DEPARTMENTS

Technological Tools

Note: Dr. David Inouye is the edi• use to researchers (see also Goldstein size, and higher a. level, and declines tor of the Technological Tools sec• 1989). We do not deal with with increasing sampling variance. tion. Anyone wishing to contribute for planning the precision of studies, Effect size is the difference between articles or reviews to this section although this is an important consid• the null and alternative hypotheses, should contact him at the Department eration if the results are to be ana• and can be measured either using raw of Zoology, University of Maryland, lyzed using confidence intervals or standardized values. Raw mea• College Park, MD 20742, e-mail: rather than P values (Greenland 1988, sures, such as the slope in a regres• di5 @umail.umd.edu. Krebs 1989). Because of software up• sion analysis or difference between dates and new program releases, our means in a t test, are closer to the A REVIEW OF program evaluations will quickly be• measurements that researchers take STATISTICAL POWER come out of date. Nevertheless, we and so are easier to visualize and in• terpret. Standardized measures, such ANAL VSIS SOFTWARE highlight some important and time• less issues to consider when evaluat• as the correlation coefficient or d Although ecologists have become ing power software: scope, flexibil• value (difference in means divided by increasingly sophisticated in applying ity, accuracy, ease of use, and ability the standard deviation), are dimen• tests for statistical significance, few to deal with prospective and retro• sionless and incorporate the sampling are aware of the power of these tests. spective analyses. variance implicitly, removing the Statistical power is the probability of Readers interested only in "the need to specify variance when calcu• getting a statistically significant re• bottom line" should skip straight to lating power. sult given that there is a biologically the Conclusions by way of the sum• Power analysis is most useful real effect in the population being mary evaluation in Table 2. Those when planning a study. Such "pro• studied. If a particular test is not sta• less experienced with power analysis spective" power analyses are usually tistically significant, is it because will find the Background, Stand• exploratory in nature, investigating there is no effect or because the study alone power and sample size soft• the relationship between the range of design makes it unlikely that a bio• ware, and Discussion sections of sample sizes that are deemed feasible, logically real effect would be de• most use. Experienced power ana• effect sizes thought to be biologically tected? Power analysis can distin• lysts will be most interested in the important, levels of variance that guish between these alternatives, and section on Programming power could exist in the popUlation (usuillly is therefore a critical component of analysis using general purpose statis• taken from the literature or from pilot designing experiments and testing re• tical software and Table 4. data), and desired levels of a. and sta• sults (Toft and Shea 1983, Roten• tistical power. The result is a decision berry and Wiens 1985, Peterman Background about the sample size and a. level that 1990, Fairweather 1991, Taylor and The concepts of statistical power will be used in the study, and the tar• Gerrodette 1993, Thomas and Juanes are covered in detail in a number of get effect size that will be "detect• 1996). texts (Kraemer and Thiemann 1987, able" with the given level of statisti• Discussions with colleagues sug• Cohen 1988, Lipsey 1990; see also a cal power. gest that one major obstacle to the use particularly clear paper by Muller and After the study is completed and of power analysis is the perceived Benignus 1992). Briefly, the power of the results analyzed, a "retrospective" lack of computer software. Our paper a test is the probability of rejecting power analysis can also be useful if a is designed to remove this obstacle, the null hypothesis given that the al• statistically nonsignificant result was by reviewing numerous packages that ternative hypothesis is true. Power obtained (e.g., Thomas and Juanes calculate power or sample size and depends on the type of test, increases 1996). Here the actual sample size determining which are likely to be of with increasing sample size, effect and a. level are known, and the vari- 126 Bulletin of the Ecological Society of America ance observed in the sample provides tables and graphs for inclusion in re• that replied, all agreed to send review an estimate of the variance in the ports; (10) allow easy transfer of re• copies, although SPSS Inc. (SPSS population. These values are used to sults to other applications; and (11) and SYSTAT DESIGN) failed to de• calculate power at the minimum ef• be well documented. liver anything. fect size thought to be of biological The third point, on accuracy, re• We reviewed three aspects of each significance, or alternatively the ef• quires further explanation. For some program: scope (points 1-3 above), fect size detectable with the minimum tests, such as z tests and those based ease of use (4-10), and ease of learn• desired level of power. Note that it is on discrete distributions like the bino• ing (11; also the intuitiveness of the rarely useful to calculate power using mial, both the P value and statistical program layout, and the clarity and the effect size observed in the power are calculated using the same infonnation content of the on-line sample: such analyses tell us nothing distribution function. Algorithms for help). For scope, we compiled a list about the ability of the test to, detect computing these functions are well of the test situations explicitly men• biologically important results (Tho• known, which means that accurate tioned in the program documentation mas 1997). power calculations are easy to per• or on screen. We also recorded Power calculations can be done form using a computer. Most t, F, and whether the program uses exact or ap• using the tables or charts provided in c2 tests, however, require calculation proximate methods to calculate many articles and texts (e.g., Kraemer of a different distribution function for power. We summarized ease of use and Thiemann 1987, Cohen 1988, power than for significance tests, and ease of learning on a subjective Lipsey 1990, Zar 1996). However, called a "noncentral" distribution scale from excellent through very these often require some hand calcu• function. Efficient algorithms for good, good, fair, and poor. Note that lations before they can be used, in• computing noncentral distribution ease of use is more important than cluding interpolation between tabled functions have been developed only ease of learning for most users, be• values, and can give inaccurate re• recently, and it was previously com• cause all the programs can be learned sults in some situations (e.g., see Bra• mon to calculate power using ap• in a day or two. dley et al. 1996 regarding the accu• proximate methods. Some programs After our initial review, we se• racy of Cohen's ANOVA tables). still use approximations, a topic we lected the four most promising pack• Computer software has the potential will return to in the Discussion. ages and asked a class of 19 graduate to make power analysis more accu• students to evaluate them as part of a rate, interactive, and easy to perform. Methods 2-week "power module" (lectures and Ideally, power analysis should be We compiled a list of software ca• seminars) in an advanced ecology integrated within the general purpose pable of performing power or sample class. Students in the class had a wide statistical software researchers use size calculations by searching the range of statistical expertise, but none for their regular analyses. This means published literature and the Internet, had prior practical experience of having a comprehensive "study plan• word of mouth, and requests to power analysis. During the module, ning" module for prospective power Internet news groups. From this pre• students were asked to complete six analysis, and options to produce esti• liminary list, we excluded a few spe• power analysis problems using each mates of retrospective power or de• cialized programs with limited scope of the four programs, and then to try a tectable effect size for each test per• that we considered unlikely to be of problem from their own research. The formed. Failing this, researchers use to ecologists (CRCSIZ, EpiiNFO, six questions covered a t test, two• could use stand-alone software de• ECHIP, HYPERSTAT, SSIZE, R2; more way ANOV A with contrasts, trend signed solely for power analysis. In information about these programs is analysis (regression), comparison of either case an ideal program should: available at our World Wide Web site proportions, nonparametric test (Wil• (1) cover the test situations most http://www.interchg.ubc.ca/cacb/ coxon), and survival analysis. Some commonly encountered by research• power/). We also excluded general were framed in tenns of study design, ers; (2) be flexible enough to deal purpose statistical software where others as retrospective analyses. As with new or unusual situations; (3) power capabilities are not built in but part of their report, students indepen• produce accurate results; (4) calculate can be programmed, although we dently completed an evaluation form power, sample size, and detectable ef• briefly discuss these programs later in and ranked the packages on the basis fect size; (5) allow easy exploration the paper. For all remaining software, of which they would recommend to of multiple values of input param• we contacted the vendors asking for a their colleagues. eters; (6) take a wide variety of effect review copy, or downloaded the soft• We sent a draft of this paper to the size measures as input, both raw and ware if it was available over the vendors or authors of the program standardized; (7) allow estimation of Internet. We received replies from all asking them to infonn us of factual sampling variance from pilot data and vendors except three: Epicenter Soft• inaccuracies and to tell us of planned from the sampling variability statis• ware (program POWER), Lionheart updates to their software, but making tics commonly reported in the litera• Press (NONCDIST and SMPLSIZE), it clear that we would not alter any of ture; (8) give easy-to-interpret output; and and Epidemiology Re• the opinions stated in the paper. We (9) produce presentation quality search Corporation (EGRET). Of those received 15 replies and made minor

