Scaling

Nominal scales

• allow us to place an object in one and only one of a set of mutually exclusive classes with no implied ordering.

• For example, a car’s registration plate is an example of nominally scaled data.

• The numbers assigned do not actually reflect the amount of the attribute possessed by the object under scrutiny

Ordinal scales: possess order

• involve ranking. This means we can say that an object has more or less or the same amount of an attribute as some other object.

• There is an implied ordered sequence so that the option listed first is less or greater than the object listed second and subsequently.

• Indicates relative position, not the magnitude of the differences between the objects

• Used to measure relative attitudes, opinions, perceptions and preferences.

interval scale: possess order, distance

• reflects how much more one object has of an attribute than another object.

• It is possible to tell how far apart two or more objects are with respect to the attribute.

• Interval data have order and distance properties and the most frequent type of measure of central tendency is the arithmetic mean.

• interval data do not allow comparisons of the absolute magnitude of the measurements to be made across objects.

• We cannot say that an object assigned the number 6 has twice as much of the characteristic being measured as the object assigned the number 3.

Ratio scales: possess order, distance, unique origin (zero point)

• possess the same kind of properties as interval-scaled data but also possess an absolute or natural origin.

• Thus, we can say that the number 6 has twice the characteristic being measured as the object assigned the number 3 on a ratio scale.

Scale types

Comparative scalingNon comparative scaling

Comparative scaling

• The respondent is asked to compare one set of objects against another.

• For eg., a respondent might be required to compare one brand of butter against the other brands that they consider when making a purchase in a supermarket.

• Results have to be interpreted in relative terms and have ordinal or rank order properties.

• The scores obtained indicate that one brand is preferred to another, but not by how much.

• Methods: Paired comparisons, Rank order scale, Constant sum scale

Paired comparisons

• The respondent is presented with two objects at a time and is required to indicate a preference for one of the two according to some stated criterion.

• The method yields ordinal scaled data, for example, brand A is better than brand B, or, brand A is cleaner than brand B and so on.

• It is often applied in cases where the objects are physical products.

• The ordinal data can be readily converted into interval-scaled data.

Rank order scale

• In this case, respondents are presented with several objects simultaneously and required to order or rank them.

Constant sum scale

• Respondents are asked to allocate a number of points – say, for instance, 100 points – among objects according to some criterion, for example, preference or importance.

• They are instructed to allocate the points such that if they like brand A twice as much as brand B, they should assign brand A twice as many points.

Non comparative scaling

• In non-comparative scaling respondents are required to evaluate each object independently of other objects being investigated.

• The respondent is not instructed to compare the object of interest either against another object or some specified criteria.

• In rating an object, the respondent assigns the rating based on whatever criteria are appropriate for that individual.

• In assigning a rating, each respondent must use some criteria of their own: it is not provided by the researcher.

Non comparative scaling methods

• Line marking/Continuous rating scale• Itemized rating scale– Scale has a number or brief description associated with

each category– Categories are ordered in terms of scale position and the

respondents are required to select the category that best describes the object being ranked

– Likert scale– Semantic differential scale– Staple scale

Line marking/Continuous (graphic) rating scale

• Can be used in a non-comparative format. • In this case the respondent is required to assign

a rating by placing a mark at the appropriate position on a line, usually five inches long, that best describes the subject under study.

• No standard for comparison is given. • The resulting scores are usually analyzed as

interval data.

• measures attitudes and comprise statements with which the respondent has to agree or disagree.

• a series of statements is provided and interviewees are required to rate each statement on the basis of the strength of their personal feeling towards it.

• The numbers assigned to the responses are numerical values associated with each possible answer.

• When analyzing the results, the signs of these numbers are reversed when a statement is unfavorable.

(or SUMMATED SCALE)

The staple scale technique differs from the semantic differential because it uses just one term and asks the respondent to describe how well that term describes the subject. Circling +5 means that the respondent agrees very strongly that the term is an appropriate description, while circling −4 indicates the reverse. The scores for each respondent can be summed and compared with the total scores of other respondents.

Select a plus number for words that you think describe the restaurant accurately. The more accurate you think the description is, the larger should be the plus number selected. Conversely, select a minus number for words that do not describe the restaurant. The less accurate you believe the description to be, the larger should be the minus number you select.

