Measurement and Operationalization of Variables

1. ALC 208 Week 7 - Topic 6: MEASUREMENT Assigned readings: text: Chapter 7; Reading 6.1 The Deprivation Index -See DSO

2. Before beginning to collect data: • Know what exact information is needed to answer your research questions/s or test you hypotheses. • Figure out the variables to be examined and their characteristics (e.g. Age etc.) • How to collect the necessary data for those variable characteristics. (e.g. Exact age/age group etc.) Getting started with data collection

3. Some variables can be directly observed or measured. e.g. Age, height, sex, level of edu. • Some variables can’t be directly observed or measured. e.g. Concepts such as happiness, a keen student, life satisfaction, a teen movie • So these concepts need to be defined as constructs (as to what it means) and operationalised (using operational definitions). • Thereafter, we can measure the concept as required. variables

4. The (Griffiths University) Deprivation Index Calculated as a composite measurement: • i) Level of employment (FT/PT etc) • ii) Level of annual income (as income brackets) • iii) Ethnicity (Anglo-Celtic, east Asian etc) • iv) Family composition (single person, couple, shared house) • v) Number of people living in household (adults---; kids….) • vi) Housing (own home, rented, buying, public housing etc.) • vii) Education (some HS, tech/trade cert, UG degree, PG degree • Viii) Post code of residence (e.g. 3217 for W Ponds etc.) • Note these variables are not measured the same way (eg. choose from list, write a number etc. The Construct of The Deprivation Index

5. Nominal level variables – names or labels e.g. colours of the rainbow, our names, flavours of ice cream etc. Categories must be Mutually exclusive (no over lapping: e.g. Neapolitan ice cream must have its own category as it has vanilla, strawberry, and chocolate together) & Exhaustive (all data collected must have a category to go into) e.g. Rum & raisin, Rocky road etc ) and also include an ‘other’ category for unique or stray ones. Levels of measurementNominal, ordinal, interval and ratio

6. Also names but has a rank order. E.g. low, moderate, high; Age groups below 18; 19-30; 31-50 etc.; Education (some high school; high school grad; UG, PG etc.) They too must be mutually exclusive and exhaustive Also add an ‘other’ category Ordinal level variable Measurements

7. Include categories with names, have a ranking order, can be numbers (1- 7 scales etc.). • Must be a standard distance from one another (property of equal distance) but has no true zero only an arbitrary zero. i.e. zero does not mean the variable does not exist. E.g. ENTER scores; temperatures • E.g. scale of 1 (not at all) to 7 (a lot) • Can be converted into nominal and ordinal but not vice versa. Interval Level variable measurements

8. May be names, numbers, have a rank order, vary from adjoining categories by a standard distance (e.g. Numbers 0 to 10) and in addition has a true zero where zero means the variable does not exist. e.g. Age 0 years is non-existence of a subject; income as zero etc. • Ratio variables too can be converted to nominal, ordinal, interval measures /variables by giving them suitable names etc. • Ratio and interval give flexibility for statistical analyses, as they can be converted to nominal and ordinal by not vice versa and nominal and ordinal have limited statistical tests available. Ratio variable measurements

9. Scale measurements too are used when measuring an unobservable construct. Likert Scales (summated ratings approach) is one such approach. • Collects data using interval variables • Uses a construct which has several statements/questions or ‘items’ posed to subjects • Their answers collected on a scale of 1-5; 1-7; 1-9; or even 1-100 • The figures given by a subject to each of the items or statements added and the total is taken as the measurement. • If the items are positively worded and scale is listed as 1 (lowest) to 7 (highest) etc., the higher the total, the more positive the attitude for the concept. Scales of measurement

