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Minimum detectable difference (MDD)
The minimum detectable difference represents the smallest difference or change that would be statistically significant when comparing different samples. Results depend on the type of statistical model you intend to use to make comparisons, e.g., a t-test, ANOVA, etc. Estimates of variance drive the analysis once you select the level of uncertainty (that is, Type I and II error) that you are willing to live with.
MAIA example | diatom example | how it works | caveats
Because site replicates were unavailable, a bootstrap resampling algorithm was used to estimate the variability of a multimetric index developed for macroinvertebrates. The variance estimate was used to calculate the MDD for the index, that is, how large a difference in index values would indicate a statistically significant change. The MDD was divided into the range of the index to determine the number of categories of biological condition that the index could reliably detect.
Figure
Figure. For a specified power of 80% and an alpha of 0.05, a difference of approximately 2.25 points represented a statistically significant change in the invertebrate index. The index ranged from 0 to 7. Dividing the range by 2.25 yielded 3 categories of biological condition, impaired, fair and good. Grey areas between categories are for borderline index values.
Measurement error of the diatom index was calculated using repeat visits to 26 sites. Sites were visited twice each year, several weeks apart. The minimum detectable difference (MDD) for all sites was 14.4. The diatom index ranged from 9-45; dividing that range by 14.4, the index could detect approximately three categories of biological condition.
Index values from more disturbed sites were more variable through time, possibly reflecting changes in human influence during the year. The MDD for nine least disturbed sites was smaller, indicating less variability and higher index precision.
To estimate MDD you must always start with an estimate of variance. You can estimate variance using replicate samples or with a bootstrap resampling technique illustrated in the MAIA example above. With an estimate of variance in hand, you can evaluate a variety of statistical designs that involve, for example, different numbers of replicates or different statistical methods.
If you can demonstrate that the variable of interest is normally distributed, you can use parametric formulas, which are simple algebraic equations. If you cannot assume normality, a more computer-intensive approach could be used that relies on resampling and randomization.
Be aware that the results are model dependent. If you change the number of replicates or use ANOVA instead of a t-test, you are going to get different results.