Nature of measurement

Transcription

1 Nature of measurement Lecturer: Dr. Emmanuel Adjei; Department of Information Studies Contact Information: College of Education School of Continuing and Distance Education 2014/ /2017

2 Session Overview College of Education School of Continuing and Distance Education 2014/ /2017

3 Session Overview Without realising it, most of us spend the day engaging in various forms of measurement. We measure various types of beverages; we stir a few table spoons of Milo, coffee or other beverages in a cup of water. We also measure the quantity of salt and pepper we want in our soup and stew, and the quantity of sugar we want in our tea. We keep an eye on the clock so that we will not be late to the office or lectures. Slide 3

4 Session Overview Most of the things we measure are fairly concrete: pounds on a scale, teaspoons of coffee, the amount of gas in a gas cylinder etc. But how do we measure a person s attitude towards say alcoholic beverages? How do we know for instance the extent of subjective feelings, attitudes or perceptions that might exist in different individuals? In research unless our variables are measured we will not be able to test our hypothesis generated from the theoretical framework. To make possible the measurement of variables in quantitative or qualitative way, researchers have developed scales. Slide 4

5 Session Overview In this Section we will discuss the four scales or levels of measurement, namely, nominal, ordinal, interval and ratio. Slide 5

6 Session Objectives Objectives After completing this Session the student should be able to: 1. Define and explain measurement 2. Name and explain the four levels of measurement 3. Identify the properties or characteristics of each level or scale of measurement Slide 6

7 Session Outline The key topics to be covered in the session are as follows: 1. Topic One:Scales / Levels of Measurement 2. Topic Two: Nominal Scale / Measurement 3. Topic Three: Ordinal Scale 4. Topic Four: Interval Scale 5. Topic Five : Ratio Scale / Measurement Slide 7

8 Reading List 1. Pickard, AJ. (2007) Research Methods in Information, London, Facet Publishing. 2. Powell, RR. (2004) Basic Research Methods for Librarians, (4 th ed.) Westport, Connecticut, Libraries Unlimited. Slide 8

9 TOPIC ONE SCALES / LEVELS OF MEASUREMENT Slide 9

10 Scales / levels of measurement Defining Measurement Churchil (2001) defines measurement as rules for assigning numbers to objects in such a way as to represent quantities of attributes. It involves categorising and / or assigning values to variables. Measurement can be qualitative or quantitative. Quantitative measurement involves numerical values and attributes. Variables that can be measured in quantitative terms include temperature, IQ score, and the number of family members, age, and income. Slide 10

11 Scales / levels of measurement Qualitative measurement concentrates on names, labels and qualities. (Sarantakos,1996). In qualitative measurement common concepts or symbols are used to describe attributes. One common procedure involves describing and classifying categories. The classification of gender into male and female is qualitative measurement. Slide 11

12 Scales / levels of measurement Quantitative measurement is believed to be more accurate, valid, reliable and objective than qualitative measurement and relies mainly on quantitative techniques. The four scales or levels of measurement we shall discuss are the, nominal, ordinal, interval and ratio scales. Slide 12

13 Scales / levels of measurement Slide 13

14 TOPIC TWO NOMINAL SCALE / MEASUREMENT Slide 14

15 Nominal Scale / Measurement The nominal scale tells us only which categories objects or events fall into. The main property of the nominal scale is that of IDENTITY: It involves classifying events into categories that must be distinct, mutually excusive, and exhaustive; and the resulting scales are naming scales. Such measures indicate that there is a difference among the categories considered. (Sarantakos, 1996). Slide 15

16 Nominal Scale / Measurement Categories are mutually exclusive if each object can be placed in one and only one category, example male or female. Categories are exhaustive if every object can be placed in a category, examples of sorting pile of marbles of various colours: red, green, yellow and blue into their respective colours. Examples of variables measured on the nominal scale include gender, classified into male and female; age (young - old); marital status (single, married, divorced, separating etc.); religious affiliation (Catholic, Presbyterian, Anglican); political affiliation (NPP, NDC. DFP, etc.); ethnicity (Ashanti, Ga, Ewe, Fanti, etc.). Slide 16

