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MEASUREMENT

This lecture discusses the different types of variables (nominal, ordinal, interval, and ratio) and the concepts of reliability and validity in research. It explains the process of assigning numbers to represent variable properties and the rules for numbering. The lecture also explores the levels of measurement and provides examples of each type of variable. The importance of maintaining consistency between the abstract set and the variable-specific set is emphasized. Finally, the lecture discusses the unequal interval distances in interval variables and the absence of a true zero point.

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MEASUREMENT

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  1. MEASUREMENT Nominal, Ordinal, Interval and Ratio variables and the concepts of Reliability and Validity

  2. This lecture is brought to you by: The letter Can you say Research?

  3. What is a variable? • Any characteristic that can take on more than one form or value. Something that can, and does, vary. • Variables are what are measured. • They represent the properties of an object that we are interested in measuring. • What is measurement?

  4. What is measurement? • Conceptualization or conceptual definition. • Assigning numbers to represent the (often hidden) values or properties of a variable. • Linking a concept (idea) to a measure (technique) to make it empirically observable.

  5. There are two systems for numbering: • The abstract set • Variable specific characteristics

  6. The abstract set • Has formal rules and procedures. • Forms the subject of mathematics.

  7. Variable specific set • Represents the properties of the variable being measured. • Specifically it represents the differences in value that a variable can take: • A,B,C,D and F represent the values of a grading system and the relationships between values: • Outstanding work ; Very good to excellent work; Adequate work ;Passing work that is minimally adequate, Failing work that is clearly inadequate and unworthy of credit.

  8. The challenge is • To merge the rules that govern the abstract set with those that govern the variable specific set, without violating the principles of either. • If A=4; B=3; C=2; D=1; and F=0is an A four times as good as a D?

  9. Abstract numbers have properties • Identity • each number has particular meaning, and the categories are discrete. • Magnitude (order) • there is an inherent order from large to small • Interval • the difference between 7 and 8 is the same increment as between 194 and 195 • A true zero • There is a true (real) absence of the property.

  10. Not all numbers are equal!! • Stevens (1946) classified variables into four levels. • These are referred to as level of measurement, or levels of data. • Nominal • Ordinal • Interval • Ratio

  11. Nominal variables • The least like “real” numbers. • The only property they have is identity or name (nominal=name). • Numbers if used are simply codes for the real names of the properties.

  12. Nominal Which recreational activities do you participate in? (Please circle the number of all that apply) 1 HIKING 2 FISHING 3 PICNICKING 4 BOATING 5 SWIMMING

  13. Nominal Which recreational activities do you participate in? (Please list the activities in the spaces below) 1__Baking brownies_________ 2__Underwater Ping-pong_____ 3__Cow tipping_____________ 4__Reading Statistics books____

  14. Four people ran in the race • We know their names! Earl Greg Mike Matt

  15. Ordinal variables • Have identity • Have magnitude (order). A>B>C>D. • We know relative order. • We DO NOT know how much better A was relative to B. • Consider two races in which we know the order of finish (ranks).

  16. Earl=1 Greg=2 Mike=3 Matt=4 KC=1 Sarah=2 Liza=3 Marci=4 Ordinal variables Can we say who was fastest overall? Was Marci, who was slowest in her race, faster or slower than Greg, who was second in his race?

  17. Four people ran in the race 1 We know the order they finished in 2 3 4 Earl Greg Mike Matt

  18. Ordinal Which recreational activities are most important to you? (In the spaces below please write in the names of the three most important activities selected form the list below) MOST IMPORTANT ACTIVITY ____________ 2nd MOST IMPORTANT ACTIVITY _____________ 3rd MOST IMPORTANT ACTIVITY __________

  19. Ordinal The interval, or distance between numbers is unequal and unknown: IdahoMNNDRANK Skiing AxeThrow AxeThrow 1 Rugby Skiing Rugby 2 Opera Opera Skiing 3 AxeThrow Rugby Opera 4 What is most popular overall?