April 1997 127 .... ~ I Table 1 - Statistical power analysis software reviewed 1

Software Version Vendor or Principal author Address Phone internet URL Z Cost Operating Calculation US$ 3 systems 4 methods S A) Stand-alone power and sample size softWare GPOWER 2.0 Edgar Erdfelder (D) I (D) Dept. of Psychology, Univ. Bonn, http://www.psychologie.uni- free D,M EandA 1:0 E.. Axel Buchner (M) Roemerstrasse 164, D53111 Bonn, Germany I trier.de:8000/projects/gpower.html ~ g. (M) Dept. of Psychology, Univ. Trier, D- 54286 Trier, Germany 0 ...., N 2.2 IDV-Datenanalyse und Wessobrunner Str. 6, D-82131 Gauting, (49-89) 149 D E ET (1) Versuchsplanung Germany 850-3666 tTl ("} NQUERY 1.0 Statistical Solutions Omni Office Plus, 60 State St., Ste. 700, (800) http://www.statsolUSA.coml 475 W E 0 0" ADVISOR Boston, MA 02109. 262-1171 q3. ("} PASS 6.0 NCSS Statistical Software 329 North 1000 East, Kaysville, UT 84037 (800) http://www.ncss.comlpass.html 249 W E e:. 898-6109 tI:l 0 PC-SIZE 2.13 I Gerrard E. Dallal 54 High Plain Road, Andover, MA 01810 ftp://ftp.coast.netlSimTeVmsdos/st 15 D E ("} (I o· CONSULTANT) 1.01 atistic/st-size.zip -< PoWER AND pre- Michael Borenstein 6 1421 Hudson Road, Teaneck, NJ, 07666 (201) TBA W95 E ....,0 > PREcISION release 692-8155 S POWPAL 5.0 Bernard S. Gorman Dept. of Psychology, Nassau Community (516) free D A (1) ::I. College, Garden City, NY 11530 572-7459 ("} ~ PoWERPACK 2.24 Russell V. Lenth 9 Wellesley Way, Iowa City, IA 52245 (319) ftp://ftp.stat.uiowa.edulpub/rlenth/ free D E 337-8549 PowerPackl (25) PoWER PLANT public CSIRO Biometrics Unit Private Bag, PO. Wembley, Western Australia - ftp://ftp.per.its.csiro.aulcsiro- free W E beta 6014, Australia. walbiometricsl PS 2.0 W. D. Dupont Vanderbilt Univ. School of Medicine, (615) ftp://ftp.vanderbilt.edulpublbiostatl free D A Nashville, TN 37232-2637 322-2001 ps.zip STATISTICAL 1.0 Lawrence Erlbaum 10 Industrial Avenue, Mahwah, NJ 07430 (800) http://www.erlbaum.comlI190.htm 140 D A POWER Associates Inc. 926-6579 ANALYSIS STAT POWER 3.01 QEI Systems I James Bavry PO Box 12734, Portland, OR 97212 (503) 180 D E 287-8072 STPLAN 4.1 Barry W. Brown Dept. of Biomathematics, Univ. of Texas, Box - http://odin.mdacc.tmc.edulanonftp/ free D,M A 237, 1515 Holcome Blvd., Houston, TX 77030 B) GeDerat:purpose statistiCal softWare with built-in power analysis eapat)ilitie5 DATASIM 1.2 Drake . Bradley Dept. of Psychology, Bates College, Lewiston, - 55 (M), M, D E and S ME 04240 35 (0) JMP 3.1 SAS Institute Inc. SAS Campus Drive, Cary, NC 27513 (919) http://www.sas.comlotherprods/jm 695 I W32,M E 677-8000 plHome.html 230 MACANoVA 4.02 Gary W. Oehlert School of Statistics, University of Minnesota, - http://www.stat.umn.edul-gary/m free (8) W32, D, E 1994 Buford Ave., St. Paul, MN 55108 acanovalmacanova. home. html M,U MSUSTAT 5.25 Research & Development Montana State University, Bozeman, MO (406) 286 D EorA Institute, Inc. 59717-0002 994-3271 NCSS 6.0 NCSS Statistical Software 329 North 1000 East, Kaysville, UT 84307 (801) http://www.ness.com/ncss 399 W E 546-0445 SHAZAM 7.0 Ken White Dept. of Economics, University of British (604) http://shazam.econ.ubc.ca 395 W,D,O, E Columbia, Vancouver, BC V6T IZl, Canada 822-5062 M,U SIOMASTAT 2.0 Jandel Scientific Software 2591 Kerner Boulevard, San Rafael, CA 94901 (800) http://www.jandeVcom/ 495 W32 ? Corp. 452-6335 5.1 Statsoft 2300 Bast 14th St., Tulsa, OK 74104 (918) http://www.statsoftinc.com/ 995 W 749-1119 4.0 Stata Corp. 702 University Drive East, College Station, (800) http://www.stata.com/ 9451 W,D,M, TX 77840 782-8272 395 U, W95 TRUE 5.0 Epistat Services 2011 Cap Rock Circle, Richardson, TX 75080- (800) 498 D A EPISTAT 3417 326-1488 WDIST 2.3 Mark Von Tress P.O. Box 171173, Arlington TX 76003 ftp://ftp.winsite.com/pub/pc/winJ/ 20 W E misc/wdist23.zip crst8nd-alone sample size softWare Ex-SAMPLE 3.0 Idea Works, Inc. 607 Jackson St., Columbia, MO 65203 (800) http://www.ideaworks.com/l50 D,W,M A 537-4866 PoWER AND 2.0 Glenn E. Meyer Dept. of Psychology, Trinity University, 715 (210) http://www.trinity.edul-gmeyer/p 50 W,M A EFFECT Stadium Drive, San Antonio, TX 78212-7200 736-8323 ower.html D) SPecialized pOwer analysis· software MONITOR 6.2 James P. Gibbs Dept. of Earth and Environmental Sciences, (212) ftp://ftp.im.nbs.gov/pub/softwarel free D S Columbia University, 1200 Amsterdam Ave., 854-8056 monitorl New York, NY 10027 NSURV 2.2 IDV-Datenanalyse und WessobrunnerStr. 6, D-82131 Gauting, (49-89) 149 D E Versuchsplanung Gennany 850-3666

