1. t-tests Comparing the means of 2 independent similar populations

2. 1 versus 2 tailed t-testing 3 possible null hypotheses 1 tailed – the mean is greater than X 1 tailed – the mean is less than X 2 tailed – the mean is equal to X

3. Hypothesis testing Null hypothesis: The means of the two populations are not different Alternative hypothesis: The means are different.

4. Signal to Noise Ratio Metaphor

5. Applying Standard Error to find denominator

6. Formula for computing the t-statistic

7. Compare Computed t value to Critical t value Critical t value affected by… The alpha level chosen (normally.05) The degrees of freedom of the samples N 1 + N 2 – 2 = df In forestry, number of trees sampled makes critical t ≈ 2 for alpha of.05 If computed t is > critical t, then we reject the null hypothesis. Conclusion: means are different at the 95% confidence level.

8. If you fail to reject the null hypothesis You can look up your computed t value for your degrees of freedom and see the certainty level it matches i.e. If your computed t = 1.65 (which doesn’t exceed the critical t value of 1.96) you cannot say the 2 populations are different at the 95% level but you could say they are at the 90% level.

9. T-test in Excel If type equalsThis test is performed 1Paired 2Two-sample equal variance (homoscedastic) 3Two-sample unequal variance (heteroscedastic) T.TEST(array1,array2,tails,type) The T.TEST function syntax has the following arguments: Array1 Required. The first data set. Array2 Required. The second data set. Tails Required. Specifies the number of distribution tails. If tails = 1, T.TEST uses the one-tailed distribution. If tails = 2, T.TEST uses the two-tailed distribution. Type Required. The kind of t-Test to perform.

10. Example 1 2 initially similar forest stands are to be compared 20 years ago, 1 stand was fertilized (treatment) the other was not (control) Today we want to see if the diameters of the fertilized stand are higher than the unfertilized stand

11. Exercise or in class assignment?