Semantic differential• The scale consists of a number of bipolar

adjectival phrases and statements that could be used to describe the objectives being evaluated

• Each bipolar adjective rating scale consists of seven categories, with neither numerical labels nor category descriptions other than for the anchor categories.

• To remove any position bias, favorable/ unfavorable adjectival phrases are randomly distributed to the left/right-hand anchor positions.

• The respondent is asked to mark one of the 7categories that best describes their views about the object along the continuum implied by the bipolar object pair.

• An overall attitude score is computed by summing the responses on each adjective pair.

• Before computing the overall score, the response categories must be coded.

• Usually the categories are assigned values from 1 to 7, where 1 is assigned to the unfavorable adjectival phrase and 7 is assigned to the favorable adjectival phrase.

Not only does the scale permit such comparisons to be taken in at a glance but it also allows us to see fairly readily where more in-depth research is required.

Non comparative itemized rating scale decisions

• The greater the no. of scale categories, the finer the discrimination among stimulus objects that is possible

• In a balanced scale the no. of favorable and unfavorable categories are equal; in an unbalanced scale they are not. If the distribution of responses is likely to be skewed, an unbiased scale with more categories in direction of skewness is appropriate

• In odd scale (no of categories are odd), the middle scale position is generally designated as neutral or impartial. If neutral response is possible from atleast some of the respondents, then odd scale must be used.

Continued..

• On forced rating scale the respondents are forced to express an opinion, because a “no opinion” option is not provided.

• The nature and degree of verbal description associated with scale categories varies considerably (verbal, numerical, pictoral description) and can have an effect on the responses. Used to remove ambiguity.

• Physical form or configuration: scales can be presented vertically or horizontally. Categories can be expressed by boxes, unique lines or boxes on a continuum and may or may not have numbers assigned to them. Numerical values may be +/- or both.

Reliability• Reliability can be defined as the extent to which measures

are free from random error, XR. If XR = 0, the measure is perfectly reliable.

• In test-retest reliability, respondents are administered identical sets of scale items at two different times and the degree of similarity between the two measurements is determined.

• In alternative-forms reliability, two equivalent forms of the scale are constructed and the same respondents are measured at two different times, with a different form being used each time.

Reliability

• Internal consistency reliability determines the extent to which different parts of a summated scale are consistent in what they indicate about the characteristic being measured.

• In split-half reliability, the items on the scale are divided into two halves and the resulting half scores are correlated.

• The coefficient alpha, or Cronbach's alpha, is the average of all possible split-half coefficients resulting from different ways of splitting the scale items. This coefficient varies from 0 to 1, and a value of 0.6 or less generally indicates unsatisfactory internal consistency reliability.

Validity

• The validity of a scale may be defined as the extent to which differences in observed scale scores reflect true differences among objects on the characteristic being measured, rather than systematic or random error. Perfect validity requires that there be no measurement error (XO = XT, XR = 0, XS = 0).

• Content validity is a subjective but systematic evaluation of how well the content of a scale represents the measurement task at hand.

• Criterion validity reflects whether a scale performs as expected in relation to other variables selected (criterion variables) as meaningful criteria.

Validity• Construct validity addresses the question of what construct

or characteristic the scale is, in fact, measuring. Construct validity includes convergent, discriminant, and nomological validity.

• Convergent validity is the extent to which the scale correlates positively with other measures of the same construct.

• Discriminant validity is the extent to which a measure does not correlate with other constructs from which it is supposed to differ.

• Nomological validity is the extent to which the scale correlates in theoretically predicted ways with measures of different but related constructs.

Relationship Between Reliability and Validity

• If a measure is perfectly valid, it is also perfectly reliable. In this case XO = XT, XR = 0, and XS = 0.

• If a measure is unreliable, it cannot be perfectly valid, since at a minimum XO = XT + XR. Furthermore, systematic error may also be present, i.e., XS≠0. Thus, unreliability implies invalidity.

• If a measure is perfectly reliable, it may or may not be perfectly valid, because systematic error may still be present (XO = XT + XS).

• Reliability is a necessary, but not sufficient, condition for validity.