Introductory Statistics Options, Spring 2008 Stat 100: MWF, 11:00 Science Center C. Stat 100: MWF, 11:00 Science Center C. –General intro to statistical methods in social and political science, public health and economics. –Text: Introduction to the Practice of Statistics Stat 101: MWF, 3:00 Science Center A Stat 101: MWF, 3:00 Science Center A –Similar to 100, but emphasis on applications and statistical reasoning in psychology and related disciplines. –Text: Statistics for Psychology Stat 104: MWF, 11:00 Science Center D Stat 104: MWF, 11:00 Science Center D –Similar to Stat 100, but with emphasis on applications to economics. Slightly faster pace than 100 and 104 –Same text as 100

Topic for Today: Measurement Basic Definitions Basic Definitions Four Types of Scales – Nominal, Ordinal, Ratio and Interval Four Types of Scales – Nominal, Ordinal, Ratio and Interval Item Scales versus Aggregate Scales Item Scales versus Aggregate Scales Domains, Psychometric Scales and Instruments Domains, Psychometric Scales and Instruments Example Items and Instruments Example Items and Instruments Characteristics of Good Items Characteristics of Good Items Instrument Development Components Instrument Development Components Summary Summary

Definition of Terms Variable Variable –A concept or entity of interest on which variability exists –Has no more than one value per subject –Numeric representation of value Sample Sample –Set of observations used in analysis –Subset of the population Population Population –Entire set of relevant observations –Findings with sample are used to generalize to population What is the Harvard Student Body? What is the Harvard Student Body?

Scales :Nominal Nominal scales allow for only qualitative classification. That is, they can be measured only in terms of whether the individual items belong to some distinctively different categories, but we cannot quantify or even rank order those categories. For example, all we can say is that 2 individuals are different in terms of variable A (e.g., they are of different race), but we cannot say which one "has more" of the quality represented by the variable. Typical examples of nominal variables are gender, race, color, city, etc. A nominal variable is a variable that consists of values from a nominal scale.

Scales :Ordinal Ordinal scales allow us to rank order the items we measure in terms of which has less and which has more of the quality represented by the variable, but still they do not allow us to say "how much more." A typical example of an ordinal variable is the socioeconomic status of families. For example, we know that upper-middle is higher than middle but we cannot say that it is, for example, 18% higher. Also this very distinction between nominal, ordinal, and interval scales itself represents a good example of an ordinal variable. For example, we can say that nominal measurement provides less information than ordinal measurement, but we cannot say "how much less" or how this difference compares to the difference between ordinal and interval scales. A nominal variable is a variable that consists of values from a nominal scale.

Scales: Interval Interval scales allow us not only to rank order the items that are measured, but also to quantify and compare the sizes of differences between them. For example, temperature, as measured in degrees Fahrenheit or Celsius, constitutes an interval scale. We can say that a temperature of 40 degrees is higher than a temperature of 30 degrees, and that an increase from 20 to 40 degrees is twice as much as an increase from 30 to 40 degrees.

Scales: Ratio Ratio scales are very similar to interval variables; in addition to all the properties of interval variables, they feature an identifiable absolute zero point, thus they allow for statements such as x is two times more than y. Typical examples of ratio scales are measures of time or space. For example, as the Kelvin temperature scale is a ratio scale, not only can we say that a temperature of 200 degrees is higher than one of 100 degrees, we can correctly state that it is twice as high. Interval scales do not have the ratio property. Most statistical data analysis procedures do not distinguish between the interval and ratio properties of the measurement scales.

Summary of Scales NominalOrdinalIntervalRatio People or objects with the same scale value are the same on some attribute. The values of the scale have no 'numeric' meaning in the way that you usually think about numbers. People or objects with a higher scale value have more of some attribute. The intervals between adjacent scale values are indeterminate. Scale assignment is by the property of "greater than," "equal to," or "less than." Intervals between adjacent scale values are equal with respect the attribute being measured. E.g., the difference between 8 and 9 is the same as the difference between 76 and 77. There is a rationale zero point for the scale. Ratios are equivalent, e.g., the ratio of 2 to 1 is the same as the ratio of 8 to 4.

