Conclusions from scab1.sas

Following up the overall test with all pairwise comparisons. Though correction for multiple testing is never mentioned in a plain language conclusion, different conclusions are given below for No correction, Tukey correction, Bonferroni correction, and Scheffé correction.

Experimental condition had an effect on the average amount of scab disease. Specifically,

• No correction: An application of 300 or 1200 pounds of sulphur per acre in the Fall, or 1200 pounds per acre in the Spring resulted in less scab disease on average than the Control. Twelve hundred pounds and 300 pounds in the Fall were both superior to 300 pounds or 600 pounds in the Spring.
• Tukey: An application of 300 or 1200 pounds of sulphur per acre in the Fall resulted in less scab disease on average than the control.
• Bonferroni: An application of 300 or 1200 pounds of sulphur per acre in the Fall resulted in less scab disease on average than the control.
• Scheffé: An application of 1200 pounds of sulphur per acre in the Fall resulted in less scab disease on average than the control.

Custom Tests: Give separate plain language conclusions for No correction, Bonferroni and Scheffé. Include the initial test in the Bonferroni family.

1. Is amount of scab disease affected by experimental treatment?
   • No correction: Yes.
   • Bonferroni: There is not quite enough evidence to conclude that treatment had an effect.
   • Scheffé: Yes.
2. Is the average amount of scab disease for each treatment different from the average amount of scab disease in the control condition? That's six tests.
   • No correction: Compared to no added sulphur, there was less scab disease with an application of 1200 pounds of sulphur per acre in the Spring, 300 pounds in the Fall or 1200 pounds in the Fall.
   • Bonferroni: An application of 300 or 1200 pounds of sulphur per acre in the Fall resulted in less scab disease on average than the control.
   • Scheffé: An application of 1200 pounds of sulphur per acre in the Fall resulted in less scab disease on average than the control.
3. Is the average amount of scab disease in the 3 Spring conditions different from the control condition? This is one test.
   • No correction: There is a suggestion that averaging over the different amounts of sulphur, application in the Spring may have resulted in less average scab disease, compared to no application of sulphur at all. However, this is a borderline trend that could be just noise.
   • Bonferroni: There is no convincing evidence of a real difference in scab disease infestation between the control condition and application of sulphur in the Spring.
   • Scheffé: These results are consistent with no real difference in scab disease infestation between the control condition and application of sulphur in the Spring.
4. Is the average amount of scab disease in the 3 Fall conditions different from the control condition? This is one test.
   • No correction: Averaging across different amounts of sulphur, there was less scab disease on average when the sulphur was applied in the Fall, compared to the control condition.
   • Bonferroni: Same conclusion.
   • Scheffé: Same conclusion.
5. Is the average amount of scab disease in the 3 Spring conditions different from the average amount of scab disease in the 3 Fall conditions? This is one test.
   • No correction: There was less average scab disease infestation when the sulphur was applied in the Fall.
   • Bonferroni: Averaging across different amounts of sulphur, there was no evidence that applying the sulphur in the Fall or Spring resulted in different levels of scab disease infestation.
   • Scheffé: Same conclusion as for Bonferroni.
6. Is amount of scab disease affected by the amount of sulfur when the sulfur is applied in the Spring? This is one test.
   • No correction: There is no evidence that the amount of scab disease was affected by the amount of sulfur when the sulfur was applied in the Spring.
   • Bonferroni: Same conclusion.
   • Scheffé: Same conclusion.
7. Is amount of scab disease affected by the amount of sulfur when the sulfur is applied in the Fall? This is one test.
8. No correction: There is no evidence that the amount of scab disease was affected by the amount of sulfur when the sulfur was applied in the Fall.
9. Bonferroni: Same conclusion.
10. Scheffé: Same conclusion.
11. For each amount of sulphur, is the average amount of scab disease different depending on whether the treatment is applied in Fall or the Spring? That's three tests.

• No correction: Three hundred pounds of sulphur applied in the Fall did a better job of suppressing scab disease than 300 pounds in the Spring.
• Bonferroni: For all three amounts of sulphur, there is no evidence that applying the sulphur in the Spring has a different result than applying it in the Fall.
• Scheffé: Same conclusion as for Bonferroni.

Notice how the conclusions from different tests need not be logically consistent with one another, even when they are simultaneously proteced against Type I error.