Social Science Reasoning Using Statistics

1. Social Science Reasoning Using Statistics Psychology 138 Spring 2004

2. This is our explanatory variable This is our response variable Measuring and Manipulating Variables Claim: Absence makes the heart grow fonder • What are the variablesin this claim? Theoretically speaking what are these variables?

3. So what do we mean by absence? Measuring and Manipulating Variables Claim: Absence makes the heart grow fonder Two people involved in a relationship having to spend substantial periods of time apart. How, in our study, are we going to measureabsence? The amount of time apart, the number of visits, the distance one of these or perhaps a combination

4. Measuring and Manipulating Variables Claim: Absence makes the heart grow fonder So what do we mean by heart grow fonder? • The strength of the relationship between two people • The level of desire between two people How, in our study, are we going to measurefondness of the heart? • Have the couple rate their fondness for one another • Hook each member up to brain monitor and record what their brain does when they see pictures of their sweetheart compared to pictures of other people

5. Operational definition • Specifies the relationship between the conceptual and operational levels Measuring and Manipulating Variables • Two levels of variables • Conceptual level of the variables • What the theory is about (absence, fondness) • Operational level of the variables • What is actually manipulated/measured in the research program • Duration of time apart • Rated fondness

6. Measuring and Manipulating Variables • Operational definition • Specifies the relationship between the conceptual and operational levels • It describes a set of operations or procedures for measuring a conceptual variable • It defines the variable in terms of the resulting measurements

7. Brainwave machine Survey Measurement • How do we measure a variable? • An instrument: The tool that is used to measure the dependent variable • e.g., fondness

8. Measurement • Properties of our measurement? • Units of measurement - whether the measurement has a minimum sized unit or not • Scales of measurement - the correspondence between the numbers representing the properties that we’re measuring

9. 3, or 2.5 cookies 2, 1 kid or 2 kids , but not 2.5 Units of Measurement • Continuous variables • Variables can take any number and can be infinitely broken down into smaller and smaller units • E.g., For lunch I can have • Discrete variables • Broken into a finite number of discrete categories that can’t be broken down • E.g., In my family I can have

10. Scales of measurement • Categorical variables • Nominal scale

11. brown, hazel blue, green, Scales of measurement • Nominal Scale: Consists of a set of categories that have different names. • Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations. • Example: • Eye color:

12. Scales of measurement • Categorical variables • Nominal scale • Ordinal scale

13. Small, Med, Lrg, XL, XXL Scales of measurement • Ordinal Scale: Consists of a set of categories that are organized in an ordered sequence. • Measurements on an ordinal scale rank observations in terms of size or magnitude. • Example: • T-shirt size:

14. Scales of measurement • Categorical variables • Nominal scale • Ordinal scale • Quantitative variables • Interval scale

15. Scales of measurement • Interval Scale: Consists of ordered categories where all of the categories are intervals of exactly the same size. • With an interval scale, equal differences between numbers on the scale reflect equal differences in magnitude. • Ratios of magnitudes are not meaningful. • Example: • Fahrenheit temperature scale 40º 20º “Not Twice as hot”

16. Scales of measurement • Categorical variables • Nominal scale • Ordinal scale • Quantitative variables • Interval scale • Ratio scale

17. Scales of measurement • Ratio scale: An interval scale with the additional feature of an absolute zero point. • With a ratio scale, ratios of numbers DO reflect ratios of magnitude. • It is easy to get ratio and interval scales confused • Consider the following example: Measuring your height with playing cards

18. Scales of measurement Ratio scale 8 cards high

19. Scales of measurement Interval scale 5 cards high

20. Scales of measurement Ratio scale Interval scale 8 cards high 5 cards high 0 cards high means ‘as tall as the table’ 0 cards high means ‘no height’

21. Errors in measurement • Validity • Does our measure really measure the construct? • Is there bias in our measurement? • Reliability • Do we get the same score with repeated measurements?

22. Center represents the true score Collection of ‘darts’ is a sample of measurements The center of the sample is the estimate of the true score Dart board example Dart board represents Population of all possible scores

23. Low variability/low bias Points are all close together (similar) & Centered on the target Dart board example

24. Low variability/high bias Points are all close together (similar) & NOT centered on the target Dart board example

25. High variability/low bias Points are NOT all close together (dissimilar) & Centered on the target Dart board example

26. High variability/high bias Points are NOT all close together (dissimilar) & NOT centered on the target Dart board example