1. Basic concepts in measurement Basic concepts in measurement Believe nothing, no matter where you read it, or who said it, unless it agrees with your own reason, knowledge, experience, and your own common sense. (adapted Sutra) Dr Niko Tiliopoulos Room 448, Brennan McCallum building Email: nikot@psych.usyd.edu.au

2. Defining psychological measurement The process of assigning numbers (e.g. psychometric test scores) to persons, in such a way that some attributes of the persons being measured are faithfully reflected by some properties of these numbers The process of assigning numbers (e.g. psychometric test scores) to persons, in such a way that some attributes of the persons being measured are faithfully reflected by some properties of these numbers Assumptions & limitations Assumptions & limitations It cannot measure the whole person It cannot measure the whole person It assesses (or should assess) a single psychological element It assesses (or should assess) a single psychological element Individual differences exist and are real (Concepts vs. Constructs) Individual differences exist and are real (Concepts vs. Constructs) Individual differences can be represented by numbers in similar (but NOT identical) ways to physical differences/properties (e.g. what is neuroticism squared?) Individual differences can be represented by numbers in similar (but NOT identical) ways to physical differences/properties (e.g. what is neuroticism squared?) Individual differences (though not necessarily the actual attributes) possess a relative, either or both temporal and spatial (situational), stability Individual differences (though not necessarily the actual attributes) possess a relative, either or both temporal and spatial (situational), stability

3. A film NOIR: Levels of measurement & scale types I Scale: A set of scores on a test (e.g. IQ scales) Scale: A set of scores on a test (e.g. IQ scales) Nominal (categorical) scales Nominal (categorical) scales An attribute is nominated an arbitrary numerical value An attribute is nominated an arbitrary numerical value E.g. E.g. Dichotomous scales: Dichotomous scales: Do you tend to conform to social norms & rules? Do you tend to conform to social norms & rules? No (0) – Yes (1) (– I don’t know) Polytomous scales: Polytomous scales: Which of the following best describes your internet activities? Which of the following best describes your internet activities? I mainly use the internet for recreational purposes (1) I mainly use the internet for recreational purposes (1) I mainly use the internet to seek information (2) I mainly use the internet to seek information (2) I mainly use the internet for communication (3) I mainly use the internet for communication (3) I mainly use the internet for adult material (4) I mainly use the internet for adult material (4)

4. Levels of measurement & scale types II Ordinal (categorical) scales Ordinal (categorical) scales An attribute is rank-ordered and a numerical value is assigned to each rank An attribute is rank-ordered and a numerical value is assigned to each rank The distances between the ranks are meaningless The distances between the ranks are meaningless E.g. 1 st vs. 2 nd vs. 3 rd E.g. 1 st vs. 2 nd vs. 3 rd Ordinal scales can be: Ordinal scales can be: Balanced = have a neutral scale-point in the middle of the scale Balanced = have a neutral scale-point in the middle of the scale Unbalanced = either not have a neutral point or that point is not in the middle of the scale Unbalanced = either not have a neutral point or that point is not in the middle of the scale

5. Levels of measurement & scale types III Common types of ordinal scales used in ID (1) Common types of ordinal scales used in ID (1) Social-distance scales Social-distance scales E.g. I would willingly admit members of the following races E.g. I would willingly admit members of the following races Rating scales Rating scales E.g. How important to you is your attractiveness to other people? E.g. How important to you is your attractiveness to other people? 1 = Not at all important 1 = Not at all important 2 = Slightly important 2 = Slightly important 3 = Rather important 3 = Rather important 4 = Extremely important 4 = Extremely important To my family To my friends As neighbours As citizens in my country As visitors to my country African12345 Asian12345 Caucasian12345

6. Levels of measurement & scale types IV Common types of ordinal scales used in ID (2) Common types of ordinal scales used in ID (2) Likert scales (5-point balanced scales) Likert scales (5-point balanced scales) Probably the most commonly used scales in ID Probably the most commonly used scales in ID Likert items (e.g. questions in a questionnaire) have ordinal properties. However, scored sets of such items tend to generate true numerical indexes of the measured attributes Likert items (e.g. questions in a questionnaire) have ordinal properties. However, scored sets of such items tend to generate true numerical indexes of the measured attributes E.g. I believe that UFOs exist E.g. I believe that UFOs exist 1 = Strongly Disagree 1 = Strongly Disagree 2 = Disagree 2 = Disagree 3 = Not sure / indifferent / Don’t know 3 = Not sure / indifferent / Don’t know 4 = Agree 4 = Agree 5 = Strongly Agree 5 = Strongly Agree Any scales that follow this format but possess other than 5-points is called Likert-like scale Any scales that follow this format but possess other than 5-points is called Likert-like scale For statistical purposes, any ordinal scale that possesses more than 7-points is treated as a true numerical scale For statistical purposes, any ordinal scale that possesses more than 7-points is treated as a true numerical scale

