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MBA SEMESTER III MB0050 Research Methodology- 4 Credits (Book ID:B1206) Assignment Set- 1 (60 Marks) Q.1 a. Differentiate between nominal, ordinal, interval and ratio scales, with an example of each. b. What are the purposes of measurement in social science research? Answer (a): Measurement may be classified into four different levels in social research, based on the characteristics of order, distance and origin, each one adding more to the next. Thus ordinal data is also nominal and so on.1. Nominal measurement:

The name 'Nominal' comes from the Latin nomen, meaning 'name' and nominal data are items which are differentiated by a simple naming system. This level of measurement consists in assigning numerals or symbols to different categories of a variable. The only thing a nominal scale does is to say that items being measured have something in common, although this may not be described. For example; a survey is conducted to study the applicants for Driving License and one of the objective of the study is to fine out the sex-wise break-up of applicants. In this case, we may assign the number 0 to male applicant and number 1 to female applicants. Thus number may be used to label individuals, events or things.

The numerals or symbols are just labels and have no quantitative value. The numbers of cases under each category are counted. Nominal measurement is therefore the simplest level of measurement. It does not have characteristics such as order, distance or arithmetic origin.

A categorical variable, also called a nominal variable, is for mutual exclusive, but not ordered, categories. For example, a study might compare five different genotypes. We can code the five genotypes with numbers if we want, but the order is arbitrary and any calculations (for example, computing an average) would be meaningless. 2. Ordinal measurement:

In this level of measurement, persons or objects are assigned numerals which indicate ranks with respect to one or more properties, either in ascending or descending order.

Example: Individuals may be ranked according to their socio-economic class, which is measured by a combination of income, education, occupation and wealth. The individual with the highest score might be assigned rank 1, the next highest rank 2, and so on, or vice versa.

The numbers in this level of measurement indicate only rank order and not equal distance or absolute quantities. This means that the distance between ranks 1 and 2 is not necessarily equal to the distance between ranks 2 and 3.

Ordinal scales may be constructed using rank order, rating and paired comparisons. Variables that lend themselves to ordinal measurement include preferences, ratings of organizations and economic status. Statistical techniques that are commonly used to analyze ordinal scale data are the median and rank order correlation coefficients.

It is one where the order matters but not the difference between values. For example, you might ask patients to express the amount of pain they are feeling on a scale of 1 to 10. A score of 7 means more pain that a score of 5, and that is more than a

score of 3. But the difference between the 7 and the 5 may not be the same as that between 5 and 3. The values simply express an order. Another example would be movie ratings, from --- to ----. 3. Interval measurement: This level of measurement is more powerful than the nominal and ordinal levels of measurement, since it has one additional characteristic equality of distance. However, it does not have an origin or a true zero. This implies that it is not possible to multiply or divide the numbers on an interval scale. A interval variable is a measurement where the difference between two values is meaningful. The difference between a temperature of 100 degrees and 90 degrees is the same difference as between 90 degrees and 80 degrees. Example: The Centigrade or Fahrenheit temperature gauge is an example of the interval level of measurement. A temperature of 50 degrees is exactly 10 degrees hotter than 40 degrees and 10 degrees cooler than 60 degrees.

Since interval scales are more powerful than nominal or ordinal scales, they also lend themselves to more powerful statistical techniques, such as standard deviation, product moment correlation and t tests and F tests of significance.

4. Ratio measurement: This is the highest level of measurement and is appropriate when measuring characteristics which have an absolute zero point. This level of measurement has all the three characteristics order, distance and origin.

Examples : Height, weight, distance and area. Since there is a natural zero, it is possible to multiply and divide the numbers on a ratio scale. Apart from being able to use all the statistical techniques that are used with the nominal, ordinal and interval scales, techniques like the geometric mean and coefficient of variation may also be used. The main limitation of ratio measurement is that it cannot be used for characteristics such as leadership quality, happiness, satisfaction and other properties which do not have natural zero points. The different levels of measurement and their characteristics may be summed up.In the table below

Levels of measurement Nominal Ordinal Interval Ratio

Characteristics No order, distance or origin Order, but no distance or origin Both order and distance, but no origin Order, distance and origin

A ratio variable, has all the properties of an interval variable, and also has a clear definition of 0.0. When the variable equals 0.0, there is none of that variable. Variables like height, weight, enzyme activity are ratio variables. Another counter example is pH. It is not a ratio variable, as pH=0 just means 1 molar of H+. and the definition of molar is fairly arbitrary. A pH of 0.0 does not mean 'no acidity' (quite the opposite!). When working with ratio variables, but not interval variables, you can look at the ratio of two measurements. A weight of 4 grams is twice a weight of 2 grams, because weight is a ratio variable. A temperature of 100 degrees C is not twice as

hot as 50 degrees C, because temperature C is not a ratio variable. A pH of 3 is not twice as acidic as a pH of 6, because pH is not a ratio variable.

Different definitions of measurement have been offered by different authors 1. According to Stevens, measurement is the assignment of numerals to objects or events according to rules. A simple example of assignment of numerals according to a rule is described below: Suppose a survey is conducted to study the applicants of an MBA program and one of the objectives of the study is to find out the sex-wise break-up of applicants. In this case, we may assign the number 0 to male applicants and the number 1 to female applicants. Thus numbers may be used to label individuals, events or things.

2. Campbell defines measurement as the assignment of numbers to represent properties.

3. In the words of Torgerson, measurement is the assignment of numbers to objects to represent amounts or degrees of a property possessed by all of the objects.

In research, it is necessary to distinguish between objects and properties or characteristics of these objects. For example, a person is an object and his/her physical characteristics include height, weight, color, etc. while his or her psychological characteristics include intelligence and attitudes. The important point to remember is that the researcher is concerned with measuring properties and not the objects themselves. While physical properties may be directly observed, psychological properties such as intelligence are inferred. For example, a childs score in an IQ test indicates his or her level of intelligence.

b. Purposes of measurement in social science research: Measurement also has several purposes : One of the primary purposes of classifying variables according to their level or scale of measurement is to facilitate the choice of a statistical test used to analyze the data. There are certain statistical analyses which are only meaningful for data which are measured at certain measurement scales. For example, it is generally inappropriate to compute the mean for Nominal variables. Suppose you had 20 subjects, 12 of which were male, and 8 of which were female. If you assigned males a value of '1' and females a value of '2', could you compute the mean sex of subjects in your sample? It is possible to compute a mean value, but how meaningful would that be? How would you interpret a mean sex of 1.4? When you are examining a Nominal variable such as sex, it is more appropriate to compute a statistic such as a percentage (60% of the sample was male). When a research wishes to examine the relationship or association between two variables, there are also guidelines concerning which statistical tests are appropriate. For example, let's say a University administrator was interested in the relationship between student gender (a Nominal variable) and major field of study (another Nominal variable). In this case, the most appropriate measure of association between gender and major would be a Chi-Square test. Let's say our University administrator was interested in the relationship between undergraduate major and starting salary of students' first job after graduation. In this case, salary is not a Nominal variable; it is a ratio level variable. The appropriate test of association between undergraduate major and salary would be a one-way Analysis of Variance (ANOVA), to see if the mean starting salary is related to undergraduate major. Finally, suppose we were interested in the relationship between undergraduate grade point average and starting salary. In this case, both grade point average and starting salary are ratio level variables. Now, neither Chi-square nor ANOVA would be appropriate;

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