1. @ 2012 Wadsworth, Cengage Learning Chapter 5 Description of Behavior Through Numerical Representation @ 2012 Wadsworth, Cengage Learning

2. Topics 1.Measurement 2.Scales of Measurement 3.Measurement and Statistics 4.Pictorial Description of Frequency Information 5.Descriptive Statistics

3. @ 2012 Wadsworth, Cengage Learning Topics (cont’d.) 6.Pictorial Presentations of Numerical Data 7.Transforming Data 8.Standard Scores 9.Measure of Association

4. @ 2012 Wadsworth, Cengage Learning Measurement

5. @ 2012 Wadsworth, Cengage Learning Measurement “What can we measure?” “What do the measurements mean?” Four properties: – Identity – Magnitude – Equal intervals – Absolute zero

6. @ 2012 Wadsworth, Cengage Learning Scales of Measurement

7. @ 2012 Wadsworth, Cengage Learning Scales of Measurement Nominal measurement – Occurs when people are placed into different categories – Example: classify research participants as men or women – Differences between categories are of kind

8. @ 2012 Wadsworth, Cengage Learning Scales of Measurement (cont’d.) Ordinal measurement – A single continuum underlies a particular classification system – Example: pop-music charts – Represents some degree of quantitative difference – Transforms information expressed in one form to that expressed in another

9. @ 2012 Wadsworth, Cengage Learning Scales of Measurement (cont’d.) Interval measurement – Requires that: Scale values are related by a single underlying quantitative dimension There are equal intervals between consecutive scale values – Example: household thermometer

10. @ 2012 Wadsworth, Cengage Learning Scales of Measurement (cont’d.) Ratio measurement – Requires that: Scores are related by a single quantitative dimension Scores are separated by equal intervals There is an absolute zero – Example: weight, length Scales of measurement are related to: – How a particular concept is being measured – The questions being asked

11. @ 2012 Wadsworth, Cengage Learning Measurement and Statistics

12. @ 2012 Wadsworth, Cengage Learning Measurement and Statistics No statistical reason exists for limiting a particular scale of measurement to a particular statistical procedure Your statistics do not know and do not care where your numbers come from

13. @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information

14. @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information Table 5.2

15. @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information (cont’d.) Figure 5.1 Bar graph of dream data

16. @ 2012 Wadsworth, Cengage Learning Pictorial Description of Frequency Information (cont’d.) Figure 5.2 Frequency polygon of dream data

17. @ 2012 Wadsworth, Cengage Learning Figure 5.3 Four types of frequency distributions: (a) normal, (b) bimodal, (c) positively skewed, and (d) negatively skewed

18. @ 2012 Wadsworth, Cengage Learning Descriptive Statistics

19. @ 2012 Wadsworth, Cengage Learning Measures of Central Tendency Mean – Arithmetic average of a set of scores Median – List scores in order of magnitude; the median is the middle score or – In the case of an even number of scores, the score halfway between the two middle scores Mode – Most frequently occurring score

20. @ 2012 Wadsworth, Cengage Learning Figure 5.4 Mean, median, and mode of (a) a normal distribution and (b) a skewed distribution

21. @ 2012 Wadsworth, Cengage Learning Measures of Variability Attempts to indicate how spread out the scores are Range: reflects the difference between the largest and smallest scores in a set of data Variance: average of the squared deviations from the mean To determine variance: – First calculate the sum of squares (SS)

22. @ 2012 Wadsworth, Cengage Learning Measures of Variability (cont’d.) Deviation method: sum of squares is equal to the sum of the squared deviation scores Second way to calculate the sum of squares: computational formula

23. @ 2012 Wadsworth, Cengage Learning Measures of Variability (cont’d.) Formula for variance: Square root of the variance: standard deviation (SD)

24. @ 2012 Wadsworth, Cengage Learning Pictorial Presentations of Numerical Data

25. @ 2012 Wadsworth, Cengage Learning Pictorial Presentation of Numerical Data Figure 5.6 Effects of room temperature on response rates in rats

26. @ 2012 Wadsworth, Cengage Learning Pictorial Presentation of Numerical Data (cont’d.) Figure 5.7 Effects of different forms of therapy

27. @ 2012 Wadsworth, Cengage Learning Transforming Data

28. @ 2012 Wadsworth, Cengage Learning Transforming Data Transformations are important – Used to compare data collected using one scale with those collected using another A statement is meaningful if: – The truth or falsity of the statement remains unchanged when one scale is replaced by another

29. @ 2012 Wadsworth, Cengage Learning Standard Scores

30. @ 2012 Wadsworth, Cengage Learning Standard Scores Formula for z score: Two important characteristics of the z score: – If we were to transform a set of data to z scores, the mean of these scores would equal 0 – The standard deviation of this set of z scores would equal 1

31. @ 2012 Wadsworth, Cengage Learning Measure of Association

32. @ 2012 Wadsworth, Cengage Learning Figure 5.10 Scatter diagrams showing various relationships that differ in degree and direction

33. @ 2012 Wadsworth, Cengage Learning Measure of Association (cont’d.) Formula for the Pearson product moment correlation coefficient (r): Correlations: – Have to do with associations between two measures – Tell nothing about the causal relationship between the two variables

34. @ 2012 Wadsworth, Cengage Learning Measure of Association (cont’d.) When you square the correlation coefficient (r 2 ) and multiply this number by 100 – You have the amount of the variance in one measure due to the other measure Regression: – Mathematical way to use data – Estimates how well we can predict that a change in one variable will lead to a change in another variable

35. @ 2012 Wadsworth, Cengage Learning Summary Three important measures of central tendency are the mean, median, and mode Some scores may be transformed from one scale to another Variability, or dispersion, is related to how spread out a set of scores is A correlation aids us in understanding how two sets of scores are related