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 Subject Before After 1 45 43 2 16 20 3 17 4 33 30 5 25 6 19 734 8 28 9 26 23 10 40 41 11 12 36 13 15 14 32

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
H0: The data do fit the model
i.e., Grades last semester are distributed the same way as they were in 1985.
H1: 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
6.67

15. Step 6: Decision Thus, if 2 > than 2critical
Reject H0, and accept H1
If 2 < or = to 2critical
Fail to reject H0

16. Step 6: Decision Thus, if 2 > than 2critical
2 = 6.67
2 crit = 9.49
Step 6: Decision
Thus, if 2 > than 2critical
Reject H0, and accept H1
If 2 < or = to 2critical
Fail to reject H0

17. Step 7: Put answer into words
H0: 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 But here is the formula == so what you did was
= 320
320 / 4 = 80

22. r =
tobs = (X - ) / Sx
r =

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:

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 problem
2) Decide what statistical test to use
3) Perform that procedure
4) Write an interpretation of the results

40. 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

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-test k. Regression
b. Dependent t-test l. Standard Deviation
c. One-Sample t-test m. Z-score
d. Goodness of fit Chi-Square n. Mode
e. Independence Chi-Square n o. Mean
f. Confidence Interval p. Median
g. Correlation (Pearson r) q. Bar Graph
h. Scatter Plot r. Range
Line Graph s. ANOVA
j. Frequency Polygon t. 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
Then you locate the each midpoints frequency point

50. Line Graph
Then you locate the each midpoints frequency point

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
Then you locate the each midpoints frequency point

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. Final Exam Test = 1 hour and 45 minutes
1:30 class is Mon, Dec 14 2:30-4:15
3:00 class is Tues, Dec 15 2:30-4:15
*Note about testing students

65. Cookbook
Due: Final exam
Early grade: Wednesday!