Unit 1: Measurement Scales

MEASUREMENT SCALES:

Scale is the continuum having graded series of numerical values. It has start and end points. Start and end points are determined by researcher. The changes in the scale are graded series, therefore, it is systematic in nature. It has numerical values so it can be used for measurement. Example is thermometer, weight machine. Scaling follows principles of maximization and minimization. Maximization principle asserts wide variation of response categories like five or seven point response scales. To understand extent of happiness, researcher can use five point response scales like very happy, happy, undecided, less happy and least happy. Sometimes, respondent can not make discrimination between very happy and happy due to low intelligence, depression etc. In this case, researcher can minimize number of response categories like happy and unhappy. Depending on characteristics of respondent, researcher selects specific measurement scale out of four. These are nominal, ordinal, interval and ratio scales. Instruction, response pattern and scoring procedure vary with types of measurement scales.

4.3.1 Nominal Scale:

It is a system of assigning number symbols for labeling. Researcher uses this scale for classification following three principles -minimization, equality and discrimination.

Minimization : Response categories are smaller. These are usually 2 or 3. For example, in the Eysenck Personality Questionnaire or EPQ, response categories are three - yes, no, don't know.

Discrimination: Assigned numbers should make adequate discrimination between the labels. In EPQ, Items measuring psychoticism do not overlap with items measuring neuroticism. Non-overlapping enhances good discrimination power of the questionnaire. Discrimination principle asserts unequal identity or dissimilar properties in the object or event.

Equality: In Nominal Scale, only rule for assigning numbers is that all members of any class shall have the same number and that no two classes shall be assigned the same numbers. This rule accepts principles of equality. Equality principle asserts that each object or event must have same identity. For example, girls with different heights have common property, i.e. they all are girls. Therefore all girl respondents are assigned ‘2’.

 INSTRUCTION: Instruction of nominal scale includes how to label the response. For example, put tick mark over 1 if you are boy and over 2 if you are girl. ITEM STEM: Item stem asks for label. Examples: a) Are you boy or girl? Boy=1, Girl=2. b) What is your religion? Hindu=1, Islam=2, Christian=3. c) What is your Caste? S.T=1, S.C=2, O.B.C=3, General=4. STATISTICS: Frequency and percentage are common descriptive statistics. Chi-square can be used for drawing inferences. Variables with nominal scale can be used as explanatory or independent variables in t-statistics. By adding frequency of similar response, score can be computed. For example, there are 20 items in the questionnaire, out of them 10 items with 'yes' response measure neuroticism. The questionnaire has been administered to patient suffering from General anxiety disorder. It is noted all the 10 items receive 'yes' response. So the score is 10. Extent of score variation indicates extent of neuroticism. Based on score, distance in traits between individuals can be possible but not between the nominal categories. Distance between Yes, No categories of two items can not be determined.

Advantages: a) Nominal scale is useful for classification or categorization. b) It is more flexible. According to hypothesis, numerical values can be assigned. c) Nominal scale is used as explanatory variable.

Disadvantages: a) Nominal scale has no metric properties therefore many parametric statistics requiring continuous distribution can not be determined through nominal scale. b) It requires different statistical conversation techniques to make it continuous.

4.3.2 Ordinal Scale: Nominal scale can not order the events. It can label the event but can not estimate successive occurrence of events. Ordinal Scale assigns numerals or rank value following principles of successive categories. These principles make discrimination among the set of objects in terms of preference. A set of students can be ordered in terms of academic performance. A set of sportsmen can be ordered in terms of sports performance. Order can be made in the form of ascending like first, second, third or descending order like third, second and first. When two students get same marks, their orders will be same. It is called paired order or tied. Tied orders are averaged and next order occurs after the last order. For example, 3 events possess equal ranks say 3. Then each event will get 3, 4, 5 ranks and the average will be 4. Next event will start from 6. Ordinal scale does not assume equal distance between orders. Distance between 1st and 2nd is not equal to distance between 3rd and 4th. This is the disadvantage of the ordinal scale. Advantage of the ordinal scale is it's flexibility. One can follow both ascending and descending orders.

Instruction: Instruction of ordinal scale includes how to arrange the events in ascending or descending order.

Item stem : Item stem includes the issue or event and it's operational definition.

Statistics : When data are arranged in order, frequency, percentage statistics are used like nominal scale. One can estimate which event has received first or second rank by analysis of frequency. One can use median when data are arranged with rank values. Most of the non-parametric statistics follow ordinal scale or ranks. Rank order cosrrelation is widely used statistics when one is interested to determine coefficient of correlation in small sample distribution.

Advantages: a) Ordinal scale is useful to arrange the objects in ascending or descending order. b) Median value can be estimated through ordinal scale. c) Relative preference of the object can be determined with ordinal scale. d) Several non-parametric statistics use ordinal scale.