7. Levels of measurement & scale types V Interval (numerical) scales Interval (numerical) scales An attribute is placed on a scale in which the scale points (intervals) have equal distances An attribute is placed on a scale in which the scale points (intervals) have equal distances Not common in ID Not common in ID IQ and some mental abilities scores may to be perceived as points on interval scales (however, not everyone agrees with this) IQ and some mental abilities scores may to be perceived as points on interval scales (however, not everyone agrees with this) Ratio (numerical) scales Ratio (numerical) scales Ratios between numbers assigned to a person correspond to ratios between the measured attribute in that person Ratios between numbers assigned to a person correspond to ratios between the measured attribute in that person Common in psychosomatic assessment (e.g. reaction times) Common in psychosomatic assessment (e.g. reaction times) Some (but not me) would argue that ratio scales should possess a true zero score Some (but not me) would argue that ratio scales should possess a true zero score

8. Scale transformations Why transform? Why transform? Often the raw scores are not sufficient for response comparisons: Often the raw scores are not sufficient for response comparisons: Results obtained from different scales that measure the same attribute Results obtained from different scales that measure the same attribute Generation of population norms (normative scores) Generation of population norms (normative scores) Standardisation of scales Standardisation of scales The following are the most common transformations used in ID: The following are the most common transformations used in ID: z-scores z-scores T-scores T-scores Area transformations (quartiles, deciles, percentiles) Area transformations (quartiles, deciles, percentiles) Stanines (standard nines) Stanines (standard nines)

10. There is approx. a 34% chance that an individual will have an IQ score between 85-100 There is approx. a 2% chance that an individual will be 2 SDs over the mean IQ (i.e. will have a z-score of +2) A T-score is a transformation of a z-score [T = (z * 10) + 50] (mean= 50, SD = 10) A z-score expresses raw scores in SD units Stanines transform the scores into an 1-9 point scale (mean = 5, SD = 2) Individuals whose IQ scores fall in the 1 st & 2 nd stanine have problems with mental retardation Individuals who fall above the 90 th percentile tend to possess some “interesting” attributes

11. Scale norms Norms are standardised scores (e.g. T- scores) that are assumed to indicate the behaviour (distribution) of an attribute in a particular (normative) group or population Norms are standardised scores (e.g. T- scores) that are assumed to indicate the behaviour (distribution) of an attribute in a particular (normative) group or population What is their use? What is their use? Records of population attributes Records of population attributes Compare an individual’s attributes with them (norm-based interpretations) Compare an individual’s attributes with them (norm-based interpretations) Construct new measurements Construct new measurements

13. Cautions for using norms Sampling limitations Sampling limitations Sample size limitations Sample size limitations Sample type limitations Sample type limitations Distribution assumptions Distribution assumptions Relative temporal (in)stability Relative temporal (in)stability

14. Main Reading Murphy, K. et al. (2010). PSYC2014: Personality & Intelligence I (3 rd ed.). Frenchs Forest: Pearson Australia(Chapters 4 & 5: “Basic concepts in measurement and statistics” & “Scales, transformations, and norms”, pp. 22-65) Murphy, K. et al. (2010). PSYC2014: Personality & Intelligence I (3 rd ed.). Frenchs Forest: Pearson Australia(Chapters 4 & 5: “Basic concepts in measurement and statistics” & “Scales, transformations, and norms”, pp. 22-65) Recommended: Recommended: Familiarise yourself with the research methods content of PSYC1001 & PSYC1002 Familiarise yourself with the research methods content of PSYC1001 & PSYC1002 Optional: Optional: Coombs, C.H. (1960). A theory of data. Psychological Review, 67, 143-159. Coombs, C.H. (1960). A theory of data. Psychological Review, 67, 143-159. Stevens, S.S. (1946). On the theory of scales of measurement. Science, 103, 677–680. Stevens, S.S. (1946). On the theory of scales of measurement. Science, 103, 677–680.