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Example: New scores on the Roberts Test of Agricultural Knowledge: 90 70 95 65 80 85 70 75 75 60

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Example: u 76.5 u 75 u 70, 75 u 10.5 u mean - arithmetic average u median - 50th percentile u mode - most frequently occuring score u standard deviation - measure of variability, based on normal curve

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Example: u frequency - the number of occurrences of a score –90 = 1 –85 = 1 –75 = 2 –80 = 1 –70 = 2 –65 = 1 –60 = 1

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Example:

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Frequency Polygon

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Descriptive Statistics u Percentage -- the frequency of a score as a percentage of the sample (population) u Correlation -- number describing the linear relationship of two variables (one group of subjects); use a scatterplot to check for nonlinear relationships

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Descriptive Statistics Scatterplot Variable A Variable B Line of best fit Outlier

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Inferential Statistics Continuous Data: u Difference between more than two groups, one ind. variable: u Analysis of Variance (ANOVA) u Difference between groups, more than one ind. variable: u Factorial ANOVA

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Inferential Statistics Continuous Data: u Difference between groups, one ind. variable, more than one dep. variable: u Multiple Analysis of Variance (MANOVA) u Difference between groups, more than one ind. variable, more than one dep. variable: u Factorial MANOVA

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Inferential Statistics Continuous Data: u Difference between groups, one ind. variable, one dep. variable with a pretest: u Analysis of Covariance (ANCOVA) u >1 ind. variable = Factorial ANCOVA u >1 dep. variable = MANCOVA

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Application -- Example u Dep. Variable: Achievement (test scores) u Independent Variable: Teaching method (3 levels) u Prestest? No u ANOVA

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Application -- Example u Dep. Variable: Achievement (test scores) u Independent Variable: Teaching method (2 levels) u Prestest? Yes u ANCOVA

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Application -- Example u Dep. Variable: Achievement (test scores), Attitudes (Likert scale) u Independent Variable: Teaching method (3 levels) u Prestest? No u MANOVA

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Application -- Example u Dep. Variable: Achievement (test scores) u Independent Variable: Teaching method (3 levels) u Other independent variable: sex (2 levels) u Prestest? No u Factorial ANOVA

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Chap 3-1 EF 507 QUANTITATIVE METHODS FOR ECONOMICS AND FINANCE FALL 2008 Chapter 3 Describing Data: Numerical.

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