Power (Reading Packet Sect III)Power(cont.)2x2 Decision Table (Ho: No disease present)What Influences Power?Example from last Wed (salary)Ex (cont.)Slide 8Other Influences on PowerSlide 10Determining PowerStat v Practical SignificancePower Power (Reading Packet Sect III)(Reading Packet Sect III)Mon, March 29Mon, March 29ththPowerPowerThe ability of your statistical test to The ability of your statistical test to correctly reject the null hypothesiscorrectly reject the null hypothesisRemember, the null hypothesis Remember, the null hypothesis generally states there is no effect or no generally states there is no effect or no differences between your sample & popdifferences between your sample & popPower refers to the Power refers to the power to find any power to find any differences that truly existdifferences that truly existWant to maximize powerWant to maximize power(cont.)(cont.)When we fail to reject Ho, we want to When we fail to reject Ho, we want to be sure it is because there are truly be sure it is because there are truly no differences that exist (or no effect)no differences that exist (or no effect)……Not because our statistical test didn’t Not because our statistical test didn’t have enough power to find a difference have enough power to find a difference that is actually there.that is actually there.In your 2x2 Decision Table,In your 2x2 Decision Table, power is = 1-probability of a Type 2 errorpower is = 1-probability of a Type 2 error2x2 Decision Table 2x2 Decision Table (Ho: No disease present)(Ho: No disease present)RealityRealityYou You DecidDecideeHo is Ho is correctcorrectHo is incorrectHo is incorrectReject Reject HoHoType 1 Type 1 error error (alpha); (alpha); False False PosPosCorrect! Correct! (POWER)(POWER)Fail to Fail to Reject Reject HoHoCorrect!Correct!Type 2 error Type 2 error (beta); (beta); False False NegNeg..What Influences Power?What Influences Power?4 factors that affect power:4 factors that affect power:1) 1) Alpha levelAlpha level: increasing alpha (chance : increasing alpha (chance of Type 1 error), increases powerof Type 1 error), increases powerGoing from alpha = .01 to alpha = .05, gives Going from alpha = .01 to alpha = .05, gives you larger chance of finding a you larger chance of finding a difference/effect that is really there.difference/effect that is really there.Consider effect on your critical region of .01 Consider effect on your critical region of .01 v .05 – region becomes larger by using alpha v .05 – region becomes larger by using alpha = .05, more likely to reject Ho= .05, more likely to reject HoExample from last Wed Example from last Wed (salary)(salary)Compare ybar = $24,100 w/ Compare ybar = $24,100 w/ yy = $28,985 = $28,985 (and (and y = $23,335, N=100)y = $23,335, N=100)For 1-sample z test, z = (ybar - For 1-sample z test, z = (ybar - y)y) / / ybarybar, where , where ybar ybar = = y / sqrt N), or y / sqrt N), or ybar = ybar = 23,335/ sqrt (100) = 2333.5Z obtained = 24,100 – 28,985 / 2333.5 = -2.09Book’s approach  look up z = -2.09 in Appendix (Col C), find its probability = .0183If alpha = .05 (1 tail) use .0183, then p < , so REJECT HoEx (cont.)Ex (cont.)Another approach is to find the critical Another approach is to find the critical z value associated with an alpha level:z value associated with an alpha level:When | z obtained | (from formula) > | z When | z obtained | (from formula) > | z critical| (from table) critical| (from table)  REJECT Ho REJECT Ho = .05, 1 tail, z critical = 1.645 = .05, 1 tail, z critical = 1.645 oror –1.645; –1.645; = .05 2 tails, z criticals = -1.96 = .05 2 tails, z criticals = -1.96 andand 1.96; 1.96;= .01, 1 tail, z critical = 2.33 = .01, 1 tail, z critical = 2.33 oror –2.33 –2.33= .01, 2 tails, z criticals = 2.57 = .01, 2 tails, z criticals = 2.57 andand –2.57 –2.57Ex (cont.)Ex (cont.)Using this approach, z obtained = -2.09, Using this approach, z obtained = -2.09, z critical (z critical ( = .05, 1 tail) = -1.645, since = .05, 1 tail) = -1.645, since obtained > critical obtained > critical  Reject HoReject HoSame conclusion as for p < alphaSame conclusion as for p < alphaNotice critical region Notice critical region becomes smallerbecomes smaller as as alpha level becomes smalleralpha level becomes smallerAnd as you move from 1 tail to 2 tailsAnd as you move from 1 tail to 2 tailsHarder to reject Ho w/ smaller critical regionHarder to reject Ho w/ smaller critical regionOther Influences on PowerOther Influences on Power2) Sample Size – larger N, more power2) Sample Size – larger N, more powerWith larger sample size, more likely a With larger sample size, more likely a representative sample with less errorrepresentative sample with less error3) 1- v 2-tailed test – 1-tailed test has more 3) 1- v 2-tailed test – 1-tailed test has more powerpowerThe critical region for rejecting Ho is larger w/1-The critical region for rejecting Ho is larger w/1-tailed test (don’t have to split into 2 tails)tailed test (don’t have to split into 2 tails)4) Effect size – larger effect size, more power4) Effect size – larger effect size, more powerRefers to the effect of the manipulation (in an Refers to the effect of the manipulation (in an experiment) or the difference betw sample & popexperiment) or the difference betw sample & pop(cont.)(cont.)If you have a strong manipulation, will If you have a strong manipulation, will create larger differences among groups create larger differences among groups or betw sample & population – or betw sample & population – easier to see the effect if it’s really thereeasier to see the effect if it’s really thereDetermining PowerDetermining PowerFailure to reject Ho could be due to many Failure to reject Ho could be due to many things:things:There really is no effect / no differenceThere really is no effect / no differenceYour study had low reliability, validity, etc.Your study had low reliability, validity, etc.Your study didn’t have enough powerYour study didn’t have enough powerHow can we determine the amount of How can we determine the amount of power of our study?power of our study?Can’t be set by you (as alpha can), but can Can’t be set by you (as alpha can), but can calculate after the fact or try to