriate numbers. Statistical software will easily produce convincing by wholly inappropriate results. For example, you may use 1 for female and 2 for male. If you tell it to, the software will compute a mean value for the sex value even though it makes no sense at all. It is your responsibility to insure that you know what kind of numbers you will be using. The statistical tests used must match the level of measurement appropriate for each of your variables. If in doubt, assume that your variables are at the lowest level [nominal]. Much useful information will be lost when you do this, but your results will not be erroneous.
Data may be classed as nominal, ordinal, or interval-ratio. These classes ascend in power and are cumulative, i.e. the higher classes include the attributes of the lower ones. Different statistical tests are used for each class.
Some research methods texts distinguish between quantitative and qualitative variables. Quantitative variables use real numbers. Examples might include the temperature in Celsius, salary in dollars, and the number of votes a candidate receives. These are real numbers and ordinary arithmetic operations apply.
Qualitative numbers use numbers as labels. These numbers cannot be used for arithmetic operations and other characters could easily replace them. Examples might include 1 for males, 2 for community college libraries, and the DDC schedules.
Nominal values represent the lowest level of qualitative variable. These values are verbal rather than quantitative. The average associated with nominal values is the mode or the value that occurs most frequently. The number of character used is arbitrary and others could easily be substituted. The order of the characters has no meaning since the characters selected to represent the values are arbitrary. Categories are mutually exclusive and exhaustive, but there is no known relationship between them. Two examples:
If you decide to impose an order, then the value will become ordinal. For example, if your values are unemployed librarian, part-time employed, and full-time employed.
This is the highest level of measurement for qualitative variables. Ordinal measures are based on rank -- greater than or less than --and that allows comparison. The order is important, but the numbers themselves have no particular meaning other than to establish rank. Other numbers could be used as long as the ranking remains the same. The intervals between the numbers have no meaning and the numbers themselves have no absolute qualities. An example would be: rank the library services below with 1 being most useful and 5 being least useful. Grading on the A - F scale is another good example of ordinal values and illustrates that letters can work as well as numbers. We know that an A is better than a B+, but not exactly how much better. In contrast, if an A = 93 and a B+ = 89 then we know how much better one is over the other. Note that we often use low numbers to represent high rankings as in the number one library school in the world.
Certain scales are associated with ordinal values. Likert scales measure the extent of agreement to statements often expressed as "strongly agree" to "strongly disagree." Values are often assigned numbers so that strongly disagree becomes one and strongly disagree becomes five or vice versa.
Statistics used with ordinal values are nonparametric. Survey research frequently uses ordinal data.
The median is the average associated with ordinal data. The median is the middle value or the mean of the two middle values if there is an even number of cases.
Here, the numbers have full arithmetic properties and mean based statistics are appropriate. Interval data has an arbitrary zero point while ratio data has a natural zero point. In practice, the distinction is usually trivial.
As with the nominal variables, values are mutually exclusive. As with the ordinal variables, values have rank. But here, values are represented by equal intervals and the size of the intervals is known. We can say by how many units this value is greater than that value.
Interval -ratio variables may have many attributes. Here, we mention discrete and continuous variables. Discrete values can take only certain numerical values, usually integers. For example, the number of periodicals held in a public library is discrete.
Continuous variables may take any numerical value and no two values will be exactly the same. Here, accuracy is limited by instrumentation. For example, when the scale says that your weight is 120 pounds, it is only an approximation since the real value might be 120.00000300000....
Parametric or mean based statistics are most powerful and allow for a much greater variety of statistical tests.
