Statistical Concepts (part III)

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. Mice weights (g): Estimation Problem: • Estimate: CI95 = Mean ± 1.96 * SE

3. Answers

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

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

6. Estimating Means or Density CI95 = Mean ± 1.96 * SE CV = Stdev / Mean

7. Estimating Totals of Target Population CI95 = Total ± 1.96 * SEtotal N = Total number of sample units CV = Stdevtotal / Total CV = Stdevmean / Mean (both CVs are the same value)

8. Example: Total number of sagebrush

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

10. 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 Estimating Totals Sagebrush per sampled plot Mean = 5.40 Stdevmean = 3.48 CV = 0.64 Total = 1917 Stdevtotal = 1230 SEtotal = 246 95% CItotal = 1435, 2399

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

12. Calculating Sample Size • How might we do this ? CI95 = Total ± 1.96 * SEtotal 1.96 * SEtotal = 250 SEtotal = 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 Stdevtotal = 1230 n = (1230 / 127.6)2 = 93