TRENDS 1.0 Tim Gerrodette Sourthwest Fisheries Science Center, National - ftp://ftp.im.nbs.gov/pub/softwarel free D E Oceanic and Atmospheric Administration, PO CSE/wsb21515/trends.zip Box 271, La Jolla, CA 92038 'Furthermformation, inCluding e-mail aadiessesand referencesUto software deSCnptions are available at http:77www.niteiChg.ubC.caJcacb/pawer/ 2 For commercial packages, URL is WWW page. For free software, URL is anonymous FTP or WWW site for downloading the program. :> 3 First number is recommended retail price, second is academic price (neither include shipping). Most commercial packages offer multi-user discounts, networking ~ options, etc. For , the number in brackets is the price of the printed manual, if available. ....- \0 4 D = DOS; M = Macintosh; 0 = OS/2; U = Unix; W = Windows 3.x; W32 = Windows 32s, W95 = Windows 95. The listed first is the \0-...l one used to review the program. S E = exact non-central distributions used when appropriate; A = approximations to non-central distribtuions; - = does not perform tests where non-central distributions are required; S = simulations. 6 A version of POWER.AND PREcISION will be distributed by SPSS, Inc .

.... N IC changes to the text and to Tables 1 form is laid out like a spreadsheet, monly included in publications such and 3. The paper was also reviewed with rows for the input and output pa• as the range of values, coefficient of by five independent researchers (see rameters, and columns for different variation, and percentiles. NQUERY Acknowledgments). scenarios. The user-selected output ADVISOR and PASS have tools for cal• Program reviews were carried out parameter is updated interactively as culating the standard deviation from on a number of 486 and Pentium Pcs the input fields are filled. This works pilot data, STAT POWER has functions running DOS, quite well, although the conventions for calculating pooled standard devia• 3.1, Windows 95, IBM OS/2 v4, and for cutting, pasting, and moving tions and variances, and NQUERY AD• on a Power Macintosh running sys• around the spreadsheet differ from VISOR and STAT POWER can calculate tem 7.5.3. All programs ran well us• those usually used in Windows appli• confidence limits about estimates of ing the operating system for which cations (such as MS EXCEL), and the sampling variance (which can be used they were intended (except for one, maximum number of columns (20) to place approximate confidence lim• NQUERY ADVISOR, which crashed on a limits the size of a sensitivity analy• its about power estimates in prospec• number of occasions). All 32-bit sis. PASS takes a different approach, tive analyses that use pilot data or in Windows programs ran under Win• with one field for each input param• retrospective power analyses). dows 95 without problems, but none eter; multiple values for that param• For graphics production, PASS is of them worked with OS/2 v4. eter are specified by separating them the most flexible, allowing plots of with commas or by specifying a range any variable against any other, Comparison of programs and step size (x to y by z). When the grouped by a third variable. STAT We reviewed a total of 29 pro• "Run" button is pressed the results POWER can plot power or sample size grams (Table 1): 13 stand-alone are presented in the "output" window against any other variable with power and sample size programs, 11 as tables andlor graphs. Again, there grouping for most tests, while general purpose statistics packages are some idiosyncrasies: e.g., the user GPOWER can plot most variables with built-in power capabilities, two must enter a value for the parameter against one another but with only one programs that deal only with deter• to be calculated even though this line per graph. NQUERY ADVISOR and mining required sample size, and value is ignored. GPOWER and POWER AND PRECISION only plot power three specialized power programs of POWER AND PRECISION take a similar against sample size, although a interest to ecologists. In the following "fill-in-the-box" approach, except grouping variable can be included. sections, we compare the programs that the resulting power is displayed Generally, the Windows-based pro• within each of these four categories, on the same screen. Only one result grams (NQUERY ADVISOR, PASS, and finishing with a section on program• can be displayed at once, although POWER AND PRECISION) produce better ming power analysis using general POWER AND PRECISION includes some quality graphs for pUblication than purpose statistical software. capabilities for producing tables. the DOS programs (GPOWER and STAT POWER'S forms are mostly of the STAT POWER). PASS and POWER AND Stand-alone power and sample spreadsheet variety (and can even ac• PRECISION use the same graphics con• size software cept formulae in the spreadsheet troller (by Bits per Second Ltd.) and We begin this section by consider• cells), although only one result can be are the easiest to configure (PASS in ing the five general purpose power displayed at once for the multi-way "interactive graphics" mode). How• analysis packages that we found the tests (two-way ANOV A and contin• ever, none of the graphics utilities are easiest to use (Table 2): GPOWER, gency tables). as flexible and interactive as those in PASS, POWER AND PRECISION, NQUERY All of the programs have utilities many widely used Windows data ADVISOR, and STAT POWER (see Ellison that allow input of various types of management or statistics programs. 