1. Chapter 12 Understanding 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 Strength of 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 and 0.00 to –1.00

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

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

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

21. Correlation Coefficients: Describing the Strength of 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