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I'm checking the effect a specific substance has in the elongation of the root of variousplants of the Solanum genus. I had my plants grow in soil with different concentration of hormones. My results are quite obscure from what I expected, so I'm guessing that at very low concentrations the substance doesn't have any effect. However, I did noticed a small difference in length from those samples that grew up without the substance. Is there any statistical method to prove that the variations I observe are not important?

user259462
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  • Just out of curiosity; do you have a plot showing the elongation as function of consentration for all your samples? Would be very nice to see this and this could also help to give you a better answer. – Kibble Nov 03 '15 at 19:58

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The first problem is, how do you quantify "not important?"

For example, if we run a clinical trial comparing the treatment effect of a new experimental drug against an existing drug that is the current standard of care, we might find that for a very large trial with thousands of patients, the experimental drug is better by only 1% compared to the existing drug, whereas the existing drug already achieves an 85% response rate. In that context, a clinician would almost certainly decide that the new drug's efficacy isn't any better (or worse) than the existing treatment. But with thousands of patients, you could statistically detect that 1% treatment difference. It just isn't clinically significant.

Similarly, in your case, you have to tell us what extent of variability is regarded as "not important." Is a variability of as much as 10% from the mean in either direction the threshold of "importance?" 20%? Or is it measured in absolute units rather than a ratio; e.g., a variability of +/- 5mm is not important? This threshold is something that is decided a priori and with the use of specific knowledge about the subject. It can be informed by previous studies or analyses; but it is almost always a decision based on a combination of subject-specific knowledge and prior statistical analysis.

Once you decide this threshold, you would perform a equivalence test. But depending on whether the threshold is a ratio or a difference, the form of the statistical hypothesis is different. For example, for a difference, the hypothesis would be structured like $$H_0 : |\mu - \mu_0| > \Delta \quad \text{vs.} \quad H_a : |\mu - \mu_0| \le \Delta,$$ where $\Delta$ is the equivalence margin that establishes the extent to which the true mean is allowed to differ from the hypothesized mean.

heropup
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