1997 for a more detailed review of effect size measure. For example, for Not surprisingly, the Windows• NQUERY ADVISOR). All of these pro• a one-way fixed-effect ANOV A de• based programs also provide gener• grams cover a wide range of tests sign the user can enter either the hy• ally better interfaces with other appli• (Table 3) and have intuitive inter• pothesized cell means (all programs), cations, such as word processors or faces with a number of helpful utili• the upper and lower cell means and graphics packages. In most cases, ties (described below). All except pattern of dispersion (POWER AND PRE• transferring program output is simply GPOWER have well-written, useful CISION), the variance of cell means a matter of cutting and pasting. The documentation. GPOWER covers (NQUERY ADVISOR, PASS, and POWER output window in PASS and the re• slightly fewer tests, has fewer utilities AND PRECISION), Cohen's standardized port window in POWER AND PRECISION and minimal documentation, but has fvalue (GPOWER, POWER AND PRECI• can be saved as a Rich Text Files the advantage of being free. SION), the h2 (Le., r) value (RTF), making importing into word All five programs have a similar (GPOWER, STAT POWER), or the processors particularly easy. For us• interface, whereby the user picks a noncentrality parameter (all except ers unsure how to present the results, test situation from an initial window GPOWER). NQUERY ADVISOR also has both NQUERY ADVISOR and POWER AND or menu and a form appears for the a tool to help estimate the sampling PRECISION can produce grammatically specified test. In NQUERY ADVISOR this variance from the information com- correct statements for pasting into

130 Bulletin of the Ecological Society of America Table 2 - Summary evaluation of power analysis software knowledge and give basic introduc• tions to power and sample size calcu• Software Ease of Ease of lations, although the NQUERY ADVISOR use 1 learping manual only discusses study planning and is mainly directed towards medi• A) stand-81Olle power and sample size cal scientists. The User's Guides for software PASS and STAT POWER give examples GPOWER ••• •• for each test available, although in N •• ••• PASS many of these are of inappro• NQUERY ADVISOR ••• •••• priate retrospective analyses where PASS •••• •••• the observed effect size is used to cal• PC-SIZE • ••• culate power (see Background). On• POWER. AND PREcISION ••• •••• line help is very good in NQUERY AD• POWPAL • •• VISOR, PASS, and POWER AND PRECI• POWERPACK •• •• SION. All have on-screen guide win• POWER. PLANT •• • dows that are displayed alongside the PS • •• input menus, as well as an extensive STPLAN • •• help system and on-line examples. In STATISTICAL POWER. •• •••• PASS the entire manual is on-line, al• ANALYSIS though the formulae were unreadable STAT POWER. ••• • ••• on some of our machines. B) GenerilI-purpose statisticill software with The four packages we asked the built-in power analysis capabilities 2 graduate students to evaluate were DATASIM ••• NQUERY ADVISOR, PASS, STAT POWER, IMP •• • •• and GPOWER. We excluded POWER MACANoVA • •• AND PRECISION because our review MSUSTAT • •• copy was a prerelease version with NCSS • ••• many of the features not fully imple• SHAZAM • •• mented. Seventeen out of 19 students SIGMASTAT •• ••• rated PASS as the package they STATISTICA • • would recommend first to their col• STATA • ••• leagues (1.1 ± 0.3; mean rank ± 1 TRUE EPISTAT •• •••• SD). NQUERY ADVISOR was ranked WDIST • •• second on average (2.1 ± 0.8), with C) Stand-atone sample size software STAT POWER third (3.1 ± 0.7), and EX-SAMPLE •• ••• GPOWER a close fourth (3.2 ± 0.7). POWER. AND EFFECT •• ••• For the remainder of this section, D) speciatizea power anatysis software we briefly describe the other stand• MONITOR •• •• alone power software we reviewed. NSURV •• ••• Five programs have a reasonably TRENDS • •• wide scope of analyses, but are not as 1 ••••• = excellent, ••"'. _ very gOOd, ••• = gOOd, •• - fair, * = poor. easy to use as the packages discussed 2 Evaluation based solely on the power analysis components of these programs above. PC-SIZE is a simple shareware package (actually two separate pro• grams) that calculates power or grant applications, etc., although the (Erdfelder et al. 1996) is very brief, sample size for a range of basic tests reports from POWER AND PRECISION are and relies heavily on the user being (Table 3), but has a relatively rudi• rather wordy. The two DOS pro• familiar with Cohen's (1988) treat• mentary user interface with no graph• grams, GPOWER and STAT POWER, ment of power analysis. (We re• ics and limited tables. The POWP AL can produce simple log files that viewed the DOS version of suite of freeware programs have a could be imported into other applica• GPOWER. An extensive hypercard similar interface, and can convert be• tions, although both would require stack is apparently available for the tween a number of different standard• some editing before they could be Macintosh version, which makes it ized measures of effect size as well as made into tables or used to generate more helpful for beginners. In addi• performing power analysis for ge• graphs. tion, a World Wide Web version of neric t, F, and c2 tests and correla• All of the packages have manuals the documentation is in preparation tions. POWERPACK is unique among that clearly explain how to use the [see Table 1 for Web site address].) the stand-alone programs we re• software. The manual for GPOWER The other manuals assume no prior viewed because it is the only one that

