2. Practice As part of a program to reducing smoking, a national organization ran an advertising campaign to convince people to quit or reduce their smoking. To evaluate the effectiveness of their campaign, they had 15 subjects record the average number of cigarettes smoked per day in the week before and the week after exposure to the advertisement. Determine if the advertisements reduced their smoking (Alpha =.05).

3. Practice SubjectBeforeAfter 14543 21620 3 17 43330 5 25 619 73334 82528 92623 104041 112826 123640 131516 142623 153234

4. Practice Dependent t-test t =.45 Do not reject Ho The advertising campaign did not reduce smoking

5. Practice You wonder if there has been a significant change (.05) in grading practices over the years. In 1985 the grade distribution for the school was:

6. Practice Grades in 1985 A: 14% B: 26% C: 31% D: 19% F: 10%

7. Grades last semester

8. Step 1: State the Hypothesis H 0 : The data do fit the model –i.e., Grades last semester are distributed the same way as they were in 1985. H 1: The data do not fit the model –i.e., Grades last semester are not distributed the same way as they were in 1985.

9. Step 2: Find  2 critical df = number of categories - 1

10. Step 2: Find  2 critical df = number of categories - 1 df = 5 - 1 = 4  =.05  2 critical = 9.49

11. Step 3: Create the data table

12. Step 4: Calculate the Expected Frequencies

13. Step 5: Calculate  2 O = observed frequency E = expected frequency

14. 22 6.67

15. Step 6: Decision Thus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0

16. Step 6: Decision Thus, if  2 > than  2 criticalThus, if  2 > than  2 critical –Reject H 0, and accept H 1 If  2 < or = to  2 critical –Fail to reject H 0  2 = 6.67  2 crit = 9.49

17. Step 7: Put answer into words H 0 : The data do fit the model Grades last semester are distributed the same way (.05) as they were in 1985.

19. The Three Goals of this Course 1) Teach a new way of thinking 2) Self-confidence in statistics 3) Teach “factoids”

21. Mean

22. r = t obs = (X -  ) / S x

23. What you have learned! Introduced to statistics and learned key words –Scales of measurement –Populations vs. Samples

24. What you have learned! Learned how to organize scores of one variable using: –frequency distributions –graphs –measures of central tendency

25. What you have learned! Learned about the variability of distributions –range –standard deviation –variance

26. What you have learned! Learned about combination statistics –z-scores –effect sizes –box plots

27. What you have learned! Learned about examining the relation between two continous variables –correlation (expresses relationship) –regression (predicts)

28. What you have learned! Learned about probabilities

29. What you have learned! Learned about the sampling distribution –central limit theorem –determine probabilities of sample means –confidence intervals

30. What you have learned! Learned about hypothesis testing –using a t-test for to see if the mean of a single sample came from a population value

31. What you have learned! Extended hypothesis testing to two samples –using a t-test for to see if two means are different from each other independent dependent

32. What you have learned! Extended hypothesis testing to three or more samples –using an ANOVA to determine if three or means are different from each other

33. What you have learned! Extended ANOVA to two or more IVs –Factorial ANOVA –Interaction

34. What you have learned! Learned how to examine nominal variables –Chi-Square test of independence –Chi-Square test of goodness of fit

35. CRN: 33496.0

37. Next Step Nothing new to learn! Just need to learn how to put it all together

38. Four Step When Solving a Problem 1) Read the problem 2) Decide what statistical test to use 3) Perform that procedure 4) Write an interpretation of the results

39. Four Step When Solving a Problem 1) Read the problem1) Read the problem 2) Decide what statistical test to use 3) Perform that procedure3) Perform that procedure 4) Write an interpretation of the results4) Write an interpretation of the results

40. Four Step When Solving a Problem 1) Read the problem 2) Decide what statistical test to use2) Decide what statistical test to use 3) Perform that procedure 4) Write an interpretation of the results

41. How do you know when to use what? If you are given a word problem, would you know which statistic you should use?

42. Example An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males.

43. Possible Answers a.Independent t-testk.Regression b.Dependent t-testl.Standard Deviation c.One-Sample t-testm.Z-score d.Goodness of fit Chi-Squaren.Mode e.Independence Chi-Squareno.Mean f.Confidence Intervalp.Median g.Correlation (Pearson r)q.Bar Graph h.Scatter Plotr. Range i.Line Graphs.ANOVA j. Frequency Polygont. Factorial ANOVA

44. Example An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males. Use regression

45. Decision Tree First Question: Descriptive vs. Inferential Perhaps most difficult part –Descriptive - a number or figure that summarizes a set of data –Inferential - use a sample to conclude something about a population hint: these use confidence intervals or probabilities!

46. Decision Tree: Descriptive One or Two Variables

47. Decision Tree: Descriptive: Two Variables Graph, Relationship, or Prediction –Graph - visual display –Relationship – Quantify the relation between two continuous variables (CORRELATION) –Prediction – Predict a score on one variable from a score on a second variable (REGRESSION)

48. Decision Tree: Descriptive: Two Variables: Graph Scatterplot vs. Line graph –Scatterlot –Linegraph Both are used to show the relationship between two variables (it is usually subjective which one is used)

49. Scatter Plot

50. Line Graph

51. Decision Tree: Descriptive: One Variable Central Tendency, Variability, Z-Score, Graph –Central Tendency – one score that represents an entire group of scores –Variability – indicates the spread of scores –Z-Score – converts a score so that is conveys the sore’s relationship to the mean and SD of the other scores. –Graph – Visual display

52. Decision Tree: Descriptive: One Variable: Central Tendency Mean, Median, Mode

53. Decision Tree: Descriptive: One Variable: Central Tendency Mean, Median, Mode

54. Decision Tree: Descriptive: One Variable: Variability Variance, Standard Deviation, Range/IQR –Variance –Standard Deviation Uses all of the scores to compute a measure of variability –Range/IQR Only uses two scores to compute a measure of variability In general, variance and standard deviation are better to use a measures of variability

55. Decision Tree: Descriptive: One Variable: Graph Frequency Polygon, Histogram, Bar Graph –Frequency Polygon –Histogram Interchangeable graphs – both show frequency of continuous variables –Bar Graph Displays the frequencies of a qualitative (nominal) variable

56. Frequency Polygon

57. Histogram

58. Bar Graph

59. Decision Tree: Inferential: Frequency Counts vs. Means w/ One IV vs. Means w/ Two or more IVs –Frequency Counts – data is in the form of qualitative (nominal) data –Means w/ one IV – data can be computed into means (i.e., it is interval or ratio) and there is only one IV –Means w/ two or more IVs – data can be computed into means (i.e., it is interval or ratio) and there are two or more IVs –Confidence Interval - with some degree of certainly (usually 95%) you establish a range around a mean

60. Decision Tree: Inferential: Frequency Counts Goodness of Fit vs. Test of Independence –Goodness of Fit – Used to determine if there is a good fit between a qualitative theoretical distribution and the qualitative data. –Test of Independence – Tests to determine if two qualitative variables are independent – that there is no relationship.

61. Decision Tree: Inferential: Means with two or more IVs –Factorial ANOVA

62. Decision Tree: Inferential: Means with one IV One Sample, Two Samples, Three or more –One Sample – Used to determine if a single sample is different, >, or < than some value (usually a known population mean; ONE-SAMPLE t-TEST) –Two Samples – Used to determine if two samples are different, >, or < than each other –Two or more – Used to determine if three or more samples are different than each other (ANOVA).

63. Decision Tree: Inferential: Means with one IV: Two Samples Independent vs. Dependent –Independent – there is no logical reason to pair a specific score in one sample with a specific score in the other sample –Paired Samples – there is a logical reason to pair specific scores (e.g., repeated measures, matched pairs, natural pairs, etc.)

64. Cookbook Due: Final exam Early grade: Wednesday! Tuesday: Work on Practice Test and Cookbook (no class)!