Disadvantages a) Like, nominal scale, it has limited use in statistics as it does not follow equidistant. b) It can not be scored.

4.3.3. Interval Scale: In ordinal scale one can not make any subtraction or addition to classify the person, object or event. For example, second rank student can not be subtracted from first rank student to find out difference in performance between two ranked persons. Another problem in rank order scale, equidistance assumption can not be made. We can not assume rank difference between 1 and 2 is equal to same between 2 and 3. But interval scale assumes equidistant points between each of the scale elements. The widely used summated rating scale or Likert type rating scale is interval scale. It has properties of metric scale in terms of the extent of differences in response. It is assumed that response difference is equidistant. Some researchers call it as quassi continuous scale as middle response category appears to be neutral. Some researchers argue that this is categorical scale as they merely consider the numerical values. Therefore, we can interpret differences in the distance along the scale. We contrast this to an ordinal scale where we can only talk about differences in order, not differences in the degree of order. Any parametric statistics are useful to analyze the item data.

 Instruction: Instruction of ordinal scale includes how to rank. But interval scale includes how to rate the response categories. Interval scale follows maximization principles. Response categories are more and equidistant. Numerals are assigned to different ratings. Widely used ratings are strongly agree, agree, undecided, disagree and strongly disagree.

Item-stem : It can be both affirmative and interrogative. To assess one's happiness, item stem may be how much happy are you ? Or I feel happy always. It must be remembered that response categories should not be in the item stem. In earlier example on 'I feel happy always', response categories should not include the text 'always' rather it can be strongly agree, agree, disagree, strongly disagree. Item stem and response categories will be framed in such a manner so that data distribution will not be skewed.

Statistics: Interval scale follows equidistant principles, so any parametric statistics can be used.

Advantages: a) Interval scale follows equidistant principles, so any parametric statistics can be used. b) It can be scored. c) it can be classified into groups by cut-off points.

Disadvantages: a) Interval scale has undecided point. This violates continuity. b) It does not have neutral point like ratio scale.

4.3.4. Ratio scale: Interval scale measures single dimension of variable across graded series. One's feeling of both happiness and unhappiness can be assessed by interval scale using two separate scales measuring happiness and unhappiness separately. Advantage of ratio scale is to assess both feeling of happiness and unhappiness simultaneously. For example, watching black cloud, farmers sometimes feel pleasant and sometimes feel unpleasant. Ratio scale is composed of two bi-polar adjectives. One adjective will be extremely opposite of another. For example, strong and weak, good and bad, active and lazy. This scale is often called as semantic differential scale as meaning of object or event is differentiated semantically with opposite adjectives. As per hypothesis, rating value is assigned to the adjective. Strong, good and active are assigned +3 and weak, bad and lazy are given -3 rating. So two opposite adjectives are located at two opposite poles of neutral point or 0. Other grades like -1,-2 are located between 0 and -3. Similarly, +1 and +2 are located between 0 and 3. So, final scale to assess strong and weak dimension will be +3, +2, +1, 0,-1,-2,-3. So, there are two interval scales ranging from +1 to +3 and from -1 to -3. Respondent assumes +3 as very strong, +2 as strong. Likewise, -3 as very weak, -2 as weak. And 0 is conceived as neutral. Here zero stands for neither more nor less than none of the property represented by the scale.

 Instruction: Instruction includes systematic rating from 0 to -3 or from 0 to +3. As there is no label from 0 to +3 or from 0 to -3, respondent can assign own label following direction of adjectives. For example, instead of very strong, respondent can think of very much strong. Item-stem Scoring: Before scoring, researcher first assumes meaning of high score. For example, +3 is highest score and -3 is lowest. Then +3 will be replaced by 7 and -3 will be replaced by 1. 0 will be replaced by 4. So, highest score will be 7 and lowest score will be 1.

 Statistics: Like interval scale, any parametric and non-parametric statistics can be used with ratio scale.

Advantages: a) Ratio scale can assess one object with bi-polar adjectives simultaneously. b) Like normal probability curve, ratio scale assumes bi-polarity. It has zero like normal probability distribution. And the successive gradation from 0 to +3 or -3 is equidistant. Therefore, it can be used in any parametric statistics. c) It is less time consuming for data collection. d) It can assess different dimensions of one object simultaneously. Osgood has noted three opposite dimensions using ratio scale.

Disadvantages: a)Theoretically, one can not say that attributes of satisfaction are opposite of dissatisfaction. Herzberg has proved that attributes of job satisfaction is not opposite of the same for assessing job dissatisfaction. Therefore, use of bi-polar adjectives for assessing one event can not provide sufficient information. b) It is complex to score as rating values during data collection are replaced by another value during scoring. c) No event can be neutral, therefore considering 0 value as neutral is not meaningful.