April 1997 131 is command-driven and can be pro• using these programs, most research• only type of power analysis NCSS grammed. This makes it very power• ers will find it easier to use the stand• will do). Unfortunately, NCSS and ful, but at the same time significantly alone software discussed in the previ• SIGMASTAT will only calculate power harder to learn than menu-driven or ous section. We emphasize, however, using the observed effect size and in question-and-answer style programs that power analysis is only a small IMP this is the default, making the re• (see O'Brien 1988 and Goldstein part of these packages' capabilities sults uninformative (see Back• 1989 for more complete reviews). and that our comments are not rel• ground). IMP can calculate bias-cor• POWER PLANT is a Windows-based evant for any other aspects of the pro• rected power and approximate confi• freeware package that contains many grams (see Ellison 1992 and subse• dence limits about the power esti• interesting features (such as interac• quent updates in the ESA Bulletin for mate, but the confidence limits are tive power curve plotting) and has the a more complete review of some of usually too wide to be helpful (see potential to be very useful, but is cur• these packages). Thomas 1997 for an example). IMP rently in public beta-testing and diffi• We first discuss the five user• also has options to compute the Least cult to use. The on-line help is par• friendly, menu-driven programs that Significant Difference (LSD) and tially operational. (The POWER PLANT are intended mainly for users with be• Least Significant Number (LSN), package now includes a file contain• ginner to intermediate levels of statis• which are basically the raw effect ing a manual.) In addition, only a few tical expertise: IMP, NCSS, SIGMA• size and sample size required for a of the ANOV A options and the statis• STAT, STATISTICA, and TRUE EPI• power of approximately 0.5 and so tical calculator work. STATISTICAL STAT. Of these, the first four are are not very useful. It is, however, the POWER ANALYSIS is the official com• general purpose data analysis pack• only one of the three to allow calcula• panion to Cohen's (1988) book. It of• ages, while TRUE EPISTAT is in• tion of retrospective power at user• fers all the tests described in the text tended for medical scientists. All specified effect sizes and so can po• (with their inherent inexactness, e.g., have large user manuals with many tentially be used to perform useful Bradley et al. 1996), as well as some examples. None offer anything like retrospective analyses. excellent tools and simulations to the same scope for power analysis as We now discuss four command• help users understand the concepts of they do for statistical hypothesis test• driven programs, which are generally statistical power and the meaning of ing. This means that a researcher re• more appropriate for intermediate or effect size measures used (see lying solely on one of these packages advanced users. DATASIM is an inex• Goldstein 1989 for a longer review). could analyze a study without being pensive simulation program with lim• Lastly, three programs are more able to plan it properly or check its ited data analysis procedures, but has limited in scope, offering power power. SIGMASTAT offers the widest the most comprehensive power analy• analysis for one- and two-sample scope for planning power or sample sis capabilities of any program in this tests. PS and STPLAN are both size (Table 3), although the ANOV A section (Table 3). Unfortunately these simple freeware programs aimed option doesn't go beyond one-way. are not documented anywhere except mostly at medical researchers. N is a IMP is the most comprehensive in in the on-line help and there is no commercial program that has few this respect, offering power calcula• search capability. The current manual tests built-in (two-sample t tests, pro• tions, tables, and power vs. sample for DATASIM is out of date, and is due portions and McNemar's test), but size graphs for almost any fixed-ef• to be rewritten soon. Some of the many examples in the manual of how fect ANOV A design (but for nothing power analysis capabilities of other problems can be reformulated else). (It is possible to make IMP cal• DATASIM are illustrated in Bradley et so as to be analyzed with the program culate power for random effects in al. (1996). The built-in commands (see Goldstein 1989 for a longer re• the ANOV A, but the results are in• ESP and ESN allow the construction view). correct. We have alerted the vendor of statistical tables of the type found to this problem.) TRUE EPISTAT can in Cohen (1988) using Cohen's • General purpose statistical calculate approximate power and dardized effect size measures, except software with built-in power sample size for a limited assortment that these cover a wider range of situ• analysis capabilities of tests and can produce graphs and ations and give exact results. There We were pleased to discover that tables of power vs. effect size. In are also power and sample size com• more than 10 regular statistics pack• STATISTICA, power and sample size mands (POWER and NSAMP) that ages have power capabilities built in, can be calculated for some one• cover a wide range of tests but re• but were disappointed to see how lim• sample tests using the Process Analy• quire specification of effect size in ited these capabilities are. In some sis module, and OC (power vs. the form of the noncentrality param• cases the power capabilities are very sample size) curves can be produced. eter (a function of the standardized poorly documented, in others the Three of the programs (IMP, effect size, the sample size, and documentation is confusing (specifi• NCSS, and SIGMASTAT) have options sample design). MACANOV A is a cally regarding retrospective power for the user to calculate the power of freeware analysis package based on tests). Although it is possible to do a a test after it is performed (retrospec• the language S, and has similar com• useful power analysis for some tests tive power analysis; indeed this is the mands for fixed-effect F tests (power,

