Chapter 3 Scatterplots & Correlation Learning Objectives PDF
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Marian University
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This document provides learning objectives and explanations of scatterplots, bivariate data, and correlation. It discusses how to interpret scatterplots to determine patterns in data relationships, positive and negative associations, and the strength and direction of correlation.
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Chapter 3: Scatterplots and Correlation Learning Objectives LO 1. Bivariate Data 1. Bivariate Data: data recorded on two variables for each individual a. Examine whether there is a relationship between these two variables 2. Response Variable: measures outcome of study; dependen...
Chapter 3: Scatterplots and Correlation Learning Objectives LO 1. Bivariate Data 1. Bivariate Data: data recorded on two variables for each individual a. Examine whether there is a relationship between these two variables 2. Response Variable: measures outcome of study; dependent 3. Explanatory Variable: explain or influence changes in response variable; independent a. When obvious, it’s plotted on x axis of scatterplot LO 2. Scatterplots 1. Scatterplot: displays quantitative bivariate data a. Each variable makes up one axis b. Each individual is a point on the graph 2. In scaling a scatterplot, both variables should be given a similar amount of space a. Plot is a rough square, and points should occupy all the plot space LO 3. Interpreting Scatterplots 1. After plotting variables, we describe the pattern of the relationship in three ways a. Form – linear, curved, clusters, no pattern b. Direction – positive, negative, none i. Positive Association: high values of one variable tend to occur together with high values of the other variables ii. Negative Association: high values of one variable tend to occur together with low values of another variable c. Strength – how closely the points fit the form i. Refers to how much variation or scatter there is around the main form 2. Clear deviations from the pattern (outliers) are also interpreted a. Outlier: data value that has a very low probability of occurrence; falls outside of overall pattern of relationship LO 4. Adding Categorical Variables to Scatterplots 1. Two or more relationships can be compared on a single scatterplot when we use different symbols for groups of points on graph LO 5. Correlation Coefficient 1. Correlation Coefficient (r): measure of direction and strength of relationship a. Calculate using mean and standard deviation of both x and y b. No units LO 6. Facts About Correlation 1. Even if x and y are flipped on scatterplot, the same correlation coefficient and the same pattern will be seen 2. Strength of correlation coefficient is indicated by absolute value a. -1 < r < 1 i. If closer to 1, the correlation coefficient is stronger ii. If closer to 0, the correlation coefficient is weaker 3. Direction of correlation coefficient is indicated by sign of r (positive or negative) 4. Correlation coefficient is not resistant to outliers because it’s calculated using means and standard deviations a. Moving even one point away from the pattern changes the correlation
