- 1. CHAPTER 19 Choosing the Right Statistics
- 2. Three Basic Data Structures Most research data can be classified into one of three categories: • Category 1: A single group of participants with one score per participant • Category 2: A single group of participants with two (or more) variables measured per participant • Category 3: Two (or more) groups of scores with each score a measurement of the same variable
- 3. Scales of Measurement Different statistics will be used depending on scales of measurement • Ratio and interval scales (numerical scores) • Height (in inches) • Weight (in pounds) • IQ scores • Ordinal scales (rank or ordered categories of scores) • Small, medium, or large size t-shirts • Job applicants: 1st, 2nd, 3rd, etc. rank • Nominal scales (named categories) • Gender (male or female) • Profession (lawyer, doctor, psychologist)
- 4. Category 1 A single group of participants with one score per participant • The goal is to describe individual variables, as they exist naturally, without attempting to examine relationships between different variables • Descriptive statistics are the most commonly used procedures for these data • 3 Examples:
- 5. Category 2 A single group of participants with two (or more) variables measured per participant • The goal is to describe and evaluate the relationship between variables as they occur naturally
- 6. Category 3 Two (or more) groups of scores with each score a measurement of the same variable • The goal is to examine relationships between variables by using the categories of one variable to define groups and then measure a second variable to obtain a set of scores within each group • If scores in one group are consistently different from scores in another group, then the data indicate a relationship between variables
- 7. CHAPTER 19.2 Statistical Procedures for Data from a Single Group of Participants with One Score Per Participant (Category 1)
- 8. Scores from Ratio or Interval Scales • Descriptive Statistics • The mean (Ch.3) and standard deviation (Ch.4) are the most commonly used • The median (Ch.3) may also be used as a measure of central tendency • Inferential Statistics • If there is a basis for a null hypothesis, a single-sample t-test (Ch.9) can be used to test the hypothesis
- 9. Scores from Ordinal Scales • Descriptive Statistics • The median is used for describing central tendency • Proportions can be used to describe the distribution of individuals across categories • Inferential Statistics • If there is a basis for a null hypothesis, a chi-square test for goodness-of-fit (Ch.17) can be used to evaluate the hypothesis • The binomial test (Ch.18) can also be used with only two categories
- 10. Scores from a Nominal Scale • Descriptive Statistics • The mode may be used for describing central tendency • Proportions can be used to describe the distribution of across categories • Inferential Statistics • A chi-square test for goodness-of-fit can be used to evaluate the null hypothesis • The binomial test can also be used with only two categories
- 12. CHAPTER 19.3 Statistical Procedures for Data from a Single Group of Participants with Two (or more) Variables Measured for Each Participant (Category 2)
- 13. Two Numerical Variables (Interval/Ratio Scales) Descriptive Statistics • The Pearson correlation (Ch.15) describes the degree and direction of the linear relationship • The regression equation (Ch. 16) identifies the slope and Y-intercept for the best-fitting line Inferential Statistics • The critical values in Table B6 determine the significance of the Pearson correlation (Ch.15) • Analysis of regression determines the significance of the regression equation (Ch. 16)
- 14. Two Ordinal Variables (Ranks/Ordered categories) • Descriptive Statistics • The Spearman correlation (Ch. 15) describes the degree and direction of monotonic relationship (the degree to which the relationship is consistently one- directional) • Inferential Statistics • The critical values in Table B7 determine the significance of the Spearman correlation
- 15. 1 Numerical and 1 Dichotomous Variable • Descriptive Statistics • The point-biserial correlation (Ch. 15) measures the strength of the relationship • Inferential Statistics • The data for a point-biserial correlation can be regrouped into a format suitable for an independent- measures t-hypothesis test • The t value determines the significance of the relationship
- 16. 2 Dichotomous Variables • Descriptive Statistics • The phi-coefficient (Ch. 15) describes the strength of the relationship • Inferential Statistics • The data from a phi-coefficient can be regrouped into a format suitable for a 2 x 2 chi-square test for independence • The chi-square value determines the significance of the relationship
- 17. 2 Variables from Any Measurement Scale • Descriptive Statistics • The data can be regrouped as a frequency distribution matrix • The frequencies or proportions describe the data • Inferential Statistics • The chi-square test for independence evaluates the relationship between variables
- 18. 3 Variables (Interval or Ratio) • Descriptive Statistics • A partial correlation (Ch.15) describes the direction and degree of the linear relationship between two variables while controlling the third variable • The multiple regression equation (Ch.16) describes the relationship between two predictor variables and the variable being predicted • Inferential Statistics • The statistical significance of the partial correlation can be evaluated by comparing the sample correlation with the critical values in Table B6 and df = n-3 • Analysis of regression evaluates the significance of the multiple regression equation
- 19. 3 Variables (Numerical and Dichotomous) • Descriptive Statistics • A partial correlation (Ch.15) describes the degree of the linear relationship between two variables while controlling the third variable • The multiple regression equation (Ch.16) describes the relationship between two predictor variables and the variable being predicted • Inferential Statistics • The statistical significance of the partial correlation can be evaluated by comparing the sample correlation with the critical values in Table B6 and df = n-3 • Analysis of regression evaluates the significance of the multiple regression equation
- 20. Statistics for Category 2 Data
- 21. CHAPTER 19.4 Statistical Procedures for Data Consisting of Two (or More) Groups of Scores with Each Score a Measurement of the Same Variable (Category 3)
- 22. Numerical Scores (Ratio/Interval) Descriptive Statistics • For both independent-measures and repeated-measures studies, the mean and standard deviation can be used to summarize and describe each group. Inferential Statistics • For independent-measures designs, the independent- measures ANOVA and independent-measures t-test are used to evaluate the mean difference • For repeated-measures designs, the repeated-measures t-test and repeated-measures ANOVA are used to evaluate the mean difference
- 23. Ranks or Ordered Categories (Ordinal scales) Descriptive Statistics • Ordinal scores can be described by the set of ranks or ordinal categories within each group. • The median may be used for both independent-measures and repeated-measures designs Inferential Statistics • For independent-measures designs, the Mann-Whitney U test evaluates the difference between two groups of scores. The Kruskal- Wallis test evaluates differences between three or more groups. • For repeated-measures designs, the Wilcoxon signed ranks test evaluates the difference between two groups of scores. The Friedman test evaluates differences among three or more groups.
- 24. Scores from a Nominal Scale Descriptive Statistics • Proportions can be used for each category Inferential Statistics • With a relatively small number of nominal categories, the data can be displayed as a frequency-distribution matrix • A chi-square test for independence can be used to evaluate differences between groups for an independent- measures design
- 25. 2-Factor Designs with Numerical Scores (interval/ratio scales) Descriptive Statistics • The mean and standard deviation can be used to summarize and describe each group for both independent-measures and repeated-measures designs Inferential Statistics • Independent-measures ANOVA and repeated- measures ANOVA evaluate the mean differences between cells
- 26. Statistics for Category 3 Data
- 27. Statistics for Category 3 Data