How to calculate input values from pilot data
1. Transform the response variable, e.g. count per unit effort, to approximately follow a normal distribution. For example, if your data are counts that follow a Poisson distribution, a log transformation might be appropriate. If your data cannot be transformed to follow a normal distribution (e.g. zero-inflated), this tool might not be appropriate.
2. Center the response variable to a mean of 1, by dividing all (transformed) observations by the global mean. Use the transformed, centered responses for all following calculations.
3. Box 1: Find the mean for each site across all years and visits to that site. Calculate the SD among sites in their mean values and choose the nearest value (SD_mu).
4. Box 2: Calculate the site-specific population trends as the proportional change per year (e.g. using linear regression with an effect of year; Trend). Calculate the SD among sites in the trend and choose the nearest value (SD_trend).
5. Boxes 3 and 4: For each site, calculate CV across years from a detrended time series to represent annual variation (Gibbs JP. 2000. Monitoring Populations. Pages 213–252 in L. Boitani and T. K. Fuller, editors. Research Technique in Animal Ecology - Controversies and Consequences. Columbia University Press, New York, New York, USA):
First, for each site: 1) calculate the mean observation for each year with pilot data (if only one survey was conducted, this is simply the observation from that survey). This will be X[s,y] for each site s and year y. 2) Fit a linear regression for each site with X[s,] as the response and the year as the explanatory variable. 3) Get the annual coefficient of variation (CV) for this site by dividing the SD of the residuals from the model by the mean observation across all years, and take the absolute value: siteCV[s] = |SD(residuals)/mean(X[s,])|. Finally, average siteCV across sites and choose the nearest value in Box 3 (CV_yr). Also calculate the SD of siteCV across sites and choose the nearest value in Box 4 (SD_CV_yr).
6. Box 5: Calculate observation error as a proportion of the mean (Obs_err). The appropriate calculation will vary depending on your sources of observation error. If you have several replicate surveys within a survey period, you could calculate the SD among surveys to estimate observer error. If you don't have replicate surveys or some other measure of error, you'll want to choose your best guess or a moderate value (not zero).
7. Box 6: Choose the number of years that you plan to survey during the monitoring program. Alternatively, this can be the number of intervals between surveys. For example, if you plan to survey every 2 years over 20 years, you will have 10 intervals (year 2, 4, 6, 8... 20). Thus the value of this box would be set to 10. If you use an interval other than one year, be sure to adjust the trend as well: to monitor a 10% change over 20 years with annual surveys, the per-interval trend is 0.01 (to be selected in Box 8 below); but if you survey every 2 years, the per-interval trend is 0.02. If you're interested in annual change, the number of visits per year would not affect the survey interval. However, if you are monitoring a change within a single year (say flowering phenology), your interval could be days, weeks, or months. The number of intervals is an important component of sample size when detecting a trend over time.
8. Box 7: Choose the number of sites that you plan to survey for the monitoring program. TrendPowerTool assumes that the same sites are monitored every year.
9. Box 8: Choose the population trend that you want to detect, expressed as a proportional change per year (e.g. 0.05 is a 5% change per year), or per the interval of interest (e.g. per 2 years if surveys will be conducted every second year). If you want to detect a 50% total change over 10 years, that would be equivalent to a 5% change per year. Given the data standardization steps above, the power to detect a negative trend will be the same as the power to detect a positive trend. A smaller trend (closer to 0) will be more difficult to detect.
10. Box 9: Choose the desired power, i.e. the probability of detecting a statistically significant trend in the correct direction (positive or negative). The default, 0.80, is often used but may not always be appropriate.
If you have insufficient data to calculate any of the above, test a range of values, or select "Any" to view the results for all values that are available in TrendPowerTool. (Select "Any" for only one parameter at a time.)