Scale (social sciences)

Scale construction decisions

• What level of data is involved ?
• What will the results be used for?
• Should you use a scale, index, or typology?
• What types of statistical analysis would be useful?
• Should you use a comparative scale or a noncomparative scale?
• How many scale divisions or categories should be used ?
• Should there be an odd or even number of divisions?
• What should the nature and descriptiveness of the scale labels be?
• What should the physical form or layout of the scale be?
• Should a response be forced or be left optional?

  Scale construction method

1. Begin by generating at least ten items to represent each of the scales. Administer the survey; the more representative and larger your sample, the more confidence you will have in your scales.
2. Review the means and standard deviations for your items, dropping any items with skewed means or very low variance.
3. Run a principal components analysis with oblique rotation on your items and the other items for scales it will be important to differentiate from your own. Request components with eigenvalues greater than 1. It is easier if you group the items by targeted scales. The more distinct the other items, the better your chances your items will load only on your own scale.
4. “Cleanly loaded items” are those that load at least.40 on one component and more than.10 greater on that component than on any others. Identify those.
5. “Cross loaded items” are those that do not meet the above criterion. These are candidates to drop.
6. Identify components with only a few items that do not represent clear concepts, these are “uninterpretable scales.” Also identify any components with only one item. These components and their items are candidates to drop.
7. Look at the candidates to drop and the components to be dropped. Is there anything that needs to be retained because it is critical to your construct ? For example, if a conceptually important item only cross loads on a component to be dropped, it is good to keep it for the next round.
8. Drop the items, and rerun asking the program to give you only the number of components after dropping the uninterpretable and single-item ones. Go through the process again starting at Step 3.
9. Keep running through the process until you get “clean factors”.
10. Run the Alpha program. Any scales with insufficient Alphas should be dropped and the process repeated from Step 3.
11. For better practices, keep the final components and all loadings of yours and similar scales selected to be used in the Appendix of your scale.

    Data types

1. Some data are measured at the nominal level. That is, any numbers used are mere labels; they express no mathematical properties. Examples are SKU inventory codes and UPC bar codes.
2. Some data are measured at the ordinal level. Numbers indicate the relative position of items, but not the magnitude of difference. An example is a preference ranking.
3. Some data are measured at the interval level. Numbers indicate the magnitude of difference between items, but there is no absolute zero point. Examples are attitude scales and opinion scales.
4. Some data are measured at the ratio level. Numbers indicate magnitude of difference and there is a fixed zero point. Ratios can be calculated. Examples include: age, income, price, costs, sales revenue, sales volume, and market share.

   Composite measures

Comparative and non comparative scaling

Comparative scaling techniques

• Pairwise comparison scale – a respondent is presented with two items at a time and asked to select one. This is an ordinal level technique when a measurement model is not applied. Krus and Kennedy elaborated the paired comparison scaling within their domain-referenced model. The Bradley–Terry–Luce model can be applied in order to derive measurements provided the data derived from paired comparisons possess an appropriate structure. Thurstone's Law of comparative judgment can also be applied in such contexts.
• Rasch model scaling – respondents interact with items and comparisons are inferred between items from the responses to obtain scale values. Respondents are subsequently also scaled based on their responses to items given the item scale values. The Rasch model has a close relation to the BTL model.
• Rank-ordering – a respondent is presented with several items simultaneously and asked to rank them. This is an ordinal level technique.
• Bogardus social distance scale – measures the degree to which a person is willing to associate with a class or type of people. It asks how willing the respondent is to make various associations. The results are reduced to a single score on a scale. There are also non-comparative versions of this scale.
• Q-Sort – Up to 140 items are sorted into groups based on rank-order procedure.
• Guttman scale – This is a procedure to determine whether a set of items can be rank-ordered on a unidimensional scale. It utilizes the intensity structure among several indicators of a given variable. Statements are listed in order of importance. The rating is scaled by summing all responses until the first negative response in the list. The Guttman scale is related to Rasch measurement; specifically, Rasch models bring the Guttman approach within a probabilistic framework.
• Constant sum scale – a respondent is given a constant sum of money, script, credits, or points and asked to allocate these to various items. This is an ordinal level technique.
• Magnitude estimation scale – In a psychophysics procedure invented by S. S. Stevens people simply assign numbers to the dimension of judgment. The geometric mean of those numbers usually produces a power law with a characteristic exponent. In cross-modality matching instead of assigning numbers, people manipulate another dimension, such as loudness or brightness to match the items. Typically the exponent of the psychometric function can be predicted from the magnitude estimation exponents of each dimension.

  Non-comparative scaling techniques

• Visual analogue scale – respondents rate items by placing a mark on a line. The line is usually labeled at each end. There are sometimes a series of numbers, called scale points, under the line. Scoring and codification is difficult for paper-and-pencil scales, but not for computerized and Internet-based visual analogue scales.
• Likert scale – Respondents are asked to indicate the amount of agreement or disagreement on a five- to nine-point response scale. The same format is used for multiple questions. It is the combination of these questions that forms the Likert scale. This categorical scaling procedure can easily be extended to a magnitude estimation procedure that uses the full scale of numbers rather than verbal categories.
• Phrase completion scales – Respondents are asked to complete a phrase on an 11-point response scale in which 0 represents the absence of the theoretical construct and 10 represents the theorized maximum amount of the construct being measured. The same basic format is used for multiple questions.
• Semantic differential scale – Respondents are asked to rate on a 7-point scale an item on various attributes. Each attribute requires a scale with bipolar terminal labels.
• Stapel scale – This is a unipolar ten-point rating scale. It ranges from +5 to −5 and has no neutral zero point.
• Thurstone scale – This is a scaling technique that incorporates the intensity structure among indicators.
• Mathematically derived scale – Researchers infer respondents’ evaluations mathematically. Two examples are multi dimensional scaling and conjoint analysis.

  Scale evaluation