# Measurements and Scaling

The first determination in any survey design is "What is to be measured?" Although our problem statement or research question will inform us as to the concept that is to be investigated, it often does not say anything about the measurement of that concept. Let us assume we are evaluating the sales performance of group sales representatives. We could define their success in numerical terms such as dollar value of sales or unit sales volume or total passengers. We could even express it in share of sales or share of accounts lost. But we could also measure more subjective factors such as satisfaction or performance influencers.

In conclusive research, where we rely on quantitative techniques, the objective is to express in numeric terms the difference in responses. Hence, a scale is used to represent the item being measured in the spectrum of possibilities. The values assigned in the measuring process can then be manipulated according to certain mathematical rules. There are four basic types of scales which range from least to most sophisticated for statistical analysis (this order spells the French word "noir"):

# Nominal Scale

Some researchers actually question whether a nominal scale should be considered a "true" scale since it only assigns numbers for the purpose of catogorizing events, attributes or characteristics. The nominal scale does not express any values or relationships between variables. Labelling men as "1" and women as "2" (which is one of the most common ways of labelling gender for data entry purposes) does not mean women are "twice something or other" compared to men. Nor does it suggest that 1 is somehow "better" than 2 (as might be the case in competitive placement).

Consequently, the only mathematical or statistical operation that can be performed on nominal scales is a frequency run or count. We cannot determine an average, except for the mode – that number which holds the most responses - nor can we add and subtract numbers.

Much of the demographic information collected is in the form of nominal scales, for example: In nominal scale questions, it is important that the response categories must include all possible responses. In order to be exhaustive in the response categories, you might have to include a category such as "other", "uncertain" or "don’t know/can’t remember" so that respondents will not distort their information by trying to forcefit the response into the categories provided. But be sure that the categories provided are mutually exclusive, that is to say do not overlap or duplicate in any way. In the following example, you will notice that "sweets" is much more general than all the others, and therefore overlaps some of the other response categories:

Which of the following do you like: (check all that apply):

 Chocolate         o Pie                  o Cake                 o Sweets            o Cookies            o Other              o

# Ordinal Scale

When items are classified according to whether they have more or less of a characteristic, the scale used is referred to as an ordinal scale (definition of ordinal scale). The main characteristic of the ordinal scale is that the categories have a logical or ordered relationship to each other.These types of scale permit the measurement of degrees of difference, but not the specific amount of difference. This scale is very common in marketing, satisfaction and attitudinal research. Any questions that ask the respondent to rate something are using ordinal scales. For example,

How would you rate the service of our wait-staff?

 Excellent   o Very Good  o Good  o Fair  o Poor  o

Although we would know that respondent X ("very good") thought the service to be better than respondent Y ("good"), we have no idea how much better nor can we even be sure that both respondents have the same understanding of what constitutes "good service" and therefore, whether they really differ in their opinion about its quality.

Likert scales are commonly used in attitudinal measurements. This type of scale uses a five-point scale ranging from strongly agree, agree, neither agree nor disagree, disagree, strongly disagree to rate people's attitudes. Variants of the Likert-scale exist that use any number of points between three and ten, however it is best to give at least four or five choices. Be sure to include all possible responses: sometimes respondents may not have an opinion or may not know the answer, and therefore you should include a "neutral" category or the possibility to check off "undecided/uncertain", "no opinion" or "don't know".

Although some researchers treat them as an interval scale, we do not really know that the distances between answer alternatives are equal. Hence only the mode and median can be calculated, but not the mean. The range and percentile ranking can also be calculated.

# Interval Scale

Interval scales (definition of interval scale) take the notion of ranking items in order one step further, since the distance between adjacent points on the scale are equal. For instance, the Fahrenheit scale is an interval scale, since each degree is equal but there is no absolute zero point. This means that although we can add and subtract degrees (100° is 10° warmer than 90°), we cannot multiply values or create ratios (100° is not twice as warm as 50°). What is important in determining whether a scale is considered interval or not is the underlying intent regarding the equal intervals: although in an IQ scale, the intervals are not necessarily equal (e.g. the difference between 105 and 110 is not really the same as between 80 and 85), behavioural scientists are willing to assume that most of their measures are interval scales as this allows the calculation of of averages mode, median and mean, the range and standard deviation.

Although Likert scales are really ordinal scales, they are often treated as interval scales. By treating this type of agreement scale or attitudinal measurement as interval, researchers can calculate mean scores which can then be compared. For instance, the level of agreement for men was 3.5 compared to 4.1 for women, or it was 3.3 for first time visitors compared to 2.8 for repeat visitors.

# Ratio Scale

When a scale consists not only of equidistant points but also has a meaningful zero point, then we refer to it as a ratio scale. If we ask respondents their ages, the difference between any two years would always be the same, and ‘zero’ signifies the absence of age or birth. Hence, a 100-year old person is indeed twice as old as a 50-year old one. Sales figures, quantities purchased and market share are all expressed on a ratio scale.

Ratio scales should be used to gather quantitative information, and we see them perhaps most commonly when respondents are asked for their age, income, years of participation, etc. In order to respect the notion of equal distance between adjacent points on the scale, you must make each category the same size. Therefore, if your first category is \$0-\$19,999, your second category must be \$20,000-\$39,999. Obviously, categories should never overlap and categories should follow a logical order, most often increasing in size.

Ratio scales are the most sophisticated of scales, since it incorporates all the characteristics of nominal, ordinal and interval scales. As a result, a large number of descriptive calculations are applicable.