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One-Way ANOVA

Updated: Jun 27, 2023


Let's consider an example involving a study on the effects of three different exercise programs (A, B, and C) on participants' heart rate. We'll compare the heart rates at three different time points: pre-exercise, immediately post-exercise, and 30 minutes post-exercise.


Here's a table representing the data for three participants:


To calculate the values for the table, we follow these steps:

Calculate the overall mean:

  • Mean Pre-Exercise = (75 + 80 + 70) / 3 = 75

  • Mean Post-Exercise = (120 + 130 + 125) / 3 = 125

  • Mean 30min Post-Exercise = (85 + 90 + 80) / 3 = 85.

Calculate the Sum of Squares (SS):

Calculate the Degrees of Freedom (df):

Calculate the Mean Squares (MS):

Calculate the F-ratio (F):

Calculate the p-value:

Final Table will look like:




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