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Chapter 8 (3-4), 9. More about Correlation. Today’s Lecture. SD Line Calculating r correlation vs causation. The SD Line. the line the points cluster around passes through the point of averages: (AVGx , AVG Y ) Has slope : . Calculating r (call variables “X” and “Y”).

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Chapter 8 (3-4), 9

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Chapter 8 3 4 9

Chapter 8 (3-4), 9

More about Correlation


Today s lecture

Today’s Lecture

  • SD Line

  • Calculating r

  • correlation vs causation


The sd line

The SD Line

  • the line the points cluster around

  • passes through the point of averages: (AVGx , AVGY)

  • Has slope :


Calculating r call variables x and y

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)


Note the correlation coefficient is unaffected if the units of measurement are changed

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.


Important note correlation does not imply causation

Important Note: Correlation DOES NOT Imply Causation

  • strong association between 2 variables is not enough to justify conclusions about cause and effect


Examples

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?


Important note correlation does not imply causation1

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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