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UW-Madison PSYCH 210 - Type I & II Errors and Power

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PSYCH 210 Lecture 14 Outline of Last Lecture I. Hypothesis Testing and z testsa. Type I and II errorsb. Powerc. Factors affecting powerOutline of Current Lecture I. Hypothesis testing and z-testsa. Finish factors affecting powerb. Power calculation for xII. One-sample t-testCurrent LectureI. Hypothesis testing and z-testsa. Four factors that affect poweri. Effect Sizeii. Alpha Leveliii. Choice of one-vs. two-tailed testiv. Sample size (n)1. Effects of Increasing sample size:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Type INo changePowerIncreasesType IIDecreases2. In research, 30 is often a good minimum to useb. Calculating Power for a z-testi. Use Supermax Prison example (Aggression Test Scores)1. Before Tx: μ=500; σ=100a. Std. Error=σM=100/√25 20; n=252. After Tx: M=5603. α=0.05ii. Find p associated with 1-β area1. Find critical values for cutoffs (z’s) (using H0 values)a. z= +/- 1.962. Convert zs to Msa. M=500+/- (1.96)(20)M=460.8, 539.23. Convert M back onto z, using H1 valuesa. z = (M-μ)/σMi. Hypothetical μ! (Sample M from experiment = μ)1. μ=560ii. Use cut-off mean for Mz= (539.2-560)/20 = -1.044. Find power area on tablea. Bodyb. p=.8508II. One-sample t-testa. Rationale for new test (Why do we need a new test?)i. Criteria for z-test1. Must have info on population (μ,σ)2. Single Tx group (one M) a. M >>> μii. What if we don’t have this much info?1. What if we have μ, but don’t know σ?iii. One-sample t-test Criteria1. μ known2. σ unknowna. Substitute s for σ (unbiased estimate)b. Changes to z formula:i. t= (M-μ)/sMii. sM = s/√n3. Single Tx group (one M)b. Use of new tablei. Degrees of Freedom1. s affected by (n-1)ii. The t distributioniii. How to use table1. For nondirectional, don’t cut α in half!a. Same idea as a z cut-off, but instead in terms of t2. Ex) α=0.05, two-tailed, n=25tcrit=+/-2.0643. What if exact df not listed on table?a. Go to next lower value (NOT the same as z-tests when we used the next closest)i. Decrease chance of Type I errorc. Application of hypothesis testing stepsi. Ex) Natural selection and bill length in Darwin’s finches1. Population mean for bill length in Darwin’s ground fincha. μ = 17 mmb. No info on σc. n=10, α = 0.05d. Treatment (natural Tx): El nino and changes in rainfalli. Pictureii. Does the presence of El Nino affect population bill length in Darwin’s finches?2. Processa. Hypotheses i. (Nondirectional)1. H0=172. H1≠17b. Critical value(s) of ti. Must have: 1. α (= 0.05)2. Two-tailed or one-tailed? (two)3. Degrees of Freedom (= 10-1 = 9)ii. tcrit= +/-2.262c. Find observed value of t (tobs)i. t = (M-μ)/sMii. (Find M, s)1. M=22.5, s=5.522. sM=s/√n = 5.52/√10 = 1.75iii. tobs = (22.5-17)/1.75 = 3.15d. Decision about H0i. 3.15 > 2.2621. Reject


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UW-Madison PSYCH 210 - Type I & II Errors and Power

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