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Understanding Correlation: Scatterplots, Coefficients, and Causation in Statistics

This guide explores the concept of correlation in statistics, focusing on how to construct a scatterplot using summer temperature and absence data. You'll learn to calculate the correlation coefficient with step-by-step instructions for using a calculator. The significance of this coefficient is analyzed through hypothesis testing and critical values, as well as the essential distinction between correlation and causation. Important considerations include assessing direct and reverse relationships and identifying other influencing factors.

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Understanding Correlation: Scatterplots, Coefficients, and Causation in Statistics

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  1. STA 2023 Section 9.1 Correlation

  2. Correlation

  3. Types of Correlation

  4. Constructing a Scatterplot • Example 1: The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a scatter plot for the data.

  5. Correlation Coefficient

  6. Example 2: Use the data from example 1 do calculate the correlation coefficient. • Steps: • Press 2nd, then 0 to enter the catalog. Scroll down until you see DiagnosticOn. Press enter to copy the command to the home screen. Then press enter. You only need to do this once to setup your calculator to find r. • Go to your list and enter your data in List 1 and List 2. • Exit from the list. Then, press STAT, arrow over to CALC and choose 4: LinReg(ax+b) • With the command copied type “L1,L2” after it. • On the read out, look at the very last line for r.

  7. Testing a Population Correlation Coefficient • After calculating the correlation coefficient, we want to know if we can make an inference based on the data we have. • To determine whether the population correlation coefficient is significant, we use the critical values in Table 11. • If |r|is greater than the critical value, there is enough evidence to decide that the correlation is significant. • Example 3: Using the data from example 1 and the result from example 2, is the correlation coefficient significant?

  8. Hypothesis Testing for a Population Correlation Coefficient

  9. Correlation and Causation • The fact that two variables are strongly correlated does not imply a cause-and-effect relationship between the variables. • If a significant correlation exists, a researcher should ask the following: • Is there a direct cause-and-effect relationship? • Is there a reverse cause-and-effect relationship? • Does another factor influence the two variables? • It the relationship just coincidence?

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