Peter, Confidence intervals are not additive but variances are. Therefore you can calculate the variances for all your “parts” and then add them up and calculate a confidence interval based upon that. There is one complicating matter and that is whether the parts are independent or not. If two variables (parts) are independent then you can simply add the variances as:
Var(ΣXi) = Σ Var(Xi) This extends easily from two to n variables. The complication arises if the parts are not independent, as they almost certainly are in your case as you have temporal autocorrelation. For two non-independent variables: Var(ΣXi) = Σ Var(Xi) + 2 Σ Cov(Xi, Xj) You can extend this to n variables by calculating all of the pairwise correlations for i < j, adding them up and then multiplying by two. The final variance estimate can then be used to calculate a confidence interval assuming you have good estimates for covariance. Temporal autocorrelation (autocovariance) generally decreases, as the time difference between the variables increases, so not every one of your samples will show a significant correlation with every other sample. This can cause the final variance to be negative due to overestimating large-lag covariances and so they may need to be downweighted. The following link shows that problem and how to potentially correct it using R. http://stats.stackexchange.com/questions/79216/summing-variance-of-autocorrelated-timeseries You will need a statistical program that allows you to calculate autocovariance or autocorrelation. ><(((º> ><(((º> ><(((º> ><(((º> ><(((º> ><(((º> Jim Novak Interim Associate Dean and MSNS Coordinator College of Sciences 2118 Old Main Eastern Illinois University Charleston, IL 61920 (217) 581-3328 (217) 581-7486 [email protected]<mailto:[email protected]> ><(((º> ><(((º> <º)))>< ><(((º> ><(((º> ><(((º> Confidentiality Notice: This e-mail message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized review, use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply e-mail and destroy all copies of the original message. On Apr 13, 2015, at 7:54 PM, Peter Novak <[email protected]<mailto:[email protected]>> wrote: Hello, I am a post grad student undertaking research on the ecology migratory freshwater shrimps in northern Australia. These shrimp undergo an mass migration from the estuary to the river at the end of the wet season and a goal of my research is to estimate the biomass of shrimp moving upstream. I have sampled the migration, to determine hourly migration rates, using fyke nets at periodic interval throughout the night over a period of 6 weeks. I couldn't sample every night and I couldn't leave nets out all night as there were significant crocodile risks. So I have half hourly migration rate data for four nights every week, for 6 weeks. I have completed multiple regression analysis to find the best model (using a range environmental predictor variables) to predict migration rate, and discharge came up as the strongest predictor. So I want to use the equation from the discharge and biomass regression to estimate migration biomass over the entire 6 week period. The end result will be an estimate of the total biomass moving upstream over 6 weeks. Because the total biomass estimate involves summing many predictions (of hourly biomass over each night) I am not sure how to calculate the confidence interval around the final prediction. Can I calculate the confidence interval for each prediction and then sum it to get the total confidence interval estimate? Is there an easy way to do this with a standard stats package such as Statisitica, SPSS or Excel? I would appreciate any feed back. Thank you Peter
