1 / 11

AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

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 :.

kennan-faulkner
Download Presentation

AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Statistical Hypothesis Testing • Two contradictory hypotheses: • Null hypothesis - H0 • Alternative hypothesis – H1 • Three sets of hypothesis: H0 : H1: H0 : H1 : H0 : H1 :

  3. Statistical Hypothesis Testing • Basic significance Test: H0 : H1: Decision rule: Reject H0 if Reject H0 Do not reject H0 Reject H0

  4. 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 _________________________________________________

  5. 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

  6. 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

  7. 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) ^ ^ ^

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

  9. 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

  10. 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.

  11. 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.

More Related