Item Scales vs Aggregate Scales Every single question on ANY instrument or survey can be classified as being a nominal, ordinal, interval or ratio scale Every single question on ANY instrument or survey can be classified as being a nominal, ordinal, interval or ratio scale In psychometrics, when we talk about a scale we are usually referring to a collection of questions that are combined to create a single score. That score ALSO can be classified into one of the four scale categories. In psychometrics, when we talk about a scale we are usually referring to a collection of questions that are combined to create a single score. That score ALSO can be classified into one of the four scale categories. A PSYCHOMETRIC SCALE usually consists of a collection of questions that are substantively or thematically related to one another – it can be psychological in nature or be called a psychometric scale because it uses a particular scale development approach that we will be talking about A PSYCHOMETRIC SCALE usually consists of a collection of questions that are substantively or thematically related to one another – it can be psychological in nature or be called a psychometric scale because it uses a particular scale development approach that we will be talking about The substance or theme that is that basis of a psychometric scale is often referred to as a DOMAIN The substance or theme that is that basis of a psychometric scale is often referred to as a DOMAIN An INSTRUMENT is usually a collection of items representing a constellation of Domains – possibly related, possibly complementary in character An INSTRUMENT is usually a collection of items representing a constellation of Domains – possibly related, possibly complementary in character

Let’s take a look at some instruments and identify the item scales (question) and think about possible domains into which these items can be classified.

SF-36 Health Survey Person helping to complete this form: ________________________________________________________________ Person helping to complete this form: ________________________________________________________________ 1. In general, would you say your health is: 1. In general, would you say your health is: Excellent Excellent Very good Very good Good Good Fair Fair Poor Poor 2. Compared to one year ago, how would you rate your health in general now? 2. Compared to one year ago, how would you rate your health in general now? Much better now than a year ago Much better now than a year ago Somewhat better now than a year ago Somewhat better now than a year ago About the same as one year ago About the same as one year ago Somewhat worse now than one year ago Somewhat worse now than one year ago Much worse now than one year ago Much worse now than one year ago 3. The following items are about activities you might do during a typical day. Does your health now limit you in these 3. The following items are about activities you might do during a typical day. Does your health now limit you in these activities? If so, how much? activities? If so, how much? a. Vigorous activities, such as running, lifting heavy objects, participating in strenuous sports. a. Vigorous activities, such as running, lifting heavy objects, participating in strenuous sports. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all.

b. Moderate activities, such as moving a table, pushing a vacuum cleaner, bowling, or playing golf? Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. c. Lifting or carrying groceries. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. d. Climbing several flights of stairs. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. e. Climbing one flight of stairs. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. f. Bending, kneeling or stooping. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all.

g. Walking more than one mile. g. Walking more than one mile. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. h. Walking several blocks. h. Walking several blocks. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. i. Walking one block. i. Walking one block. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. j. Bathing or dressing yourself. j. Bathing or dressing yourself. Yes, limited a lot. Yes, limited a lot. Yes, limited a little. Yes, limited a little. No, not limited at all. No, not limited at all. 4. During the past 4 weeks, have you had any of the following problems with your work or other regular daily activities as a 4. During the past 4 weeks, have you had any of the following problems with your work or other regular daily activities as a result of your physical health? result of your physical health? a. Cut down the amount of time you spent on work or other activities? a. Cut down the amount of time you spent on work or other activities? Yes Yes No No b. Accomplished less than you would like? b. Accomplished less than you would like? Yes Yes No No c. Were limited in the kind of work or other activities c. Were limited in the kind of work or other activities Yes Yes No No d. Had difficulty performing the work or other activities (for example, it took extra time) d. Had difficulty performing the work or other activities (for example, it took extra time) Yes Yes No No

5. During the past 4 weeks, have you had any of the following problems with your work or other regular daily activities as a result of any emotional problems (such as feeling depressed or anxious)? a. Cut down the amount of time you spent on work or other activities? Yes Yes No No b. Accomplished less than you would like Yes Yes No No c. Didn't do work or other activities as carefully as usual Yes Yes No No 6. During the past 4 weeks, to what extent has your physical health or emotional problems interfered with your normal social activities with family, friends, neighbors, or groups? Not at all Not at all Slightly Slightly Moderately Moderately Quite a bit Quite a bit Extremely Extremely 7. How much bodily pain have you had during the past 4 weeks? Not at all Not at all Slightly Slightly Moderately Moderately Quite a bit Quite a bit Extremely Extremely

