Basic Concepts
To carry out Scheffé’s test follow the following steps:
- Calculate the planned comparison t-test
- Square the t-statistic to get F (since F = t2)
- Find the critical value of F with dfB, dfW degrees of freedom for the given value of α and multiply it by dfB. Thus the critical value is dfB* F.INV.RT(α, dfB, dfW).
- If F > the critical value then reject the null hypothesis
Since Scheffé’s test is very conservative, it is not recommended for pairwise comparisons where better tests are available, but it can be useful for more complicated comparisons where the other unplanned tests don’t apply.
Data Analysis Tool
Real Statistics Data Analysis Tool: Scheffé’s test can be carried out using the Single Factor Anova and Follow-up Tests data analysis tool provided by the Real Statistics Resource Pack. We show how this is done in the following example.
Example 1: Carry out the test in Example 2 from Planned Comparisons for ANOVA using Scheffé’s test.
We can perform this test using the Single Factor ANOVA tool. When the dialog box shown in Figure 1 of ANOVA Analysis Tool appears, fill in the Input Range with I21:L29, make sure that the Column headings included with data option is checked, choose the Scheffe’s option, and click on the OK button.
A report similar to that shown in Figure 1 will appear but with no numbers in the shaded range O23:O26. You must now enter the contrast values. Setting the contrast coefficients for Method 1 and 2 to -0.5 and the contrast coefficient for Method 4 to 1, we get the output shown in Figure 1.
Figure 1 – Scheffé data analysis for Example 6
This figure shows there is no significant difference between Method 4 and the average of Methods 1 and 2.
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
Reference
Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf