Figure 1.
Hypothetical scenario comparing diversity values with 95% and 84% confidence intervals.
In the example on the left (A vs. B), with 95% confidence intervals, no conclusion can be drawn regarding statistical difference in diversity values at P = 0.05. In the example on the right (A′ vs B′), with 84% confidence intervals but the same means as on the left, we can confidently infer that diversity values differ at P<0.05.
Table 1.
Simulation results of 10,000 iterations calculating the overlap of confidence intervals of various sizes generated from log-normal populations with mean of 12.2 and variance of 0.08 (log-normal parameter values of μ = 2.5 and σ2 = 0.0005).
Table 2.
Appropriate sizes of confidence intervals to simulate P = 0.05 and P = 0.10 size tests for various combinations of log-normal parameter values and associated means and variances.
Figure 2.
Comparison of the use of 95% and 84% confidence intervals in three replicates of our simulations.
For this representative example, the data were created from a log-normal population with a mean of 90.2 and variance of 32.6. In case 1, the both sets of intervals overlap, both suggesting that no significant (NS) differences exist. Note, however, that the 95% confidence intervals will yield an error rate of less than 1%, while the 84% confidence intervals better mimic a 0.05 level test. In case 2, 95% confidence intervals slightly overlap, while 84% ones do not. For this situation, these two approaches would lead to different conclusions: (a) significant differences (*) when considering 84% confidence intervals, and (b) no statistical differences can be inferred using 95% confidence intervals (?). In case 3, none of the sets of intervals overlap, both suggesting that significant differences exist. Note, however, that statistical differences using 95% confidence intervals are assumed with an error rate of less than 1%, while that of 84% confidence intervals better mimic a 0.05 level test.