1. Statistics

2. Overview 1. Confidence interval for the mean 2. Comparing means of 2 sampled populations (or treatments): t-test 3. Determining the strength of the relationship between 2 variables: linear regression 4. Test of independence for 2 populations with binary (e.g. yes/no) response: Χ 2 - test

3. Confidence interval Based on mean(μ), sample size (n), & variance (s 2 ) unit #sample 1sample 2 1158 2 31 3145 41512 51614 61523 71517 81510 mean:15.0 95% CI:14.6 to 15.49.1 to 20.9 95% CI:14.4 to 15.65.1 to 22.9 Mean:15.014.0

4. Comparing treatments or populations T-test unit #sample 1sample 2 11821 21819 3 20 41620 51822 619 71719 81720 mean:17.820.0 unit #sample 1sample 2 11820 22426 31115 41617 52022 61820 721 81520 mean:17.920.0 t = -4.27df = 14P = 0.0004t = -1.27df = 14P = 0.12

5. Relationship between variables Linear regression R 2 = 0.76 df = 11 P = 0.0002

6. Test of independence (binary) Χ 2 -test caught colddid not catch cold Medicine15153204 Placebo10232134 25385338 Χ 2 = 0.19 df = 1 P = 0.70

7. Statistical statements 1-population parameter estimate –Based on our sample, the estimated population mean is # (95% confidence interval from # to #). Difference between 2 populations –The mean _____ for pop1 was significantly greater than for pop2 (t-test; t = #, df = #, P = 0.###). Relationship between variables –There was a statistically significant correlation between x and y (linear regression; R 2 = 0.##, df = #, P = 0.###). Test of independence (binary) –We found no convincing evidence for a relationship between x and y (Χ 2 -test; Χ 2 = #, df = #, P = 0.###).