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

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

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

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

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

Variable specific set Represents the properties of the variable being measured. Represents the properties of the variable being measured. Specifically it represents the differences in value that a variable can take: 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: 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. 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.

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. 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=0 is an A four times as good as a D? If A=4; B=3; C=2; D=1; and F=0 is an A four times as good as a D?

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

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

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

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

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 ____

Four people ran in the race We know their names! We know their names! EarlGregMikeMatt

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

Ordinal variables Earl=1Greg=2Mike=3Matt=4KC=1Sarah=2Liza=3Marci=4 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?

Four people ran in the race EarlGregMikeMatt We know the order they finished in

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 ____________ 2 nd MOST IMPORTANT ACTIVITY_____________ 3 rd MOST IMPORTANT ACTIVITY __________

Ordinal The interval, or distance between numbers is unequal and unknown: IdahoMNNDRANK SkiingAxeThrowAxeThrow1 RugbySkiingRugby2 OperaOperaSkiing3 AxeThrowRugbyOpera4 What is most popular overall?

Ordinal The interval, or distance between numbers is unequal and unknown: “AVERAGE Rank” “overall” RANK Skiing2.01 AxeThrow 2.32 Rugby 2.73 Opera 3.34

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

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

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

Interval What is your current age? (Please check the letter that best matches your age) A B C D C etc.

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 EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 2. FISHING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 3. PICNICKING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 4. BOATING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 5. SWIMMING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT

Wondering where /what is the interval here? Pause to talk about the Bass et al. handout on magnitude estimation ….. 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), 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), The LILAC /LAVENDER sheet The LILAC /LAVENDER sheet

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 EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 2. FISHING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 3. PICNICKING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 4. BOATING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT 5. SWIMMING EXTREMELYQUITEMODERATELY SOMEWHATNOT VERY IMPORTANTIMPORTANTIMPORTANTIMPORTANTIMPORTANT From Table 2: ~48 ~36 ~24~12 ~0 Interval = 12 “semantic units” (units of meaning)

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

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

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

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

Reliability and Validity Reliability = dependability; consistency; repeatability 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. 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.

Reliability Repeated use of the measure with identical subjects yields identical and consistent results. It is improved by: 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

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

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

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