Confidence limits (95% or 99%) are calculated either for mean and proportion. In either case the underlying distribution is Normal when sample size is adequately large. Fiducial limts is applicable only in the case of lethal dose required for 50% mortality(LD50) or 90% mortality (LD90). The underlying distribution is logistic growth or S-shaped curve. Even though we transform the data (% values into probit and dose values into logdose) to fit a linear regression equation (Y(probit)=a+b*logdose), the upper limit of conventional confidence limits may be beyond the value (say 110%), which is not true in the case of logistic growth. In such situations Fiducial limits is more appropriate than confidence limits.

Dr.P.Vanamail

[email protected]

If we calculate 95% confidence limits for mean or proportion, the interpretation is that we can be 95% confident that the true mean or proportion at population level will lie between lower limit and upper limit of confidence limits. Therefore, the more samples will give us narrow margin of confidence limits. In the similar way, when we calculate 95% fiducial limits for LD50, the interpretation is that with 95% confident the required lethal dose to achieve 50% mortality  in the study population species will be within  the lower limit and upper limit. 

Dear Perumal, Thank you very much for your explanation.

Professor Vanamail:

How could I know if my fiducial limits are narrow enough? Is there a percent of variation acceptable between the limits and the LD50 value?

Thank you in advance.

Very Good Dr. Vanamail!!!

Hello Dr. Perumal,

Will you please explain the significance of Heterogeneity in computing LC 50 value?

suppose FL is ranged 2.41-9.72 what does it signify?

regards