  20. Ordinal The interval, or distance between numbers is unequal and unknown: “AVERAGE Rank”“overall” RANK Skiing 2.0 1 AxeThrow 2.3 2 Rugby 2.7 3 Opera 3.3 4

  21. Interval variables • Have identity and magnitude. • Also have known distance between values. • Form a true scale, but without a zero point. • Temperature: • Is August 31, at 100F twice as hot as September 18 at 50F? • There is a true zero, isn’t there??

  22. Four people ran in the race We know how far apart they finished, but when did they START? 3:15pm 3:21pm 3:22pm 4:19pm Earl Greg Mike Matt

  23. Four people ran in the race We know how far apart they finished, but when did they START? 3:15pm 3:21pm 3:22pm 4:19pm Earl is 1:04 faster than Matt Earl Greg Mike Matt

  24. Interval What is your current age? (Please check the letter that best matches your age) A. 11-15 B. 16-20 C. 21-25 D. 26-30 C. 31-35 . . . . . . .etc.

  25. Interval How important are each of the following activities to you? How important is each activity to you? ACTIVITY(Please circle one response for each activity) 1. HIKING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT 2. FISHINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT 3. PICNICKINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT 4. BOATINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT 5. SWIMMINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANT IMPORTANT IMPORTANT IMPORTANT

  26. Wondering where /what is the interval here? • Pause to talk about the Bass et al. handout on magnitude estimation ….. • Bass, B. M., Cascio, W. F. & O'Connor, E. J. (1974). Magnitude estimations of expressions of frequency and amount. Journal of Applied Psychology, 59(3), 310-320. • TheLILAC /LAVENDERsheet 

  27. Interval How important are each of the following activities to you? How important is each activity to you? ACTIVITY(Please circle one response for each activity) 1. HIKING EXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANTIMPORTANTIMPORTANTIMPORTANT 2. FISHINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANTIMPORTANTIMPORTANTIMPORTANT 3. PICNICKINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANTIMPORTANTIMPORTANTIMPORTANT 4. BOATINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANTIMPORTANTIMPORTANTIMPORTANT 5. SWIMMINGEXTREMELY QUITE MODERATELY SOMEWHAT NOT VERY IMPORTANT IMPORTANTIMPORTANTIMPORTANTIMPORTANT From Table 2: ~48 ~36 ~24 ~12 ~0 Interval = 12 “semantic units” (units of meaning)

  28. Ratio Variables • Have identity, magnitude and interval. • And since they have a true zero, they can be expressed as ratios of each other. • They are true numbers. • All mathematical properties apply. • The represent score data.

  29. Four people ran in the race 1:45 The race started at 1:30 P.M. 1:51 1:52 2:49 Greg Mike Matt Earl

  30. Four people ran in the race 1:45 The race started at 1:30 P.M. 1:51 1:52 2:49 Earl is 58.23% faster than Matt Greg Mike Matt Earl

  31. Ratio How much time did you spend participating in each of these activities? (Please write in the number of hours for each activity in the spaces below) I SPENT ______ HOURS HIKING I SPENT ______ HOURS FISHING I SPENT ______ HOURS PICNICKING I SPENT ______ HOURS BOATING I SPENT ______ HOURS SWIMMING

  32. Reliability and Validity • Reliability = dependability; consistency; repeatability • Validity = accuracy; truthfulness; the degree of match between the construct or the way it is conceptualized or defined) and a measure of the concept. How well an idea fits reality.

  33. Reliability • Repeated use of the measure with identical subjects yields identical and consistent results. It is improved by: • Clear conceptualization • Precise measurement • Multiple indicators • Pilot-testing

  34. Validity • Specifically, measurement validity • Measures are valid for a single purpose • Three types of validity: • Face—as judged by others or by logic • Content—captures the entire meaning of the experience • Criterion—agrees with a validates, reliable external source: • Concurrent, agrees with a preexisting measure • Predictive, agrees with a future behavior or outcome

  35. Validity • Internal Validity– design and measurement concerns that reduces chances for internal errors. • External Validity– describes our ability and intent to generalize to subjects beyond our study sample. Largely an issue of design and sampling.

  36. Validity and Reliability Reliable, NOT valid Valid, NOT Reliable Valid AND Reliable NOT Valid, NOT Reliable

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