METHODS IN BEHAVIORAL RESEARCH NINTH EDITION PAUL C. COZBY Copyright © 2007 The McGraw-Hill Companies, Inc.

CHAPTER 12 UNDERSTANDING RESEARCH RESULTS: DESCRIPTION AND CORRELATION

LEARNING OBJECTIVES Contrast the three ways of describing results: comparing group percentages, correlating scores, and comparing group means Describe a frequency distribution, including the various ways to display a frequency distribution

LEARNING OBJECTIVES Describe the measures of central tendency and variability Define a correlation coefficient Define effect size

LEARNING OBJECTIVES Describe the use of a regression equation and a multiple correlation to predict behavior Discuss how a partial correlation addresses the third-variable problem Summarize the purpose of structural models

SCALES OF MEASUREMENT: A REVIEW Nominal No numerical, quantitative properties Levels represent different categories or groups Ordinal – minimal quantitative distinctions Order the levels from lowest to highest Interval – quantitative properties Intervals between levels are equal in size Can be summarized using means No absolute zero Ratio – detailed quantitative properties Equal intervals Absolute zero Can be summarized using mean

ANALYZING THE RESULTS OF RESEARCH INVESTIGATIONS Three basic ways of describing the results: 1. Comparing Group Percentage 2. Correlating Individual Scores 3. Comparing Group Means

FREQUENCY DISTRIBUTIONS Graphing Frequency Distributions Pie charts Bar graphs Frequency polygons Histograms

PIE CHART

BAR GRAPH

FREQUENCY POLYGONS

DESCRIPTIVE STATISTICS Central Tendency Mean Found by adding all the scores and dividing by the number of scores Indicates central tendency with interval or ratio scales Median (Mdn) Score that divides the group in half (with 50% scoring below and 50% scoring above the median) Indicates central tendency with ordinal, interval, and ratio scales Mode Most frequent score Indicates central tendency with all scales including nominal scales

MEAN

DESCRIPTIVE STATISTICS Variability – the amount of spread in the distribution of scores Standard deviation = (s) (SD) in reports Range Difference between highest and lowest score Variance (s²) Square root of the standard deviation

GRAPHING RELATIONSHIPS y-axis x-axis

CORRELATION COEFFICIENTS: DESCRIBING THE STRENGTH OF RELATIONSHIPS Pearson r Correlation Coefficient Strength of relationship Direction of relationship Values of r range from 0.00 to ±1.00 Scatterplots

CORRELATION COEFFICIENT OF ±1.00

SCATTERPLOTS

IMPORTANT CONSIDERATIONS Restriction of Range Curvilinear Relationship

EFFECT SIZE General Term that Refers to the Strength of Association Between Variables Pearson r Correlation Coefficient is One Indicator of Effect Size Advantage of Reporting Effect Size is that it Provides a Scale of Values that is Consistent Across All Types of Studies

EFFECT SIZE Differences in effect sizes 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

STATISTICAL SIGNIFICANCE Inferring whether the results will hold up if the experiment is repeated several times, each time with a new sample of research participants Inferential Statistics

REGRESSION EQUATIONS Calculations used to predict a person’s score on one variable when that person’s score on another variable is already known General Form: Y=a + bX Y = Score we wish to predict X = Score that is known a = constant b = weighing adjustment

MULTIPLE CORRELATION Used to combine a number of predictor variables to increase the accuracy of prediction of a given criterion or outcome variable Symbolized R

PARTIAL CORRELATION AND THE THIRD-VARIABLE PROBLEM Provides a Way of Statistically Controlling Third Variables

STRUCTURAL MODELS Expected Pattern of Relationships Among a Set of Variables Path analysis