mm2 - Association between variables Two variables are...

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Unformatted text preview: Association between variables Two variables are associated if knowing the values of one variable helps a lot in predicting the values of the other variable. If there’s a weak association, then knowing the values of one variable doesn’t help much in predicting the values of the other. Associations are tendencies, not ironclad rules. Association does not necessarily mean causation. What might be the association between IQ test scores & family income? What would such an association signify concerning causation? Caution: be careful if the variables are measured on different sets of observations . E.g., association of human body-weight or blood pressure with age—but what if the data are cross-sectional , not longitudinal? That is, what are the pitfalls of cross-sectional data on ostensibly longitudinal trends? See Freedman et al., Statistics , pages 58-61. Key questions about variables: How are the variables defined & measured (i.e. operationalized)? Are these theoretically & empirically adequate? Are the variables categorical (nominal, ordinal) or quantitative (interval, ratio)? Are there response (i.e. outcome, dependent) variables & explanatory (i.e. independent, predictor) variables? Do these make sense? What if they were reversed? Who do the data represent? How were the data collected? Was this adequate? Scatterplot: shows the relationship between the values of two quantitative variables. Look for the overall pattern & striking deviations, including outliers. Describe the overall pattern by its form, direction & strength. Look for outliers. W.N. Venables and B.D. Ripley, Modern Applied Statistics with S (119). "Outliers are sample values that cause surprise in relation to the majority of the sample." As commentator Austin Nichols wrote in Stata listserv (February 21, 2008), this definition implies that “such surprise is a function of the model contemplated and the subject-matter knowledge of the researcher, and not an inbuilt characteristic of the data.” “Outlier” Defined . scatter read math || lfit read math 30 40 50 60 70 80 30 40 5 0 60 70 8 0 m ath score re ad ing sco re Fitted valu es Commonly—not always, however—the following two kinds of variables are inspected in a scatterplot: Explanatory (or independent or predictor) variable: predicts, explains, or perhaps causes changes in the response variable....
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This note was uploaded on 07/11/2011 for the course SYA 6305 taught by Professor Tardanico during the Fall '08 term at FIU.

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mm2 - Association between variables Two variables are...

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