Message-ID: <1063877145.164.1563829663549.JavaMail.confluence@encore> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_163_1059686188.1563829663549" ------=_Part_163_1059686188.1563829663549 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html The Issue of Power Analysis

# The Issue of Power Analysis

Recently, I am working on a paper that based on an apprentice pr= oject I did before. I cannot remember how, but the concept of "power a= nalysis" came into my mind. It seems that power analysis is very impor= tant in statistical analysis, but ignored by many, if not most, educational= researchers. "[I]t is extremely surprising that very few researchers = conduct and report power analyses for their studies (Brewer, 1972; Cohen, 1= 962, 1965, 1988, 1992; Keselman et al., 1998; Onwuegbuzie, 2002; Sherron, 1= 988) even though statistical power has been promoted actively since the 196= 0s (Cohen, 1962, 1965, 1969) and even though for many types of statistical = analyses (e.g., r, z, F, ?2), tables have been provided by Cohen (1988, 199= 2) to determine the necessary sample size. Even when a priori power has bee= n calculated, it is rarely reported (Wooley & Dawson, 1983)." (Onw= uegbuzie & Leech, 2004, p. 207)

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The "power analysis" concept was less or even not talked about= in my previous research methods and statistics courses. Here are some reas= ons why power analyses were less used or reported (Onwuegbuzie & Leech,= 2004).

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1. Researchers do not sufficiently understand the concept of statistical p= ower.
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3. The concept and applications of power are not taught, or adequately cov= ered, in many undergraduate- and graduate-level statistical courses. And, p= ower is not recognized as important as other concepts.
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5. No sufficient information is provided on how to report statistical powe= r.
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7. Research resource constraints do not allow research have enough sample = size as required by the result of a priori power analysis.
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9. It is difficulty to estimate effect sizes and standard deviations befor= e conducting a research because of the uncertainties involved.
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11. SPSS, SAS, and other software package do not have the function of condu= cting power analyses. Users need to use other software to do that. And, sof= tware for power analysis normally do not do other analysis.
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### Definition

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• The power of a statistical test of a null hypothesis is the probability= that it will lead to the rejection of the null hypothesis, i.e., the proba= bility that it will result in the conclusion that the phenomenon exists. (C= ohen, 1988, p. 4)
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• Power is the probability of detecting an effect, given that the effect = is really there. In other words, it is the probability of rejecting the nul= l hypothesis when it is in fact false. (UCLA: Academic Technology Services,= Statistical Consulting Group)
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### Why it should be r= eported

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• It clearly represents a vital piece of information about a statistical = test applied to research data. (Cohen, 1988, p. 4)
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• APA publication manual requires reporting power analysis. (see APA publ= ication manual 5th edition on page 24)
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• Post hoc power analyses can be used to improve the design of independen= t replications (Onwuegbuzie & Leech, 2004, p. 225).
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### A priori or post hoc= ?

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When I first touched the term "power analysis", I thought, aha= , I can use the power analysis result to prove how confident (or correct) I= was with the result of my statistical analysis, especially if I got a sign= ificant result (p < .05). However, this thought is wrong. First, many researchers did not like the idea of performing power analys= is after the data has been collected and analyzed, they call it "post = hoc power analysis". They propose a priori power analysis, meaning tha= t power analysis should be performed as a part of research plan. Second, ev= en post hoc power analysis is favored by some researchers, most of them sug= gest reporting post hoc power analysis only when there is a non-significant= result.

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• For the situations where significant statistical results were gained, w= hat should we do? The answer is reporting effect size and confidence interv= al (CI) around effect size. (see Onwuegbuzie & Leech, 2004)
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• A priori power analyses should be conducted and reported; post hoc anal= yses should never be used to replace a priori analyses (Onwuegbuzie & L= eech, 2004).
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• Post hoc power analyses should accompany statistically non-significant = findings. Statistically non-significant results in a study with high power = contribute to the body of knowledge because power can be ruled out as a thr= eat to internal validity. (Onwuegbuzie & Leech, 2004, p. 219, p. 210)=20
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### How to Perform= Power Analysis

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• The most primary method is using the tables Cohen (1988) presented. Thi= s method sounds simple but actually complex, and not so "automaticly&q= uot;. • =20
• Using Power Analysis Software=20
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• How to conduct post hoc power analysis for multivariate tests such as m= ultivariate analysis of variance and multivariate analysis of covariance? -= Please see Onwuegbuzie and Leech, 2004.
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### Resources

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• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sci= ences(2nd Ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.
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• Onwuegbuzie, A. J., & Leech, N. L. (2004). Post hoc power: A concep= t whose time has come. Understanding Statistics, 3, 2001-230. - Av= ailable at UT online resources.
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• UCLA: Academic Technology Services, Statistical Consulting Group. <= a href=3D"http://www.ats.ucla.edu/stat/seminars/Intro_power/default.htm" cl= ass=3D"external-link" rel=3D"nofollow">Statistical Computing Seminars: = Introduction to Power Analysis. - The References section of t= his page has many useful resources.
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• StatSoft, Inc.. Pow= er Analysis.
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