17 Nominal scale / measurement Apart from categorising objects or events into discrete groups, numbers or symbols are used to identify the categories for purposes of coding or entering data into a computer. Example people can be placed in each of the following religious categories: Catholic, Presbyterian, Anglican, Pentecostal and Other We might assign numbers 1, 2, 3 4, and 5 to indicate these categories. For instance, we can label Catholic 1; Presbyterian 2; Anglican 3 and Pentecostal 4; and 5 Other for the purpose of coding information into the computer. However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaning. Assigning the number 1 to Catholic does not mean, for instance that Catholic are superior to the other demoninations. Slide 17

18 Nominal Scale / Measurement NOTE: It is typically used for variables that are qualitative rather than quantitative. It does not possess any mathematical attribute; it has no magnitude, rank, or equal interval spacing or absolute zero. It merely labels or defines discrete categories into which variables can be classified. Slide 18

19 TOPIC THREE ORDINAL SCALE Slide 19

20 Ordinal scale / measurement The important thing you should note about the ordinal scale is that it has 2 properties which are IDENTITY and MAGNITUDE. IDENTITY means we can classify into groups and categories Examples Age (youngest; young; old; older). Size (smallest; small; big; biggest). Quality (Poor; good; excellent). Income (low; middle; upper). Achievement at school (poor; moderate; high). Slide 20

21 Nominal scale / measurement MAGNITUDE means we can rank order variables in a continuum according to some order. Examples Some examples Age (youngest; young; old; older). Size (smallest; small; big; biggest). Quality (Poor; good; excellent). Income (low; middle; upper). Achievement at school (poor; moderate; high). Slide 21

22 Ordinal scale / measurement More Examples Socioeconomic status ( lower class, middle class, or upper class. A rank of 1 is assigned to upper class, 2 middle class, and 3 to lower class and so on. In this situation, the numbers have some mathematical meaning: Families in category 1 have a higher socioeconomic status than families ranked 2. It is important to note that in ordinal measurement, attributes can be rank-ordered in an ascending or descending order, but distances between attributes do not have any meaning because we do not know the relative difference between two magnitudes Slide 22

23 Ordinal scale / measurement Let s use some example to illustrate this point. Example 1. Respondents are asked to state whether or not they are satisfied with a phenomenon (eg. teaching quality) using a scale similar to the one below: Very satisfied Satisfied Neither satisfied nor dissatisfied Dissatisfied Very dissatisfied Slide 23

24 Ordinal scale / measurement The ranking of these categories from very satisfied to very dissatisfied implies a hierarchy or ordering of satisfaction. In coding responses from this type of question, the researcher may allocate numbers as follows: Very satisfied (5) Satisfied (4) Neither satisfied nor dissatisfied (3) Dissatisfied (2) Very dissatisfied (1) Slide 24

25 Ordinal scale / measurement While those categorised by 5 have a higher satisfaction than those by 4, there is no equal distance implied between the numbers. For instance those who are Satisfied ( 4) are not twice as satisfied as those who are Dissatisfied (2). Slide 25

26 Ordinal scale / measurement Another Example In a survey you might label Educational Attainment as follows: 0 = Junior High School Certificate; 1 = Senior High School Certificate; 2 = Diploma; 3 = Bachelors degree; 4 = Masters Degree; 5 = Ph.D. In this example, higher numbers mean more education but the distance from 0 to 1 is not the same as 3 to 4. The intervals between numbers have no interpretation or meaning. Slide 26

27 Ordinal Scale Another Example In an examination candidates are graded A, B, C, D, ect. according to performance. We know that A is better than B which is also better than D. But is A 4 times better than D? Is it 2 times better than D. We do not know this. Slide 27

28 TOPIC FOUR INTERVAL SCALE Slide 28

29 Interval Scale This scale has the following characteristics: Identity (Helps researcher to determine whether 2 values are the same or different Can determine whether one values is greater or smaller than the other Can also determine the degree of difference between values Contains equal interval But it has no zero point Slide 29

