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Power (Reading Packet Sect III) Mon, March 29 th.

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1 Power (Reading Packet Sect III) Mon, March 29 th

2 Power The ability of your statistical test to correctly reject the null hypothesis The ability of your statistical test to correctly reject the null hypothesis Remember, the null hypothesis generally states there is no effect or no differences between your sample & pop Remember, the null hypothesis generally states there is no effect or no differences between your sample & pop Power refers to the power to find any differences that truly exist Power refers to the power to find any differences that truly exist Want to maximize power Want to maximize power

3 (cont.) When we fail to reject Ho, we want to be sure it is because there are truly no differences that exist (or no effect) When we fail to reject Ho, we want to be sure it is because there are truly no differences that exist (or no effect) …Not because our statistical test didn’t have enough power to find a difference that is actually there. …Not because our statistical test didn’t have enough power to find a difference that is actually there. In your 2x2 Decision Table, In your 2x2 Decision Table, power is = 1-probability of a Type 2 error power is = 1-probability of a Type 2 error

4 2x2 Decision Table (Ho: No disease present) Reality You Decide Ho is correct Ho is incorrect Reject Ho Type 1 error (alpha); False Pos Correct! (POWER) Fail to Reject Ho Correct! Type 2 error (beta); False Neg.

5 What Influences Power? 4 factors that affect power: 4 factors that affect power: 1) Alpha level: increasing alpha (chance of Type 1 error), increases power 1) Alpha level: increasing alpha (chance of Type 1 error), increases power Going from alpha =.01 to alpha =.05, gives you larger chance of finding a difference/effect that is really there. Going from alpha =.01 to alpha =.05, gives you larger chance of finding a difference/effect that is really there. Consider effect on your critical region of.01 v.05 – region becomes larger by using alpha =.05, more likely to reject Ho Consider effect on your critical region of.01 v.05 – region becomes larger by using alpha =.05, more likely to reject Ho

6 Example from last Wed (salary) Compare ybar = $24,100 w/  y = $28,985 (and  y = $23,335, N=100) Compare ybar = $24,100 w/  y = $28,985 (and  y = $23,335, N=100) For 1-sample z test, z = (ybar -  y) /  ybar, where  ybar =  y / sqrt N), or  ybar = For 1-sample z test, z = (ybar -  y) /  ybar, where  ybar =  y / sqrt N), or  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 Ho

7 Ex (cont.) Another approach is to find the critical z value associated with an alpha level: Another approach is to find the critical z value associated with an alpha level: When | z obtained | (from formula) > | z critical| (from table)  REJECT Ho When | z obtained | (from formula) > | z critical| (from table)  REJECT Ho  =.05, 1 tail, z critical = 1.645 or –1.645;  =.05 2 tails, z criticals = -1.96 and 1.96;  =.01, 1 tail, z critical = 2.33 or –2.33  =.01, 2 tails, z criticals = 2.57 and –2.57

8 Ex (cont.) Using this approach, z obtained = -2.09, Using this approach, z obtained = -2.09, z critical (  =.05, 1 tail) = -1.645, since obtained > critical  Reject Ho Same conclusion as for p < alpha Same conclusion as for p < alpha Notice critical region becomes smaller as alpha level becomes smaller Notice critical region becomes smaller as alpha level becomes smaller And as you move from 1 tail to 2 tails And as you move from 1 tail to 2 tails Harder to reject Ho w/ smaller critical region Harder to reject Ho w/ smaller critical region

9 Other Influences on Power 2) Sample Size – larger N, more power 2) Sample Size – larger N, more power With larger sample size, more likely a representative sample with less error With larger sample size, more likely a representative sample with less error 3) 1- v 2-tailed test – 1-tailed test has more power 3) 1- v 2-tailed test – 1-tailed test has more power The critical region for rejecting Ho is larger w/1- tailed test (don’t have to split into 2 tails) The critical region for rejecting Ho is larger w/1- tailed test (don’t have to split into 2 tails) 4) Effect size – larger effect size, more power 4) Effect size – larger effect size, more power Refers to the effect of the manipulation (in an experiment) or the difference betw sample & pop Refers to the effect of the manipulation (in an experiment) or the difference betw sample & pop

10 (cont.) If you have a strong manipulation, will create larger differences among groups or betw sample & population – If you have a strong manipulation, will create larger differences among groups or betw sample & population – easier to see the effect if it’s really there easier to see the effect if it’s really there

11 Determining Power Failure to reject Ho could be due to many things: Failure to reject Ho could be due to many things: There really is no effect / no difference There 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 power Your study didn’t have enough power How can we determine the amount of power of our study? How can we determine the amount of power of our study? Can’t be set by you (as alpha can), but can calculate after the fact or try to predict before the experiment Can’t be set by you (as alpha can), but can calculate after the fact or try to predict before the experiment Can calculate needed sample size for certain level of power (in adv stat class you’ll do this!) Can calculate needed sample size for certain level of power (in adv stat class you’ll do this!)

12 Stat v Practical Significance It’s also possible to have too much power! It’s also possible to have too much power! With large enough sample sizes, you’ll have so much power that even very small differences & effects will turn out statistically significant With large enough sample sizes, you’ll have so much power that even very small differences & effects will turn out statistically significant w/N=5,000, a difference between μ=3.4 and μ=3.5 on a 1-7 scale is significant, but is it important? Practical? w/N=5,000, a difference between μ=3.4 and μ=3.5 on a 1-7 scale is significant, but is it important? Practical? Pay attention to whether a statistically signif finding has any practical significance (is it meaningful? Important?) Pay attention to whether a statistically signif finding has any practical significance (is it meaningful? Important?)


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