Statistics Lecture 5: Null and Alternative Hypotheses

Lecture 5: Null and Alternative Hypotheses Hypothesis: an idea or theory about a population, OR a decision-making process for evaluating claims about a population Review: Type 1 and Type 2 Error: -​ Type 1 Error: you said there was a difference when there really was no difference = false positive -​ Alpha (a): the probability of committing a type 1 error (1-a) -​ Normally set at 0.5 -​ Type 2 Error: you said there was no difference but actually there was a difference = false negative -​ Beta (B): the probability of committing a type 2 error (1-B) -​ Normally set at 0.2 Types of Hypotheses -​ Null Hypothesis (Ho): a claim that there is no difference between the population parameter and the hypothesized value -​ No observed effect -​ No difference between two or more interventions -​ P >0.05 -​ Alternative Hypothesis (Ha): a claim that disagrees with the null hypothesis, stating that there is indeed a difference -​ There is an observed effect -​ There is a difference -​ P <0.05 -​ Hypothesis testing is designed to detect evidence against the null hypothesis rather than prove your hypothesis true -​ The evidence is P <0.05 -​ p-value is the probability that your results are due to chance. P should be less than 0.05 in order to prove your hypothesis is not due to chance. -​ If the P is less than the alpha then it is statistically significant (null is false), if P is more than alpha it is not statistically significant (null is true) Power -​ Power: the chance that you will correctly reject a false null hypothesis -​ 80% power implies a 20% chance of making a type 2 error (or 20% chance of missing a true effect) -​ If power is high, then the chance of making a type 2 error is reduced -​ Increase the sample size to increase the power and reduce type 2 error Basic Elements of Testing Hypothesis 1.​ State null and alternative hypothesis 2.​ Choice of appropriate level of significance 3.​ Test Statistic (Formula): Application of sample results in the formula to calculate the value of test statistic use for decision purpose 4.​ Rejection Region (Critical Region): Based on alternative hypothesis and level of significance (a) 5.​ Decision: Decide whether or not to reject the null hypothesis Assumptions for Testing Hypotheses -​ Random sampling -​ Population is normally distributed (or n is greater than or equal to 30) -​ Population variance or sample variance is approximately equal to population variance when n is large Research Process -​ Generating the idea -​ Generating the hypothesis -​ Deciding on risk of type 1 or type 2 error -​ Collecting the data -​ Analyzing the data -​ Deciding whether data supports or rejects the null -​ Dissemination -​ Etc. (blah blah it's a long process)