132 Bulletin of the Ecological Society of America power2, and samplesize). The disad• program aimed mostly at social scien• and for determining trends at multiple vantage of using the noncentrality pa• tists (reviewed in more detail by sites (Thomas 1996). Note also that rameter is that one must go through Goldstein 1989). It is unique in being the "Plot variance" requested by some intermediate calculations in or• the only package we reviewed that MONITOR is the residual variance in der to translate it into an effect size explicitly incorporates factors such as counts over multiple years after the measure that is interpretable in terms the cost of collecting data, time con• trend line has been fit (e.g., residual of the biology of the test situation. straints, multiple response measures, mean square from a regression of pi• SHAZAM is an econometrics pro• and sample design (stratified, clus• lot data against time), and not the gram, with a similar command for the tered, etc.) in determining sample within-year variance in counts as im• non central F distribution, although size. Note, however, that some of the plied by the manual (J. Gibbs, per• the manual shows how the INCOEF sample size calculations are based on sonal communication). command can be used to calculate the so-called "classic" methods, which We also reviewed one commercial noncentrality parameter using hy• do not take account of the desired program (NSURV) that specializes in pothesized cell means. Lastly, STATA level of power and which we do not power analysis for survival tests (also is a powerful and extensible data recommend. called failure-time analysis). It is analysis program that, surprisingly, POWER AND EFFECT calculates re• similar to the survival modules in has only one sample size and power quired sample size and various mea• NQUERY ADVISOR, PASS, and command (sampsi), which is re• sures of effect size based on Cohen STPLAN (Table 3). As with trend stricted power analyses of one- and (1988). It has some interesting ani• analysis, appropriate methods are still two-sample comparisons of means mated tutorials, but is basically simi• being developed for survival analysis and proportions using the z distribu• lar in function to some of the pro• and especially for calculating power tion. All four of these programs are grams mentioned in the previous sec• (G. Fox and G. White, personal com• designed to be extended by program.: tion, such as POWPAL. munications). Our informal test runs ming extra procedures as necessary. showed large differences in results In all four cases, a useful power Specialized power analysis between packages for what appeared analysis, including sensitivity analy• software to be the same problem. The survival sis and presentation quality graphic We reviewed three single-purpose module in PASS produces incorrect output, is best achieved by writing programs that are of potential interest results when accrual time is set to O. short programs (see below). to ecologists. Two freeware programs If all individuals are marked at the Two packages remain to be cov• (MONITOR and TRENDS) are de• same time, then accrual time will be ered in this section. MSUSTAT is a signed to calculate the power to de• corrected in the next version of the simple command-line and question• tect trends in species abundance over program. We could not account for and-answer style program intended time (although both could be used for the other differences in results be• mostly for introductory level biosta• any data that will be analyzed using tween programs. We therefore advise tistics. It has a limited selection of linear regression). TRENDS takes an caution when interpreting the results power and sample size options for analytical approach, and is limited to of power analysis for survival tests. biostatistics (Table 3), some of which situations in which monitoring occurs Because most survival packages are give only approximate results. WDIST at regular intervals at one site. MONI• medically oriented, ecologists may is a shareware statistical probability TOR estimates power using Monte need some translation to understand calculator that includes a small but Carlo simulations and can handle un• the terms they use. eclectic collection of hypothesis test• equal sampling intervals and multiple ing and power routines (Table 3). sites. One advantage of these pro• Programming power analysis Neither of these programs is particu• grams over the regression modules in using general-purpose larly easy to use for power analysis general purpose power software is statistical software (Table 2). that they use trend as the effect size For more advanced users, writing measure rather than a standardized programs to do power analyses using Stand-alone sample-size measure such as the ,-2. Both pro• regular general-purpose statistical software grams can also estimate power for ex• software has three advantages: no Programs that are restricted to cal• ponential trends, and for different new software is required, the program culating required sample size given variance structures (e.g., variance can be customized for the analysis at the desired level of power cannot be proportional to mean), although nei• hand, and new advances in statistical used for retrospective power analysis, ther takes account of the auto• theory can be quickly implemented. but they could be useful when plan• correlation between data points We know of seven packages that have ning experiments if they offer some through time. Potential users should macro languages and full comple• functions not available in the power note that there has been some debate ment of distribution functions (in• and sample size programs. regarding appropriate methods for cluding noncentral distributions) EX-SAMPLE is a comprehensive power analysis of trends (Gerrodette built-in, and can therefore be pro• survey sample size determination 1987, 1991, Link and Hatfield 1990), grammed to calculate exact power for

April 1997 133 .... ~ Table 3 - A selection of situations where the calculation of power (p), sample size (S) or detectable effect size (D) is discussed in the "'" documentation of the programs reviewed. 1, 2

Situation::!" z-test t-test Fixed.-etfects Random-eiffects Repeated Regression Correlation ANOVA ANOVA measures r----2.:- ITen- 1- 2- Gen- 1- I-way 2- 3- I -way----z-way Om- Multl- Smtple Compare Muhlple LOptic pearson DilT. m !:Xi Software samp samp eric 4 samp samp eric 4 way contrasts way way variate variat 2 slopes COrIS. E. e A) Stand-alone pOWerand sample size software &t:l o GPOWER PS PS P PS PS P PS PS PS ..." g N PSD PSD ·NQUERy··ADViS'Oit·············································PSI5···PSI>···_········PSI>·······PSI5········JiS················································'PSrr················p-s15·······························p-s15..········~········· ...p-s[j ...... __ .... _ .. ?;1 o PASS PSD PSD PSD PSD PSD PS PS PS PS PS PS PS PSD PSD 0" PC-SIZE PS PS PS PS PS PS PS

1 A complete listing of test situations is available at http://www.interchg.ubc.calcacb/power/ 1 Because of their narrow scope, the three specialized power analysis packages reviewed (MONITOR, NSURV and TRENDS) are not listed. MONITOR and TRENDS calculate P, S, or D for trend analysis; NSURV calculates P, S ,or D for survival analysis. 3 Note some situations are special cases of others: for example a program that can perform. power analysis for an M x N contingency table will also work for 2 x N and 2 x 2 tables, and 2 and N category goodness-of-fit tests. 4 For "Generic" tests, standardized effect size measures are used and the user inputs the appropriate degrees of freedom for the test. Table 3 (contd.)

