1. Measures of Dispersion 9/26/2013

2. Readings Chapter 2 Measuring and Describing Variables (Pollock) (pp.37-44) Chapter 6. Foundations of Statistical Inference (128-133) (Pollock) Chapter 3 Transforming Variables (Pollock Workbook)

3. OPPORTUNITIES TO DISCUSS COURSE CONTENT

4. Office Hours For the Week When – Friday 10-12 – Monday 10-12 – And by appointment

5. Homework Chapter 2 – Question 1: A, B, C, D, E – Question 2: B, D, E (this requires a printout) – Question 3: A, B, D – Question 5: A, B, C, D – Question 7: A, B, C, D – Question 8: A, B, C

6. Course Learning Objectives 1.Students will learn the basics of research design and be able to critically analyze the advantages and disadvantages of different types of design. 2.Students Will be able to interpret and explain empirical data.

7. MEASURES OF DISPERSION

8. What are They? these measure the uniformity of the data they measure how closely or widely cases are separated on a variable.

9. The Standard Deviation A More accurate and precise measure than dispersion and clustering Is the average distance of values in a distribution from the mean

10. What it tells us When the value of the standard deviation is small, values are clustered around the mean. When the value of the standard deviation is high, values are spread far away from the mean.

11. About the Standard Deviation its based on the mean the larger the standard deviation, the more spread out the values are and the more different they are if the standard deviation =0 it means there is no variability in the scores. They are all identical.

12. From 2008 Who was more divisive?

13. The Standard Deviation It is a standardized measure…. So what? This means it has ratio ( the actual value)and ordinal properties (the number of standard deviations 0,1,2,3.. From the mean This means we can compare different means (e.g. test scores)

14. The Standard Deviation and Outliers Any case that is more than 2 standard deviations away from the mean These cases often provide valuable insights about our distribution

15. 2011 Baseball Salaries

16. How to determine the value of a standard deviation

17. The value of +/- 1 s.d. = mean + value of s.d – e.g. if the mean is 8 and the s.d is 2, the value of -1 s.d's is 6, and + 1 s.d.'s is 10 The value of +/- 2 s.d. = mean + (value of s.d. *2) – e.g. if the mean is 8 and the s.d is 2, the value of -2 s.d's is 4, and + 2 s.d.'s is 12 Any value in the distribution lower than 4 and higher than 12 is an outlier

18. ECU POL Sci

19. An Example from 2008 States Database What is the Value of +/- 1 S.D?. (mean+ 1.s.d) What is the Value of +/-2 S.D? (mean +/- 2 s.d)

20. Unwrapping The Results Which are Outliers How did that shape the 2012 campaign

21. THE NORMAL CURVE

22. Different Kinds of Distributions

23. Rectangular

24. Camel Humps Dromedary (one hump)Bactrian (bi-modal)

25. The Normal/Bell Shaped curve Symmetrical around the mean It has 1 hump, it is located in the middle, so the mean, median, and mode are all the same!

26. Why we use the normal curve To determine skewness The Normal Distribution curve is the basis for hypothesis/significance testing

27. SKEWNESS

28. What is skewness? an asymmetrical distribution. Skewness is also a measure of symmetry, Most often, the median is used as a measure of central tendency when data sets are skewed.

29. How to describe skewness

30. The Mean or the Median? In a normal distribution, the mean is the preferred measure In a skewed distribution, you go with the median

31. Deviate from the norm? 1.Divide the skewness value 2.By the std. error of skewness

32. A distribution is said to be skewed if the magnitude of (Skewness value/ St. Error of Skew) is greater than 2 (in absolute value)

33. If the Value is Two or More Use the Median 2 or More

34. If the Value Is Two or Less Mean Less Than 2

35. Baseball Salaries again Divide the Skewness by its standard error –.800/.427 = 1.87 This value is less than 2 so we use the mean (92 million) What does the positive skew value mean???

36. Lets Try another One (Per Capita income in the states) Divide the Skewness by its standard error.817/.337 = 2.42 The value is greater than two, and the skewness value is positive What is the better measure and what might cause this distribution shape?

37. CO2 Emissions by State

38. Percent Hispanic

39. World Urban Population

40. STATISTICAL SIGNIFICANCE

41. Testing Causality Statistical Significance Practical Significance

42. Statistical Significance A result is called statistically significant if it is unlikely to have occurred by chance You use these to establish parameters, so that you can state probability that a parameter falls within a specified range called the confidence interval (chance or not). Practical significance says if a variable is important or useful for real-world. Practical significance is putting statistics into words that people can use and understand.

43. Curves & Significance Testing

44. What this Tells us Roughly 68% of the scores in a sample fall within one standard deviation of the mean Roughly 95% of the scores fall 2 standard deviations from the mean (the exact # for 95% is 1.96 s.d) Roughly 99% of the scores in the sample fall within three standard deviations of the mean

45. A Practice Example Assuming a normal curve compute the age (value) – For someone who is +1 s.d, from the mean – what number is -1 s.d. from the mean With this is assumption of normality, what % of cases should roughly fall within this range (+/-1 S.D.) What about 2 Standard Deviations, what percent should fall in this range?

46. Life Expectancy in Latin America and Caribbean Compute the estimated values for Average Life Expectancy for +/- 2 standard deviations from the mean. With this is assumption of normality, what % of cases should fall within this range (+/-2 s.d).

47. If you find this amusing or annoying, you get the concept

48. STANDARD DEVIATION AND CHARTS IN SPSS

49. Standard Deviation

50. For Ratio Variables Step 1 Step 2 Step 3 Step 4

51. Standard Deviation in SPSS Open up the States.Sav dataset and use the union07 variable. Analyze – Descriptive Statistics Descriptives – Select your options

52. Testing for Skewness In the Descriptives CommandIn the Frequencies Command Click Here

53. Simple Bar Charts In SPSS OPEN GSS 2008 Analyze – Descriptive Statistics Frequencies