Hypothesis Testing - Null Hypothesis Decision Strategy (NHDS) PDF

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Hypothesis Testing - Null Hypothesis Decision Strategy (NHDS) Thursday, October 31, 2019

15:41

(…background information…) What can you conclude about the effect of vaping on lung function? SAMPLE OUTCOMES VARY!!! Using the Null Hypothesis Decision Strategy (NHDS) • Step 1: State hypothesis about mu (the parameter of the population of interest) ○ The Null Hypothesis (H0): the hypothesis TO BE TESTED. "Null" - "no effect'" ○ The Alternative Hypothesis (HA): the research hypothesis. This is NOT the hypothesis being tested • Step 2: Obtain a random sample from population and calculate (the statistic of interest) • Step 3: Find the probability of sample means this distance (2.85 vs. 3.00 = 0.15L) or more from the hypothesizes mu • Step 4: State conclusions about H0 and the research hypothesis ○ H0 is either rejected ("findings are statistically significant") or retained ("findings are not statistically significant"), based on probability of the sample outcome being due to a sampling error ○ If findings are statistically significant (H0 rejected), we have support for the research hypothesis. If findings are not statistically significant (H0 not rejected), we do not have support for the research hypothesis.

Importance of Having a Pre-Selected "Significance" Level for the Test • i.e. the alpha level

• To avoid being arbitrary about conclusion about H0… select in advance how improbable the outcome must be to reject H0 • Alpha is often 0.05 (p less than 5%) • The critical value of Z (Zcrit) for alpha of 0.05 can be used to evaluate the test outcome…Zcrit = +/-1.96 Type I and Type II Errors • Type I Error: Failing to accept H0, when H0 is true ○ Occurs when we get an extreme test statistic as a result of sampling error ○ P(Type I Error) = alpha ○ Alpha specified by investigators • Type II Error: Failing to reject H0, when H0 is false ○ Must be calculated ○ P(Type II Error) = beta

"Power" - The Probability of Rejecting a False Null Hypothesis • Power is determined by: ○ N - sample size ○ Alpha level - probability of Type I error ○ Signa - the population standard deviation ○ One vs. Two-tailed test ○ Effect size Effect Size: How "Big" is the Effect, in Terms of Standard Deviations? • Cohen's d • D = (sample mean - population mean) / (population standard deviation) = (x-bar - mu) / (sigma) Testing Hypotheses About Population Parameters • Categorical Variables (population proportions): z statistic • Quantitative Variables (population means): ○ One sample: ▪ Z statistic; sigma known ▪ T statistic; sigma unknown ○ Two samples: ▪ Independent samples ▪ Dependent samples ○ >2 samples ▪ F statistic ○ Relationship ▪ R statistic • ALWAYS TEST THE NULL HYPOTHESIS - EXAM MATERIAL...