Chapter 12 Understanding Research Results: Description and Correlation

1. Chapter 12Understanding Research Results:Description and Correlation

2. Scales of Measurement • Scales of measurement: A review • Levels of nominal scale variables • No numerical, quantitative properties • Levels are different categories or groups

3. Scales of Measurement (con’t) • Scales of measurement: A review • Variables with ordinal scale levels involve minimal quantitative distinctions • Rank order the levels from lowest to highest

4. Scales of Measurement (con’t) • Scales of measurement: A review • Interval scale variables – quantitative properties • Intervals between the levels are equal in size • No absolute zero

5. Scales of Measurement (con’t) • Scales of measurement: A review • Ratio scale variables - detailed quantitative properties • Equal intervals • Absolute zero

6. Analyzing the Results of Research Investigations • Scales of measurement have important implications • Three basic ways of describing the results • Comparing group percentages • Correlating scores of individuals on two variables • Comparing group means

7. Analyzing the Results of Research Investigations(con’t) • For all types of data, it is important to understand the results by carefully describing the data collected • Frequency distributions • Graphing frequency distributions • Directly observe how participants responded • Examine which scores were the most frequent • Examine the shape of the distribution of scores • Identify outliers • Compare the distributions of different groups

8. Analyzing the Results of Research Investigations (con’t) • Graphing frequency distributions (con’t) • Pie charts – very useful for nominal scale information

9. Analyzing the Results of Research Investigations (con’t) • Bar graphs use a separate and distinct bar for each piece of information

10. Analyzing the Results of Research Investigations (con’t) • Frequency polygons – a line is used to represent frequencies • Most useful when data are interval or ratio scales

11. Descriptive Statistics • Descriptive statistics allow researchers to make precise statements about the data • Two statistics are needed to describe the data • Central tendency • Variability

12. Descriptive Statistics (con’t) • Central tendency • Mean M in scientific reports • Mathematical average • Appropriate for interval or ratio scale data • Median • Divides the group in half • Appropriate for ordinal scale data • Mode • Most frequent score • Appropriate for nominal scale data

13. Descriptive Statistics (con’t)

14. Descriptive Statistics (con’t)

15. Descriptive Statistics (con’t) • Variability - the amount of spread in the distribution of scores • Standard deviation = s or SD in reports • Variance = s2 • Range

16. Graphing Relationships (con’t) • Levels of IV are shown on horizontal x-axis • DV values are shown on the vertical y-axis y-axis x-axis

17. Correlation Coefficients: Describing the Strengthof Relationships • Correlation coefficient – a statistic that describes how strongly variables are related to one another • Pearson Product-Moment correlation coefficient • Interval or ratio scale data • r • Values range from 0.00 to +1.00 and 0.00 to –1.00

18. Correlation Coefficients: Describing the Strengthof Relationships (con’t) • Correlation coefficients (con’t) • Sign of the value indicates direction • Value indicates the strength

19. Correlation Coefficients: Describing the Strengthof Relationships (con’t) • Correlation coefficient – the nearer a correlation is to 1.00 (plus or minus), the stronger the relationship

20. Correlation Coefficients: Describing the Strengthof Relationships (con’t) Scatterplots reveal the pattern of the relationship

21. Correlation Coefficients: Describing the Strengthof Relationships (con’t) • Important considerations • Restriction of range • Curvilinear relationship

22. Effect Size • Effect size is a general term that refers to the strength of the association between variables • A scale of values that is consistent across all types of studies • Values range from 0.00 to 1.00

23. Effect size (con’t) • Pearson r is one indicator of effect size • Small effects near r = .15 • Medium effects near r = .30 • Large effects above r = .40 • Squared value of the coefficient r2 - transforms the value of r to a percentage • Percent of shared variance between the two variables

24. Statistical Significance • Decision about the statistical significance of the results • Will the results hold up if the experiment is repeated several times? • Topic discussed in Chapter 13.

25. Regression Equations • Regression equations are calculations used to predict a score on one variable using a known score on another variable Y = Score we wish to predict (criterion variable) X = Score that is known (predictor variable)

26. Multiple Correlation • Multiple correlation is uses (symbolized R) is the correlation between a combined set of predictor variables and a single criterion variable • Permits greater accuracy of predictor than if any single predictor is used alone (never a perfect predictor) • R2 = effect size

27. Partial Correlation and the Third-Variable Problem • Partial correlation is a way of statistically controlling third variables • Correlation between the two variables of interest, with the influence of the third variable “partialed out of” the original correlation

28. Structural Models • Structural models of relationships among variables using the nonexperimental method • An expected pattern of relationships • Based on a theory of how the variables are causally related to one another • Approach called structural equation modeling • Older but related tool is called path analysis

29. Structural Models (con’t) • Arrows depict paths that relate the variables in the model • Coefficients similar to the weights derived in regression equations (indicating the strength of the relationship)

30. The End