Chapter 10

1. Chapter 10 http://members.aol.com/johnp71/javastat.html

2. Goal • Not only to be able to analyze your own data but to understand the literature that you read.

3. Data Analysis • Statistics • Parameter

4. Reporting your Results • With words…. • With numbers…. • With Charts/Graphs…

5. Data • Categorical • Quantitative

6. Quantitative • In this chapter: • Correlation • Frequency • distributions • Measures of Central Tendency • Mean • Variability • Standard deviation

7. Distributions • Skewed Distributions • Positive – scores trailing to the right with a majority at the lower end • Negative – scores trailing to the left

8. Curve “Skewness”

9. Distributions • Normal • Large majority of scores in the middle • Symmetrical • Bell-shaped • Mean, median, and mode are identical

10. Types of Curves... The Normal Curve:

11. Measures of Central Tendency • Mode • Median • Point at which 50% of scores fall above and below • Not necessarily one of the actual scores in the distribution • Most appropriate if you have skewed data

12. Measures of Central Tendency • Mean • Uses all scores in a distribution • Influenced by extreme scores • Mean = sum of scores divided by the number of scores

13. Variability • Range • Low to High • Quick and dirty estimate of variability • Standard Deviation

14. Standard Deviation • 1. Calculate the mean • 2. Subtract the mean from each score • 3. Square each of the scores • 4. Add up all the squares • 5. Divide by the total number of scores = variance • 6. Take the square root of the variance.

15. Standard Deviation • The more spread out the scores the larger the standard deviation. • If the distribution is normal then the mean + two standard deviations will encompass about 95% of the scores. (+ three SD = 99% of scores)

16. Normal Curve: By Standard Deviation

17. % of Scores in 1 SD 1 SD = 68% of sample

18. 2 Standard deviations? 2 SD = 95% of sample

19. Group A 30 subjects Mean = 25 SD = 5 Median = 23 Mode = 24 Group B 30 subjects Mean = 25 SD = 10 Median = 18 Mode= 13 What can you tell me about these groups?

20. Use your text (p. 207-208) Check your scores with this link. Scores: 12, 10, 6, 15, 17, 20, 16, 11, 10, 16, 22, 17, 15, 8 Mean = ?? SD = ?? Calculate the Standard Deviation and Average

21. Excel • Now go to the following web page and click on “class data”: assignments • Calculate mean, median, mode, SD for the ACT and Writing column data.

22. Standard Scores • A method in which to compare scores • Z scores – expressed as deviation scores • Example: • Test 1= 80 • Test 2 = 75

23. Example • Test 1: mean = 85, SD = 5 • Test 2: mean = 65, SD = 10

24. Probability • We can think of the percentages associated with a normal curve as probabilities. • Stated in a decimal form. • If something occurs 80% of the time it has a probability of .80.

25. Example • We said that 34% of the scores (in a normal distribution) lie between the mean and 1SD. • Since 50% of the scores fall above the mean then about 16% of the scores lie above 1SD

26. Example • The probability of randomly selecting an individual who has a score at least 1SD above the mean? • P=.16 • Chances are 16 out of 100.

27. Example • Probability of selecting a person that is between the mean and –2SD?

28. Z-Scores • For any z score we know the probability • Appendix B

29. Z-Scores • Can also be calculated for non-normal distributions. • However, cannot get probabilities values if non-normal. • If have chosen a sample randomly many distributions do approximate a normal curve.

30. Determining Relationships Between Scores Correlation

31. Relationships • We can’t assign blame or cause & effect, rather how one variable influences another.

32. Correlation • Helpful to use scatterplots

33. Plotting the relationship between two variables Age = 11 Broad Jump = 5.0 feet Y axis Age 11 5.0 X axis 5 Feet

34. Plot some more (Age & Broad Jump) y Do you see a relationship?? Age x Feet

35. Outliers • Differ by large amounts from the other scores

36. Correlation…. • Is a mathematical technique for quantifying the amount of relationship between two variables • Karl Pearson developed a formula known as “Pearson product-moment correlation”

37. Correlation • Show direction (of relationship) • Show strength (of relationship) • Range of values is 0 - 1.0 (strength) • 0 = no relationship • 1 = perfect relationship • Values may be + or - (direction)

38. Correlation r= 1.0 r = 0 r = -1.0

39. Correlation Strength • Very Strong .90 - 1.0 • Strong .80 - .89 • Moderate .50 - .79 • Weak < .50

40. Types of relationships Curvalinear Sigmoidal Linear

41. Test Your Skill Guess the Correlation

42. Quick Assignment • For the same excel spreadsheet that we opened earlier calculate a correlation coefficient for the ACT vs. Tricep. • Make a scatterplot of tricep vs. ACT. • Scatterplot and correlation for ACT vs. Writing

43. Coefficient of Determination • Determines the amount of variability in a measure that is influenced by another measure • I.e. how much does the broad jump vary due to varied ages? • Calculated as r2 (Corr. Squared)

44. Example: • Say that strength and 40yard sprint time have an r = .60 • How much does a variation in strength contribute to the variation in sprint speed?

45. Summarizing Data • Frequency Table • Bar Graphs/Pie Charts • Crossbreak Table • A graphic way to report a relationship between two or more categorical variables.

46. Assignment • Under assignments on my web page there is an excel spreadsheet published entitled “assignment 1”. • Download the spreadsheet by clicking here assignments

47. Assignment • 1. Calculate the mean, mode, and median for body density, ACT Score, and Reading Score on sheet 1 • 2. Calculate the mean and SD for TC, Trig, HDL, and LDL on sheet 2

48. Assignment • 3. Calculate a correlation coefficient for body density and age, ACT and Reading Scores, TC and LDL, and Trig and HDL • 4. Make a scatterplot for HDL and Trig as well as LDL and Total

49. Assignment • 5. Make a bar graph for the mean Total, Trig, LDL, HDL values.