Scaling and measurement, Essays (university) of Abnormal Psychology

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Chapter Eight

Measurement and Scaling:

Fundamentals and

Comparative Scaling

Measurement

Measurement means assigning numbers or other symbols to characteristics of objects according to certain pre specified rules.  (^) One-to-one correspondence between the numbers and the characteristics being measured.  (^) The rules for assigning numbers should be standardized and applied uniformly.  Rules must not change over objects or time.

What is measured?



Variables is research may be

classified as objects or properties.



Objects include the concepts of

ordinary experience e.g. People,

furniture or also include abstract

things like attitude, group pressure,

etc.



Properties are characteristics of

objects. (Physical, Psychological,

Social)

Characteristics of Mapping rules



Classification



Order



Distance



Origin

7 8 3

Primary Scales of Measurement

Scale Nominal Numbers Assigned to Runners Ordinal Rank Order of Winners Interval Performance Rating on a 0 to 10 Scale Ratio Time to Finish, in Figure 8. Third place Second place First place Finish Finish 8.2 9.1 9. 15.2 14.1 13.

Primary Scales of Measurement Nominal Scale  (^) The numbers serve only as labels or tags for identifying and classifying objects.  (^) When used for identification, there is a strict one-to-one correspondence between the numbers and the objects.  (^) The numbers do not reflect the amount of the characteristic possessed by the objects.  The only permissible operation on the numbers in a nominal scale is counting.  (^) Only a limited number of statistics, all of which are based on frequency counts, are permissible, e.g., percentages, and mode.  (^) E.g. Attendance, Religion  (^) Very useful in exploratory studies when the relationships are explored.

Primary Scales of Measurement Ordinal Scale  (^) A ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic.  Can determine whether an object has more or less of a characteristic than some other object, but not how much more or less.  (^) Any series of numbers can be assigned that preserves the ordered relationships between the objects.  (^) In addition to the counting operation allowable for nominal scale data, ordinal scales permit the use of statistics based on centiles, e.g., percentile, quartile, median.  (^) E.g. Preferences, rankings

Primary Scales of Measurement Interval Scale  (^) Numerically equal distances on the scale represent equal values in the characteristic being measured.  It permits comparison of the differences between objects.  (^) The location of the zero point is not fixed. Both the zero point and the units of measurement are arbitrary. E.g. degree Celsius, Fahrenheit  (^) Statistical techniques that may be used include all of those that can be applied to nominal and ordinal data, and in addition the arithmetic mean, standard deviation, and other statistics commonly used in marketing research.

Primary Scales of Measurement

Table 8.

A Classification of Scaling

Techniques

Likert Semantic Differential Stapel Figure 8. Scaling Techniques Noncomparative Scales Comparative Scales Paired Comparison Rank Order Constant Sum Q-Sort and Other Procedure s Continuous Rating Scales Itemized Rating Scales

A Comparison of Scaling

Techniques

 Comparative scales involve the direct comparison of stimulus objects. Comparative scale data must be interpreted in relative terms and have only ordinal or rank order properties.  (^) In noncomparative scales , each object is scaled independently of the others in the stimulus set. The resulting data are generally assumed to be interval or ratio scaled.

Relative Advantages of Comparative Scales  Small differences between stimulus objects can be detected.  (^) Same known reference points for all respondents.  (^) Easily understood and can be applied.  (^) Involve fewer theoretical assumptions.  (^) Tend to reduce halo or carryover effects from one judgment to another.

Comparative Scaling Techniques Paired Comparison Scaling  A respondent is presented with two objects and asked to select one according to some criterion.  (^) The data obtained are ordinal in nature.  (^) Paired comparison scaling is the most widely used comparative scaling technique.  (^) With n brands, [n(n - 1) /2] paired comparisons are required  (^) Under the assumption of transitivity, it is possible to convert paired comparison data to a rank order.

Obtaining Shampoo Preferences Using Paired Comparisons Figure

Instructions: We are going to present you with ten pairs of shampoo brands. For each pair, please indicate which one of the two brands of shampoo you would prefer for personal use. Recording Form : J hirmack Finesse Vidal Sassoon Head & Shoulders Pert J hirmack (^0 0 1 ) Finesse 1 a (^0 1 ) Vidal Sassoon (^1 1 1 ) Head & Shoulders (^0 0 0 ) Pert 1 1 0 1 Number of Times Preferred b (^3 2 0 4 ) a A 1 in a particular box means that the brand in that column was preferred over the brand in the corresponding row. A 0 means that the row brand was preferred over the column brand. b The number of times a brand was preferred is obtained by summing the 1s in each column.