BIOL 570 1st EditionExam 2 Study Guide Steps in hypothesis testing. Step 1. Question. Step 2. null (Ho-no effect/difference, specific- state proportion) and alternative hypotheses (Ha-has effect/difference, all other possibilities). 2 sided (p is greater, or p is less)Step 3. Collect a random sampleStep 4. Calculate descriptive statistics (descriptive statistic = results)Step 5. P- valuea. test statistic (“successes”, allows us to see how compatible the data are with Ho)b. Compare the test statistic to a null distribution (a sampling distribution of outcomes for a test statistic under the assumption that Ho is true) c. P-value (shaded area, probability of obtaining data as extreme or more extreme given Ho is true) (take the sum of one tail and multiply by two- P= 2 x Pr[x]…)Step 6. Make a decision regarding the null hypothesis.  If P < α, then reject Ho (if p is small: reject) If P > α, then do not reject Ho (if p is not small: do not reject)Step 7. answer the original question and report results (sample size, test statistic, and P-value) Type I and Type II errors RealityDecision HO true HO falseReject HOType I error correctDo NOT reject HOCorrect Type II error** To reduce Type I error reduce alpha, Reducing alpha increases the chance of Type II errorType II error occurs when: small sample size (not enough evidence), large amount of variability Power = 1- Type II errorOne sided (one tailed) test ← discouraged [HO: P = .5; HA:P <,> .5]1) Only in a rare situation where the other tail is essentially impossible or very unlikelyPopulation proportion: p-hat = X/nWald Method: P-hat ± (value from statistical distribution) x (SE of p-hat) 95% CI= 1.96 MARGIN OF ERRORSampling distribution: how much spread (large spread = large SE)SE= SE (dealing with proportions) =Agresti-Coull method: p’ = (X + 2)/(n + 4)95% CI for p= Binomial Test(provide exact P values)-when there are only 2 categories and n is smallx2 goodness of fit-when there is a large sample size, cannot violate assumptionsUse data to test whether a populationproportion (p) matches the null expectation (pO) for the proportionMethod for comparing observed frequency distribution with an expectedTwo categories: success, failure One variableNull and alternative hypothesisHo: specific proportion between 0 and 1 (po)HA: ≠ po (can be < or >)Ho: same, equalHA: not the sameTest statistic observed number of successes x2= ∑ (Observed-Expected)2 /ExpectedP-value 2 x Pr [number of successes] Probability of getting a x2 value greater than the observed, only use the right tailmean of binomial distribution= n x p Expected: frequency expected in that category (grand total x proportion)Assumptions Binomial distribution (exact prob)Describes the probability of a given number of “successes”(2 outcomes – success, failure) from a fixed number of independent trials when the probability of a success is the same inall trialsNone of the expected numbers should be less than 1, no more than 20% should be less than 5 Binomial coefficient Probabilitiesdf = (# of categories) – 1 – (# of parameters estimated)X: between 0 and nBinomial coeffiecient: Number of unique ordered sequencesContingency Table Test: 2 categorical variables- Allows us to determine whether two (or more ) categorical variables are independent (Ho: independent, HA: dependent) - step 4: create contingency tableIf two events are independent: P (A and B) = Pr (A) x Pr (B)Expected # for any cell= (row total x column total) / grand total df = (# rows -1) x (# columns -1) Odds ratio= OR=1: equally likely, OR> 1: more likely in first group, OR<1: odds are higher in the second group95% CI: if it includes 1, little or no