10. 5 items on a Likert Scale of 1 to 7: 1 (strongly disagree) and 7 (strongly agree) 1. Biometric devices provide more security at an ATM than passwords or PINs. (4) 2. I am willing to use biometric identifiers online for e-commerce. (5) 3. Biometrics are a good way to keep track of employee work hours. (2) 4. Biometrics should be used for air travel security purposes. (5) 5. Biometric devices make computer log on faster. (3) Response given by a subject given within brackets at end of item. Total: 4 +5+2+5+3 = 19. Higher the total, the more positive a subject’s attitude towards biometrics is. Construct: Peoples’ attitude towards Biometric devices

11. Another type of interval scale used to measure a construct. Uses a bipolar ratings system. e.g. Bad (1) --- Good (7) at each end of continuum on a scale of 1 to 7 etc. and uses several such items to measure a given concept. e.g. Popularity of a politician etc. Semantic Differential Scales

12. The Construct measured as a composite score to 5 items for “I think politician A is” given by one subject is underlined as: • Dishonest 1 2 3 4 5 6 7 Honest • Untrustworthy 1 2 3 4 5 6 7 Trustworthy • Unlikeable 1 2 3 4 5 6 7 Likeable • Bad for the 1 2 3 4 5 6 7 Good for the economy economy • Bad for 1 2 3 4 5 6 7 Good for • National security national security Composite score is: 3+2+4+6+ 6= 21. The higher the composite score, the more positive the respondent’s attitude is. Concept: AttituDe towards a Politician

13. The same variable can sometimes be measured at all four levels. • e.g. Income: poor, low income, middle income, high income, wealthy (nominal/ordinal) • 1 (poor) ……. 5 (wealthy) (interval) • Exact figure of income / year as $54, 000- (ratio) Significance of the levels of measurement

14. 1. Need to use specific statistical tests • E.g. Central tendency of a variable (mean, median, mode) can only be calculated for some levels • Mean: Average of distribution of numbers . Only for interval and ratio. E.g. Average of a set of 9 numbers . • e.g. 0 2 2 5 6 17 18 19 67= Total is 136 • Average= 136/9= 15.1 • We cannot calculate the mean of categories such as colours of the rainbow (nominal) or levels of education (ordinal) What level of measurement to use?

15. Think of the median strip of a road • The mid point of a distribution of numbers when arranged in ascending/descending order. • Half the values fall above the median and the other half below it. • Only calculated for interval and ratio levels. • Median of an odd numbered distribution of 9 numbers: 0 2 2 5 6 17 18 19 67 = 6 (median) • Median of an even numbered distribution of 10 numbers is: 0 2 2 5 6 17 18 19 67 75 = the average of 6 + 17= 23/2= 11.5(median) median

16. The value that occurs most often in the distribution of values of the variable. • Can be calculated for all four measurements of nominal, ordinal, interval and ratio. • e.g. the flavour of ice cream sold the most that day (nominal); • The year levels of students in a class as 2 nd year – (ordinal); • Most often cited answer on a scale of 1 – 7 as 5 (interval) – no true zero; • and • Most common amount of pocket money given to kids between 10 and 12 yrs old as $10 (ratio). • Some kids get none so there is a true zero. MODE

17. Exercises: 1. Prepare lists of categories for variables that fall under the nominal, ordinal, interval and ratio levels of measurement. List at least 2 under each level. Be Creative! • 2. Taking the Billboard or ARIA top 40 list, examine how you can use those data to create variables under each of the levels of measurement (i.e. Nominal, ordinal, interval, ratio). • Hint: You can use the name of the song, singer/group; genre of music represented in the list; the list of songs in the top 10; number of weeks each song has been on the top 40 list; number of records sold / revenue the week after the figures were taken for each song on the list etc. • 3. Take a look at the Deprivation Index and its categories of variables listed on page Identify the level of measurement used in each variable (nominal, ordinal, interval and ratio). E.g. Level of employment; Level of annual income; ethnicity; family composition; number of people living in household art present; Housing; Education; Post code of residence. • Think of other levels of measurement that can be used for each of these variables. EXERCISEs (in addition to those in tutes for Stern (2005)