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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH. Chapter 12: Hypothesis Testing. 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 :.
AAEC 4302ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 12: Hypothesis Testing
Statistical Hypothesis Testing • Two contradictory hypotheses: • Null hypothesis - H0 • Alternative hypothesis – H1 • Three sets of hypothesis: H0 : H1: H0 : H1 : H0 : H1 :
Statistical Hypothesis Testing • Basic significance Test: H0 : H1: Decision rule: Reject H0 if Reject H0 Do not reject H0 Reject H0
Statistical Hypothesis Testing 2 types of mistakes: H0 is true H0 is false (H1 is false) (H1 is true) _________________________________________ Reject H0 Error –Type I Correct Decision __________________________________________ Do not Reject H0 Correct Decision Error – Type II _________________________________________________
Statistical Hypothesis Testing Linear transformation that yields a random variable Z that has a normal distribution ( µ=0, σ=1) • Critical value Zc is determined from Pr(|Z|≥ Zc ) = ά
Statistical Hypothesis Testing • How to conduct the t-test: • State the hypotheses • Choose the level of significance α • Construct the decision rule • Determine the value of the test statistics t* • State and interpret the conclusion of the test
Statistical Hypothesis Testing Example: Yi = B0 + B1X1 + B2X2 + Ui Ŷi = B0 + B1X1 + B2X2 Ŷi = 474.05 + 1.46X1 +26.32X2 Where: Yi = Cotton Yields (lbs/ac) X1 = Phosphorous Fertilizer (lbs/ac) X2 = Irrigation Water (in/ac) ^ ^ ^
Interpreting Summary Output from Excel Total number of observations 134
Some General Remarks • A “rule of thumb” is that: |tj*| ≥ 2 • βj is statistically different from zero, at least at the 95% level of statistical certainty
Some General Remarks • One-tail test vs. two-tail test Advantage • If you properly justify that Xj has only a positive (negative) effect on the dependent variable Yi, 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.
Some General Remarks • One-tail test vs. two-tail test Disadvantage • If you decide that Xj has only a positive effect on Y, than you cannot change your decision after running the regression.