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UNDERSTANDING RESEARCH RESULTS: DESCRIPTION AND CORRELATION © 2012 The McGraw-Hill Companies, Inc. Contrast three ways of describing result Compare group percentages Correlating scores Comparing group means Describe frequency distributions © 2012 The McGraw-Hill Companies, Inc. Describe the measures of central tendency and variability Define a correlation coefficient Define effect size © 2012 The McGraw-Hill Companies, Inc. 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 © 2012 The McGraw-Hill Companies, Inc. Nominal Ordinal Order the levels from lowest to highest Interval No numerical, quantitative properties Levels represent different categories or groups Intervals between levels are equal in size Can be summarized using means No absolute zero Ratio Equal intervals Absolute zero Can be summarized using mean © 2012 The McGraw-Hill Companies, Inc. Three basic ways to describe results: Comparing Group Percentage Correlating Individual Scores Comparing Group Means © 2012 The McGraw-Hill Companies, Inc. Graphing Frequency Distributions Pie charts Bar graphs Frequency polygons Histograms © 2012 The McGraw-Hill Companies, Inc. © 2012 The McGraw-Hill Companies, Inc. © 2012 The McGraw-Hill Companies, Inc. © 2012 The McGraw-Hill Companies, Inc. Central Tendency Mean Median (Mdn) Found by adding all the scores and dividing by the number of scores Indicates central tendency with interval or ratio scales The middlemost score, or 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 frequently occurring score Indicates central tendency with all scales including nominal scales © 2012 The McGraw-Hill Companies, Inc. © 2012 The McGraw-Hill Companies, Inc. 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 of the standard deviation © 2012 The McGraw-Hill Companies, Inc. y-axis or ordinate x-axis or abscissa © 2012 The McGraw-Hill Companies, Inc. Pearson r: the Correlation Coefficient Pearson’s r indicates: Strength of relationship Direction of relationship Values of r range from 0.00 to ±1.00 Can be described visually using scatterplots © 2012 The McGraw-Hill Companies, Inc. © 2012 The McGraw-Hill Companies, Inc. © 2012 The McGraw-Hill Companies, Inc. Restriction of Range Curvilinear Relationship © 2012 The McGraw-Hill Companies, Inc. Refers to the strength of association between variables Pearson r 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 © 2012 The McGraw-Hill Companies, Inc. 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 © 2012 The McGraw-Hill Companies, Inc. Infers whether the results will hold up if the experiment is repeated several times, each time with a new sample of research participants Inferential Statistics © 2012 The McGraw-Hill Companies, Inc. 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 © 2012 The McGraw-Hill Companies, Inc. Used to combine a number of predictor variables to increase the accuracy of prediction of a given criterion or outcome variable Symbolized R © 2012 The McGraw-Hill Companies, Inc. Provides a Way of Statistically Controlling Third Variables © 2012 The McGraw-Hill Companies, Inc. Structural Equation Models Describe expected pattern of relationships between / among quantitative, non-experimental variables After data collection statistics describe how well the data fits the model Path diagrams A visual representation of the model being tested Show theoretical causal paths © 2012 The McGraw-Hill Companies, Inc. Path analysis Used to study modeling Arrows lead from variable to variable Statistics provide path coefficients Similar to standardized weights in regression equations Indicate the strength of relationship between variables in the path © 2012 The McGraw-Hill Companies, Inc. Expected Pattern of Relationships Among a Set of Variables © 2012 The McGraw-Hill Companies, Inc.
