1. Chapter Nine: Using Statistics to Answer Questions
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

2. Using Statistics to Answer Questions
Statistics is a branch of mathematics that involves the collection, analysis, and interpretation of data.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

3. Using Statistics to Answer Questions
Statistics is a branch of mathematics that involves the collection, analysis, and interpretation of data.
Two main branches of statistics assist your decisions in different ways.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

4. Using Statistics to Answer Questions
Statistics is a branch of mathematics that involves the collection, analysis, and interpretation of data.
Two main branches of statistics assist your decisions in different ways.
Descriptive Statistics
Descriptive statistics are used to summarize any set of numbers so you can understand and talk about them more intelligibly.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

5. Using Statistics to Answer Questions
Statistics is a branch of mathematics that involves the collection, analysis, and interpretation of data.
Two main branches of statistics assist your decisions in different ways.
Descriptive Statistics
Inferential Statistics
Inferential statistics are used to analyze data after you have conducted an experiment to determine whether your independent variable had a significant effect.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

6. Descriptive Statistics
We use descriptive statistics when we want to summarize a set or distribution of numbers in order to communicate their essential characteristics.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

7. Descriptive Statistics
We use descriptive statistics when we want to summarize a set or distribution of numbers in order to communicate their essential characteristics.
One of these essential characteristics is a measure of the typical or representative score, called a measure of central tendency.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

8. Descriptive Statistics
We use descriptive statistics when we want to summarize a set or distribution of numbers in order to communicate their essential characteristics.
One of these essential characteristics is a measure of the typical or representative score, called a measure of central tendency.
A second essential characteristic that we need to know about a distribution is how much variability or spread exists in the scores.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

9. Scales of Measurement Measurement
The assignment of symbols to events according to a set of rules.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

10. Scales of Measurement Measurement Scale of measurement
The assignment of symbols to events according to a set of rules.
Scale of measurement
A set of Measurement rules
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

11. Scales of Measurement Nominal Scale
A scale of measurement in which events are assigned to categories.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

12. Scales of Measurement Nominal Scale Ordinal Scale
A scale of measurement that permits events to be rank ordered.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

13. Scales of Measurement Nominal Scale Ordinal Scale Interval Scale
A scale of measurement that permits rank ordering of events with the assumption of equal intervals between adjacent events.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

14. Scales of Measurement Nominal Scale Ordinal Scale Interval Scale
Ratio Scale
A scale of measurement that permits rank ordering of events with the assumption of equal intervals between adjacent events and a true zero point.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

15. Measures of Central Tendency
Mode
The score in a distribution that occurs most often.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

16. Measures of Central Tendency
Mode
The score in a distribution that occurs most often.
Median
The number that divides a distribution in half.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

17. Measures of Central Tendency
Mode
The score in a distribution that occurs most often.
Median
The number that divides a distribution in half.
Mean
The arithmetic average of a set of numbers. It is found by adding all the scores in a set and then dividing by the number of scores.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

18. Graphing Your Results Pie Chart
Graphical representation of the percentage allocated to each alternative as a slice of a circular pie.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

19. Graphing Your Results Pie Chart Histogram
A graph in which the frequency for each category of a quantitative variable is represented as a vertical column that touches the adjacent column.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

20. Graphing Your Results Pie Chart Histogram Bar Graph
A graph in which the frequency for each category of a qualitative variable is represented as a vertical column. The columns of a bar graph do not touch.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

21. Graphing Your Results Pie Chart Histogram Bar Graph Frequency Polygon
A graph that is constructed by placing a dot in the center of each bar of a histogram and then connecting the dots.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

22. Graphing Your Results Pie Chart Histogram Bar Graph Frequency Polygon
Line Graph
A graph that is frequently used to depict the results of an experiment. The vertical or y axis is known as the ordinate and the horizontal or x axis is known as the abscissa.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

23. Calculating and Computing Statistics
You can find statistical formulas in Appendix B of your text.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

24. Calculating and Computing Statistics
You can find statistical formulas in Appendix B of your text.
All statistical formulas merely require addition, subtraction, multiplication, division, and finding square roots.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

25. Calculating and Computing Statistics
You can find statistical formulas in Appendix B of your text.
All statistical formulas merely require addition, subtraction, multiplication, division, and finding square roots.
Your department may have access to some standard statistical packages such as SPSS, SAS, BMD, Minitab, etc.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

26. Measure of Variability
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

27. Measures of Variability
Range
A measure of variability that is computed by subtracting the smallest score from the largest score.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

28. Measures of Variability
Range
Variance
A single number that represents the total amount of variation in a distribution.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

29. Measures of Variability
Range
Variance
Standard Deviation
The standard deviation is the square root of the variance. It has important relations to the normal curve.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

30. Measures of Variability
Normal distribution
A symmetrical, bell-shaped distribution having half the scores above the mean and half the scores below the mean.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

31. Correlation Correlation Coefficient
A single number representing the degree of relation between two variables.
The value of a correlation coefficient can range from –1 to +1.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

