1. Statistical Concepts (part III) Concepts to cover or review today: –Population parameter –Sample statistics –Mean –Standard deviation –Coefficient of variation –Standard error –Confidence interval –Estimating totals –Estimating standard deviation, standard error, confidence intervals, coefficient of variation for totals –Sample size estimation You should understand these terms by the end of the lecture and be able to conduct estimations.

2. Estimation Problem: Mice weights (g): CI 95 = Mean ± 1.96 * SE Estimate:

3. Answers

4. Distribution of Means n = 100 1 se 2 se 2.5 % (truth) Mean 1 se 2 se 1 se 2 se 1 se 2 se

5. Elzinga et al. (2001:76) Target/Statistical Population Sample Unit Individual objects (in this case, plants) Density to Totals

6. Estimating Means or Density CI 95 = Mean ± 1.96 * SE CV = Stdev / Mean

7. Estimating Totals of Target Population CI 95 = Total ± 1.96 * SE total CV = Stdev total / Total CV = Stdev mean / Mean ( both CVs are the same value ) N = Total number of sample units

8. Example: Total number of sagebrush

9. Target/Statistical Population Sample Unit Individual objects in sample unit (sagebrush plants) Estimating Total Sagebrush Plants N = 355 n = 25

10. Estimating Totals 6 8 4 2 0 10 5 7 9 2 0 12 5 4 3 8 9 2 0 6 8 11 4 7 3 Mean = 5.40 Stdev mean = 3.48 CV = 0.64 Total = 1917 Stdev total = 1230 SE total = 246 95% CI total = 1435, 2399 Sagebrush per sampled plot

11. Target/Statistical Population Sample Unit Individual objects in sample unit (sagebrush plants) Want Total to be ± 250 plants  our first attempt was ± 482 plants N = 355 n = 25

12. How might we do this ? Calculating Sample Size CI 95 = Total ± 1.96 * SE total 1.96 * SE total = 250SE total = 250 / 1.96

13. Sagebrush Example: We want to get within ± 250 shrubs How many units do we need to sample ? SE = 250 / 1.96 = 127.6 Stdev total = 1230 n = (1230 / 127.6) 2 = 93