1. 1 AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 12: Hypothesis Testing

2. 2 Statistical Hypothesis Testing Two contradictory hypotheses: –Null hypothesis - H 0 –Alternative hypothesis – H 1 Three sets of hypothesis: H 0 : H 1 : H 0 : H 1 : H 0 : H 1 :

3. 3 Statistical Hypothesis Testing Basic significance Test: H 0 : H 1 : Decision rule: Reject H 0 if Reject H 0 Do not reject H 0 Reject H 0

4. 4 Statistical Hypothesis Testing 2 types of mistakes: H 0 is trueH 0 is false (H 1 is false)(H 1 is true) _________________________________________ Reject H 0 Error –Type ICorrect Decision __________________________________________ Do not Reject H 0 Correct DecisionError – Type II _________________________________________________

5. 5 Statistical Hypothesis Testing Linear transformation that yields a random variable Z that has a normal distribution ( µ=0, σ=1) Critical value Z c is determined from Pr(|Z|≥ Z c ) = ά

6. Statistical Hypothesis Testing 6 How to conduct the t-test: 1)State the hypotheses 2)Choose the level of significance α 3)Construct the decision rule 4)Determine the value of the test statistics t* 5)State and interpret the conclusion of the test

7. 7 Statistical Hypothesis Testing Example: Y i = B 0 + B 1 X 1 + B 2 X 2 + U i Ŷ i = B 0 + B 1 X 1 + B 2 X 2 Ŷ i = 474.05 + 1.46X 1 +26.32X 2 Where:Y i = Cotton Yields (lbs/ac) X 1 = Phosphorous Fertilizer (lbs/ac) X 2 = Irrigation Water (in/ac) ^^ ^

8. 8 Interpreting Summary Output from Excel Total number of observations 134

9. 9 Some General Remarks A “rule of thumb” is that: |t j * | ≥ 2  β j is statistically different from zero, at least at the 95% level of statistical certainty

10. 10 Some General Remarks One-tail test vs. two-tail test Advantage If you properly justify that X j has only a positive (negative) effect on the dependent variable Y i, then the one-tail test will help you reject the null hypothesis. Under a one-tail test, the critical t-value is smaller than the critical t-value under a two-tail test.

11. 11 Some General Remarks One-tail test vs. two-tail test Disadvantage If you decide that X j has only a positive effect on Y, than you cannot change your decision after running the regression.