30 Interval Scale Example We can group students according to their IQ This means that the students have different IQs (remember that this is a nominal measurement). Slide 30

31 Interval Scale Example continued. We can also rank and order the students from the highest to the lowest (Remember that this is an ordinal measurement). So in ordinal terms the first student has a higher IQ than the second and third. Slide 31

32 Interval Scale We can also calculate the difference in IQ among the students and conclude that the IQ of the first student is 100 points higher than the second student. (This is a characteristic which the ordinal and nominal scales don t have). One other characteristic of the interval scale is that it has equal interval but has no true zero point. Slide 32

33 Interval Scale Example - Celsius temperature is an interval variable. It is meaningful to say that 25 degrees Celsius is 3 degrees hotter than 22 degrees Celsius, and that 17 degrees Celsius is the same amount hotter (3 degrees) than 14 degrees Celsius. Notice, however, that 0 degrees Celsius does not have a natural meaning. That is, 0 degrees Celsius does not mean the absence of heat! Slide 33

34 These properties of the interval scale allow the researcher to determine whether two values are the same or different (as in nominal measure); whether one value is greater or smaller than the other (as in ordinal scale); and the degree of difference between the values. (Sarantakos, 1996). Slide 34

35 Interval Scale The property of degree of difference makes addition and subtraction of values on the scale possible and allows us to make valid statements about differences between and among categories or values Slide 35

36 Interval Scale In mathematical terms, at this level of measurement, numbers assigned to categories are used to count and rank but can also be added to or subtracted from each other. This makes the interval scale superior to the nominal and ordinal scales. However, because the scale has no true zero point numbers assigned to categories cannot be multiplied or divided. Slide 36

37 Consider again the IQ two students 105 and 125. In nominal terms they have different IQ; in ordinal terms the second student has a higher IQ than the first; in interval terms the IQ of the second student is 20 points higher than the first student, but we cannot say the second student is 5 times smatter than the first. The 20 points difference does not tell us how much smatter the first student is than the second. Slide 37

38 TOPIC FIVE RATIO SCALE / MEASUREMENT Slide 38

39 Ratio scale / measurement The ratio scale has all the properties of the nominal, ordinal, and interval scale. (Categorisation, rank-order, and equal intervals). It has an important additional property: a true absolute zero point. This means the zero point on a ratio scale corresponds to a total absence of the property being measured. Height, weight and age are examples. Because there is an absolute zero, it is legitimate to compare the absolute magnitude of the numbers. Slide 39

40 Ratio scale / measurement The absolute zero point makes it possible to meaningfully multiply and divide the numbers used to measure on a ratio scale. In the social sciences this level of measurement is used mainly when measuring demographic variables but it is not appropriate for measuring attitudes and opinions. (Sarantakos,1996) The geometric mean, as well as the arithmetic mean, median and mode are a meaningful measure of average when attributes are measured on the ratio scale. Slide 40

41 Sample questions for consideration 1. Joe has an IQ score of 7.5 John has an IQ score of 150. is John twice as much as Joe?. Defend your answer. 2. Name all the four levels at which measurement occur. 3. In conducting research explain why you should pay attention to levels of measurement. 4. The left column lists four levels of measurement. The right column lists permissible operations. Match each levels of measurement with all the operations corresponding to that (Hint:) Except for the nominal level, all levels allow for more than one permissible operation Slide 41

42 Summary This session examined the four levels or scales of measurement which are the NOMINAL, ORDINAL, INTERVAL and RATIO. We learned that the main property of the nominal scale is IDENTITY. The ordinal scale has two properties (identity and magnitude) while the interval scale has the properties of identity, magnitude, and equal interval). The Ratio scale has all the properties of the others in addition a natural zero point. Slide 42

43 Summary Nominal scales--qualitative, not quantitative distinction (no absolute zero, not equal intervals, not magnitude) Ordinal scales--ranking individuals (magnitude, but not equal intervals or absolute zero) Interval scales--scales that have magnitude and equal intervals but not absolute zero Ratio scales--have magnitude, equal intervals, and absolute zero (so can compute ratios) Slide 43

44 END OF LECTURE Slide 44