32. The Pearson Product-Moment Correlation Coefficient
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

33. The Pearson Product-Moment Correlation Coefficient
Pearson Product-Moment Correlation Coefficient (r)
This type of correlation coefficient is calculated when both the X variable and the Y variable are interval or ratio scale measurements and the data appear to be linear.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

34. The Pearson Product-Moment Correlation Coefficient
Pearson Product-Moment Correlation Coefficient (r)
This type of correlation coefficient is calculated when both the X variable and the Y variable are interval or ratio scale measurements and the data appear to be linear.
Other correlation coefficients can be calculated when one or both of the variables are not interval or ratio scale measurements or when the data do not fall on a straight line.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

35. Inferential Statistics
What is Significant?
An inferential statistical test can tell us whether the results of an experiment can occur frequently or rarely by chance.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

36. Inferential Statistics
What is Significant?
An inferential statistical test can tell us whether the results of an experiment can occur frequently or rarely by chance.
Inferential statistics with small values occur frequently by chance.
Inferential statistics with large values occur rarely by chance.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

37. Inferential Statistics
Null Hypothesis
A hypothesis that says that all differences between groups are due to chance (i.e., not the operation of the IV).
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

38. Inferential Statistics
Null Hypothesis
A hypothesis that says that all differences between groups are due to chance (i.e., not the operation of the IV).
If a result occurs often by chance, we say that it is not significant and conclude that our IV did not affect the DV.
If the result of our inferential statistical test occurs rarely by chance (i.e., it is significant), then we conclude that some factor other than chance is operative.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

39. The t Test
t Test
The t test is an inferential statistical test used to evaluate the difference between the means of two groups.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

40. The t Test t Test Degrees of Freedom
The t test is an inferential statistical test used to evaluate the difference between the means of two groups.
Degrees of Freedom
The ability of a number in a specified set to assume any value.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

41. The t Test Interpretation of t Value
Determine the degrees of freedom (df) involved.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

42. The t Test Interpretation of t Value
Determine the degrees of freedom (df) involved.
Use the degrees of freedom to enter a t table.
This table contains t values that occur by chance.
Compare your t value to these chance values.
To be significant, the calculated t must be equal to or larger than the one in the table.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

43. One-Tail Versus Two-Tail Tests of Significance
Directional Versus Nondirectional Hypotheses
A directional hypothesis specifies exactly how (i.e., the direction) the results will turn out.
A nondirectional hypothesis does not specify exactly how the results will turn out.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

44. One-Tail Versus Two-Tail Tests of Significance
One-Tail t Test
Evaluates the probability of only one type of outcome (based on directional hypothesis).
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

45. One-Tail Versus Two-Tail Tests of Significance
One-Tail t test
Evaluates the probability of only one type of outcome (based on directional hypothesis).
Two-Tail t test
Evaluates the probability of both possible outcomes (based on nondirectional hypothesis).
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

46. The Logic of Significance Testing
Typically our ultimate interest is not in the samples we have tested in an experiment but in what these samples tell us about the population from which they were drawn.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

47. The Logic of Significance Testing
Typically our ultimate interest is not in the samples we have tested in an experiment but in what these samples tell us about the population from which they were drawn.
In short, we want to generalize, or infer, from our samples to the larger population.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

48. When Statistics Go Astray: Type I and Type II Errors
Type I Error
Accepting the experimental hypothesis when the null hypothesis is true.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

49. When Statistics Go Astray: Type I and Type II Errors
The experimenter directly controls the probability of making a Type I error by setting the significance level.
You are less likely to make a Type I error with a significance level of .01 than with a significance level of .05
However, the more extreme or critical you make the significance level to avoid a Type I error, the more likely you are to make a Type II (beta) error.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

50. When Statistics Go Astray: Type I and Type II Errors
Type II (beta) Error
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

51. When Statistics Go Astray: Type I and Type II Errors
Type II (beta) Error
A Type II error involves rejecting a true experimental hypothesis.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

52. When Statistics Go Astray: Type I and Type II Errors
Type II (beta) Error
A Type II error involves rejecting a true experimental hypothesis.
Type II errors are not under the direct control of the experimenter.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

53. When Statistics Go Astray: Type I and Type II Errors
Type II (beta) Error
A Type II error involves rejecting a true experimental hypothesis.
Type II errors are not under the direct control of the experimenter.
We can indirectly cut down on Type II errors by implementing techniques that will cause our groups to differ as much as possible.
For example, the use of a strong IV and larger groups of participants.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

54. Effect Size Effect Size
The magnitude or size of the experimental treatment.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

55. Effect Size Effect Size
The magnitude or size of the experimental treatment.
A significant statistical test tells us only that the IV had an effect; it does not tell us about the size of the significant effect.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education

56. Effect Size Effect Size (Cohen’s d )
The magnitude or size of the experimental treatment.
A significant statistical test tells us only that the IV had an effect; it does not tell us about the size of the significant effect.
Cohen (1977) indicated that d values greater than .80 reflect large effect sizes.
The Psychologist as Detective, 4e by Smith/Davis © 2007 Pearson Education