Winning the Biodiversity Jackpot and Losing It: Reflections on Resource Over-exploitation Degradation, and Recovery

Biology 180 Lecture 1: Hypothesis Testing

Jonathan A. Anticamara, Ph.D.Office: IB 118 Email: jonathan.anticamara@gmail.comSource: Groombridge B. And Jenkins M (2002) World Atlas of Biodiversity Associates. University of California Press

1.1 HypothesisHypothesis a statement about a distribution (e.g., the distribution is normal); or a statement about its underlying parameter (e.g., = 50); or a statement about the relationships between probability distributions (e.g., there is no statistical relationship); or its parameters (e.g., 1 = 2); (put simply: a statement about one or more populations)

For Discussion:What are the differences between Scientific Questions, Research Objectives, and Hypotheses?

What is a Null Hypothesis?

21.2 Null and Alternative HypothesisNull Hypothesis is the Hypothesis to be tested, is usually expressed in null form (i.e., no relationships or no differences), and is expressed as H0

Definition 3: Alternative Hypothesis is a Hypothesis that in some sense contradicts the Null Hypothesis, and is expressed as HA. (put simply: a statement of what we believe is TRUE if the data rejects the Null Hypothesis)

For Discussion:Why is Hypothesis testing important?

1.3 Hypothesis Testing: ConsiderationsData the nature of the data that form the basis of the testing procedure.

Assumptions the testing procedures are often modified depending on the assumptions.

Stating the Null and Alternative Hypotheses the Null Hypothesis is the hypothesis to be tested; and the Alternative Hypothesis is a statement of what we believe is TRUE if the data rejects the Null Hypothesis.

1.4 Rules for Stating Statistical Hypotheses An indication of equality (e.g., =, , ) must appear in the Hypothesis.

For example:

H0: = 50

HA: 50

1.5 Rules of Thumbs Hypothesis TestingWhat you hope or expect to be able to conclude as a result of the the test should be placed in the Alternative Hypothesis;

The Null Hypothesis should contain statement of equality;

The Null Hypothesis is the Hypothesis that is tested;

The Null and Alternative Hypothesis are complimentary/contradictory.

Question: Can you PROVE anything with statistics?

1.6 Statistical EvidenceA Null Hypothesis is often concerned with a parameter or parameters of population/s. However, it is often impossible or too costly to obtain the entire Population Data. Thus, statistical decisions are often made based on Sample Data.

Test Statistic is a statistic that can be computed from the Sample Data (e.g., x) and can be used to measure the difference between (1) the Sample Data and (2) What is expected if the Null Hypothesis is TRUE.

1.7 Statistical Decisions and Errors

1.8 Hypothesis Testing: Alpha

Example 1A

1.9 Hypothesis Testing: BetaExample 1B

1.10 Steps in Hypothesis Testing Step 1. Formulate Null Hypothesis and an Alternative Hypothesis;

Step 2. Design the experiment and obtain data;

Step 3. Choose a Test Statistic;

Step 4. Summarize findings and appropriate conclusions.

1.11 Rejection Region

1.12 One-Sided vs. Two-Sided Rejection

1.13 Test Significance

1.14 P-Values - A

1.15 P-Values B

1.16 P-Values Interpretation