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Understanding Correlation: Calculating r and Distinguishing It from Causation

In today's lecture, we will explore the concept of correlation, specifically how to calculate the correlation coefficient (r) using the Standard Deviation Line (SD Line). We will walk through the steps to find the averages and standard deviations of two variables, standardize them, and calculate the correlation. Additionally, we will emphasize the crucial distinction between correlation and causation, illustrating with examples like firefighters and property damage, as well as shoe sizes and exam scores. Understanding this difference is vital for drawing accurate conclusions.

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Understanding Correlation: Calculating r and Distinguishing It from Causation

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Presentation Transcript

  1. Chapter 8 (3-4), 9 More about Correlation

  2. Today’s Lecture • SD Line • Calculating r • correlation vs causation

  3. The SD Line • the line the points cluster around • passes through the point of averages: (AVGx , AVGY) • Has slope :

  4. Calculating r(call variables “X” and “Y”) • Step 1: Calculate AVGx and AVGy • Step 2: Calculate SDx and SDy • Step 3: Standardize each variable • Step 4: Find average of products of z-scores (standard scores)

  5. NOTE: The Correlation Coefficient is unaffected if the units of measurement are changed Example: Correlation between height and weight remains the same whether height is measured in inches, cm., feet, etc.

  6. Important Note: Correlation DOES NOT Imply Causation • strong association between 2 variables is not enough to justify conclusions about cause and effect

  7. Examples Strong association between: • number of firefighters and amount of damage • Does sending more firefighters cause more damage? • shoe size and score on a reading comprehension exam for elementary school children • What’s the explanation? • SAT and GPA scores • What’s the explanation?

  8. Important Note: Correlation DOES NOT Imply Causation • strong association between 2 variables is not enough to justify conclusions about cause and effect • best way to get evidence that X causes Y is through a controlled experiment

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