Situation: 3 Proportions i? Goodness-of- Contingencyta6les Survival Non-parametric ProoabiIity fit calcu1ator 5 prop. DdT. m ~2 cats. N cats. 2 x 2 With FISher' 2 x M x LOg- Expon- Slgn WdCOxon Speannan Program = p props. eric 4 Yates s N N . rank ential test A) stand-alOne power and sample size softWllre GPOWER PS N PSD PSD ·NQi:':iiiRy..AiiVISOii ...... •.... ·PS .... ·• .. · .. PS· .. ·• .... ··· .. ···• .... · .... · ...... ·· ...... ·• .. ·PS .. ·• ...... ·...... ·PS .... ·• .. PS .. · ...... •.... ·PS .... ·• ...... PS .. · .. ·• ...... ·.... · .. _- ..- ...... ·...... ·•...... PO ...... · PASS PSD PSD PSD PSD PSD PSD PSD p 6 PC-SIZE PS PS ·fiOWiiR·AND..~i'oN· ....·~ ....·• .... ·PS .... ·.... ·}S· .... •...... •...... •.... •.... ••.... 'tiS...... ~ ...... _._ ...... POWPAL PS PoWERPACK P P P P P PS J' P ·fiOWiiR·Pi.i\:NT...... ·...... ·.... ·...... •.. · .... ·.. · .. ·• .... · .... ·.. • .... · .... ·...... ·...... p ...... PS PSD STPLAN PSD PSD PSD PSD PSD PSD 7 ·STA'TISncAI...POWEii ...... •...... ·...... •.. · .. PS·· .. • .... ·.... ·.. • .... · .... · .. • ...... ·...... ~ ...... ~ ...... - ...... ANALYSIS STAT PoWER PS PS PS P P PS PS P B) GeDeraI-pnrpoSe-statisticilrsortware-WRh built-m power analYSis cilpaDilities DATASIM PS P JMP P ·MACANovA'...... ·•...... ·...... •.. · ...... ·•.... ·.... · .. • .... · .... · .. • ...... - ...... p ...... MSUSTAT NCSS P ·sRAZm...... ·.. · ...... ·...... ·.. · ...... ·.. · ...... ··.... ·.... ·.. · .... ·.... ·.. · ...... _...... SIGMASTAT PS PS P P P STATISTICA S ·STATA'...... ·...... ·.... • .... ·~ ....·• .. ··'PS'· .. ·• .... · .... · .. · .... · ...... TRUE EPISTAT S PS S S WDIST PS PS P P P P P i C) Stand-alone sample size software \0 EX-SAMPLE S S S S S S S -\0 -.l PoWER AND EFFE.Cl' S S S S S 5 Only programs thllt can compute probabilities for the binOlDlaI distribUtion and central and noncentI'8l t, F, and c2 diStributions are listed. Apart from POWERPACK.and STAT POWER, the use of the probability calculators for power analysis is not documented in the program manuals 6 The probability calculator from PASS is available as a stand-alone freeware program from http://www.ncss.comlshareware.html 7 The probability calculator for STPLAN is actually a separate program DSTATTAB, by the same authors (available from the same internet site)

~ ~ ,... ~ ="

to E.. &. ::l .....,o g- Table 4 - Published programs that enable general-purpose statistical software to perform power or sample size calculations.

T ow SoftW8re -- PrograniI Macro Principal' Auili~SourceI Reference 0- O

~. GUM SAMG N. Andrews http://www.nag.co.uklstats/GDGE/sample/sample.html SHAZAM not named K. White User's reference manual, v7.0 (p345-348) g, > SAS AOVPOWER.SAS SAS Institute Inc. . SAS sample library R. G. O'Brien SAS sample library §. (") POWER.SAS K. E. Muller ftp:l/ftp.uga.edu/pub/sas/contrib/cntbOOI4 I» POWERLIB.SAS R. G. O'Brien ftp:l/ftp.bio.ri.ccf.orglUnifyPow.all UNIFYPOW.SAS M. Friendly ftp://hotspur.psych.yorku.calpub/sas/macros/fpower.sas FPOWER.SAS L. Thomas http://www.interchg.ubc.calcacb/peoplellthomas/download.htm several programs A. F. Nemec I several programs Nemec 1991 SIMSTAT not named N. Peledau Peladeau and Lacoutre 1993 S-PLUS POWER D. F. Heitjan ftp://lib.stat.cmu.edu/s/power/ asypower B. W. Brown ftp://odin.mdacc.tmc.edu/pub/S/asypow/ XLISP- power.lsp 1. Bond http://www.stat.ucla.edu/code/statistics/distributions STAT Power-Sim 1. T. Behrens http://seamonkey.ed.asu.edu/-behrens/asulreports/power/