8. During the past 4 weeks, how much did pain interfere with your normal work (including both work outside the home and housework)? Not at all Not at all Slightly Slightly Moderately Moderately Quite a bit Quite a bit Extremely Extremely 9. These questions are about how you feel and how things have been with you during the past 4 weeks. For each question, please give the one answer that comes closest to the way you have been feeling. How much of the time during the past 4 weeks. a. did you feel full of pep? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time b. have you been a very nervous person? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time

c. have you felt so down in the dumps nothing could cheer you up? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time d. have you felt calm and peaceful? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time e. did you have a lot of energy? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time

f. have you felt downhearted and blue? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time g. did you feel worn out? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time h. have you been a happy person? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time i. did you feel tired? All of the time All of the time Most of the time Most of the time A good bit of the time A good bit of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time

10. During the past 4 weeks, how much of the time has your physical health or emotional problems interfered with your social activities (like visiting friends, relatives, etc.)? social activities (like visiting friends, relatives, etc.)? All of the time All of the time Most of the time Most of the time Some of the time Some of the time A little of the time A little of the time None of the time None of the time 11. How TRUE or FALSE is each of the following statements for you? a. I seem to get sick a little easier than other people Definitely true Definitely true Mostly true Mostly true Don't know Don't know Mostly false Mostly false Definitely false Definitely false b. I am as healthy as anybody I know Definitely true Definitely true Mostly true Mostly true Don't know Don't know Mostly false Mostly false Definitely false Definitely false c. I expect my health to get worse Definitely true Definitely true Mostly true Mostly true Don't know Don't know Mostly false Mostly false Definitely false Definitely false d. My health is excellent Definitely true Definitely true Mostly true Mostly true Don't know Don't know Mostly false Mostly false Definitely false Definitely false

Questions What item scales are being used here? What item scales are being used here? Without looking back – what time frame was provided for the basis of the questions? Without looking back – what time frame was provided for the basis of the questions? How would you describe the language used in the questions? How would you describe the language used in the questions? What domains do you think are contained in this set of items? How many domains do you think the instrument contains? What domains do you think are contained in this set of items? How many domains do you think the instrument contains?

Questions –some possible answers What item scales are being used here? What item scales are being used here? –Ordinal? Interval? LIKERT! Without looking back – what time frame was provided for the basis of the questions? Without looking back – what time frame was provided for the basis of the questions? Four weeks. How would you describe the language used in the questions? Simple, colloquial, “slang”, brief, common vocabulary, combination of negatively framed and positively framed questions…. How would you describe the language used in the questions? Simple, colloquial, “slang”, brief, common vocabulary, combination of negatively framed and positively framed questions….

Questions – published answer What domains do you think are contained in this set of items? How many domains do you think the instrument contains? What domains do you think are contained in this set of items? How many domains do you think the instrument contains? The SF-36 is a multipurpose, 36-item survey that measures eight domains of health: physical functioning, role limitations due to physical health, bodily pain, general health perceptions, vitality, social functioning, role limitations due to emotional problems, and mental health. It yields scale scores for each of these eight health domains, and two summary measures of physical and mental health: the Physical Component Summary (PCS) and Mental Component Summary (MCS). SF 36 is a generic health-related quality of life instrument- other kinds? Disease specific, population specific, utility-oriented….

Characteristics of Good Items Cover domains of interest as a collection Cover domains of interest as a collection Clear Clear Brief Brief Simple vocabulary Simple vocabulary Unambiguous Unambiguous Culturally appropriate Culturally appropriate Well anchored scale Well anchored scale Capture variability in populations of interest Capture variability in populations of interest

Instrument Development Components Conceptual and Measurement Model Conceptual and Measurement Model Reliability Reliability Validity – statistical, construct, concurrent, predictive…. Validity – statistical, construct, concurrent, predictive…. Responsiveness Responsiveness Interpretability Interpretability Respondent and administrative burden Respondent and administrative burden Alternate forms Alternate forms Cultural and language adaptations Cultural and language adaptations

Reliability and Validity Reliability and Validity – are statistical tools used to make sure that when a psychological or attitudinal instrument is constructed 1) the collection of items proposed measures the construct consistently and in a way that can be replicated and 2) that various relationships exist with between the new instrument and established measures to assure that the instrument in measuring what it is hoped to measure.

Today’s Summary Basic Definitions Basic Definitions Four Types of Scales – Nominal, Ordinal, Ratio and Interval Four Types of Scales – Nominal, Ordinal, Ratio and Interval Item Scales versus Aggregate Scales Item Scales versus Aggregate Scales Domains, Psychometric Scales and Instruments Domains, Psychometric Scales and Instruments Example Items and Instruments Example Items and Instruments Characteristics of Good Items Characteristics of Good Items Instrument Development Components Instrument Development Components