One-Way ANOVA Post Hoc Tests in Excel

Even Non-Statisticians Can Perform ANOVA Post Hoc Tests

After a one-way ANOVA finds a significant difference in means, Post Hoc testing helps identify which of the differences are significant.

Post Hoc Tests  

Post Hoc tests compare the differences between the means with various factors to identify significant differences. There are a number of ways that these factors are determined, but LSD, HSD and Scheffe's are three of the more common ones:

  • LSD - Fisher's Least Significant Difference
  • HSD - Tukey's Honestly Significant Difference reduces Type 1 error.
  • Scheffe's is the most conservative of the three
 

Note: Excel does not do post hoc tests; QI Macros adds this functionality.

Example Using QI Macros Add-in and Data From Montgomery's Intro to SPC book

Using the tensile strength data in columns A to F, QI Macros calculations are shown in columns G to P. The Post Hoc tests are in cells M2:P8.

Interpretation of Results

Since the p-value is less than 0.05, the Means are considered Different. If the mean difference is greater than LSD, HSD or Scheffe's, the difference is considered significant.

Since Scheffe > HSD > LSD, QI Macros identifies significant differences by shading the results as follows:

  • greater than Scheffe's it is shown in red
  • less than Scheffe but greater than HSD it is shown in rose
  • less than HSD but greater than LSD, it is shown in yellow
  • less than LSD, no shading

In the example below the difference between these tensile strengths is:

  • greater than Scheffe (5.797) so they are shaded in red: 5% and 15%, 5% and 20%
  • less than Scheffe (5.797) but greater than HSD (4.122) so they are shaded in yellow: 5% and 10%, 10% and 20%, 15% and 20%
  • less than HSD (4.122) but greater than LSD (3.072) so they are shaded in rose: none
  • less than LSD (3.072) so they are not shaded at all: 10% and 15%

What's Cool About QI Macros One-Way ANOVA Post Hoc Tests? 

Unlike other statistical software, QI Macros is the only SPC software that compares the p-value (0.000) to the signficance (0.05) and tells you to "Reject the Null Hypothesis because p<0.05" and that the "Means are Different".

Then the Post Hoc tests tell you which differences are significant.


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