Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Choosing the right statistics

1,325 views

Published on

Behavioral Statistics

Published in: Education
  • Login to see the comments

Choosing the right statistics

  1. 1. CHAPTER 19 Choosing the Right Statistics
  2. 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. 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. 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. 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. 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. 7. CHAPTER 19.2 Statistical Procedures for Data from a Single Group of Participants with One Score Per Participant (Category 1)
  8. 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. 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. 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
  11. 11. StatisticsforCategory1Data
  12. 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. 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. 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. 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. 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. 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. 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. 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. 20. Statistics for Category 2 Data
  21. 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. 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. 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. 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. 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. 26. Statistics for Category 3 Data
  27. 27. Statistics for Category 3 Data

×