# 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 rose: 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 yellow: 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 significance (0.05) and tells you to "Reject the Null Hypothesis because p<0.05" and that the "Means are Different/Means are not the Same".

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

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