I A list of vendors and contact informatIon for these packages is available at http://www.mterchg.ubc.ca7cacb/power/ any test where the appropriate for• General comments the level of accuracy that can be ex• mula is known: DATASIM, GAUSS, Accuracy.-For most parametric pected in the results. Many manuals MACANOV A, SAS, SPSS, S-PLUS, and tests commonly used by ecologists, say that the program has been vali• SST. In addition, two programs have the statistical theory of power analy• dated, but only GPOWER, N, NSURV, almost all of the requisite functions: sis is well developed and algorithms and PC-SIZE state exactly how the SHAZAM is missing the noncentral are available for calculating the ap• validation was done and give the re• c2, and STATA does not have noncen• propriate distribution functions to the sults of the tests. Perhaps vendors are tral Fort distributions. We found desired level of accuracy. Despite concerned by the large amount of ex• published programs for three of these this, a number of programs use ap• tra paper required to properly report packages (Table 4), but in many cases proximate methods (Table 1). We did validation tests in the manual, know• the code could be easily ported to the not attempt to evaluate rigorously the ing that few will read them. One solu• others. accuracy of these programs, but tests tion is implemented by the vendors of Several other programmable pack• by Goldstein (1989) showed that NQUERY ADVISOR, who have posted ages, such as GUM, , some programs gave power estimates their validation report on the Internet STATISTIC A, and XUSP-STAT do not that were wrong by as much as 0.3 for (http://www.statsoLie/valid.htm; this have noncentral distribution functions a t test. Some may argue that such in• is not yet documented in the User's built-in, but have other probability accuracies are relatively small com• Guide). We encourage others to do distribution functions including the pared with those due to the uncer• likewise. central t, F, and c2 distributions. tainty in input parameters such as Flexibility.-Many of the pro• These packages can be used to calcu• sampling variance. However inaccu• grams we have reviewed can deal late exact power for some tests and racies due to the use of approximate with the vast majority of power tests approximate power for others, as algorithms are unnecessary, and required by ecologists. Nevertheless, demonstrated by the programs for should be avoided. there may be some occasions when SAMG for GUM and power.lsp for In some areas of statistics, appro• the built-in tests are not enough. In XUSP-STAT (Table 4). priate methods of analysis are still be• this event, the "generic" t, F, and c2 A plug-in module enabling MS ing developed (e.g., survival analysis, tests offered by some programs EXCEL to calculate noncentral distri• trend analysis) or are controversial (Table 3) allow for a wider range of bution probabilities has been written (e.g., contingency table analysis; Zar situations by letting the user specify by R. Lenth (Table 4). The sample 1996:489). For others (e.g., most the appropriate degrees of freedom workbooks that come with the pack• multivariate statistics) appropriate for the test. For example, the "Other age demonstrate the ease with which tests are available but current meth• F tests" option in GPOWER can be user-friendly spreadsheet applications ods of power analysis produce only used to calculate power for a planned can be built. Another alternative for approximate results. In both cases, comparison of means (contrasts), or those without access to one of the users should pay close attention to the the fixed effect in a randomized com• above programs is POWERPACK (Table particular method implemented by plete block design. Even more flex• 1), a free power analysis package the package they use and its underly• ible are the probability calculators in• with a built-in command language. ing assumptions and limitations. Re• cluded with some packages (Table 3), Note that MACANOV A and XUSP• sults should be treated as rough which typically calculate cumulative STAT are also freeware. guides to supplement the researcher's and inverse probabilities for central Power analysis may also be per• intuition. This also highlights the im• and noncentral t-, F- and c2 distribu• formed using Monte Carlo simula• portance of specifying the program tions, as well as many others (z, bino• tions, either using specialized simula• and version number used when re• mial, negative binomial, exponential, tion software (e.g., DATASIM, SIM• porting results. etc.). These require that the user STAT) or general purpose software Surprisingly, some packages do know the appropriate formula for cal• that contains pseudo-random number not document the calculation methods culating power, and are laborious to functions (all of the programs listed used (NCSS, POWER AND PRECISION, use when many values are to be cal• above). An example of this approach AND SIGMAS TAT; the methods used by culated. IMP and NCSS have the is Power-Sim for XUSP-STAT POWER AND PRECISION will apparently built-in ability to automate and save (Table 4); other examples are given be documented in the final version of the formulae used, although the use by Bradley et al. (1992) and Thomas the manual). Most merely reference of the distribution functions for and Iuanes (1996). Simulations are the methods, while only a third power analysis are not documented in particularly useful to assess the (DATASIM, EX-SAMPLE, IMP, their manuals. Similar functionality is power of nonparametric tests given MSUSTAT, NQUERY ADVISOR, PASS, available via Lenth's plug-in macro different plausible underlying distri• STATA, STAT POWER, TRENDS, and for MS EXCEL (Table 4). For those butions (a discussion of other ap• TRUE EPISTAT) show the actual for• willing to write short programs, either proaches to power analysis for non• mulae used. Few manuals mention POWERPACK or one of the statistics parametric tests is in the POWERPACK accuracy, and only GPOWER, packages listed in the previous sec• User's Guide). POWERPACK, and STAT POWER specify tion on programming power could be

April 1997 137 used to automate the process. of 1997, as is the promising new pro• high-quality statistical software we Retrospective power analysis.• gram POWER AND PRECISION. Users have reviewed here. There appears to be some confusion with more specialized needs may about the appropriate approach to ret• consider other commercial packages, Acknowledgments rospective power analysis. At least such as EX-SAMPLE for survey design. We thank Richard Goldstein for one manual (PASS) gives examples For those unable or unwilling to helping us to locate programs, and for where the actual effect size found in purchase , there much helpful advice. Thanks also to the test is used to compute power, and are a large number of freeware or the hard-working students of ZOOL all three general statistical programs shareware programs available. 502. Reviews by Aaron Ellison, Rich• that have options to calculate retro• GPOWER is a reasonably compre• ard Goldstein, Wesley Hochachka, spective power automatically (JMP, hensive free program, and POWER David Inouye, and Jennifer Ruesink NCSS, SIGMASTAT) do so using this PLANT also has the potential to be helped to improve the manuscript. unhelpful approach by default. Most very useful once the final version is Lastly, we thank the authors/vendors of the other manuals ignore retrospec• released. Other free software may of the programs for providing evalua• tive power completely; the only ones also be helpful in some situations, for tion copies and feedback regarding that give useful examples (see Back• example STPLAN for survival analy• the accuracy of our statements. ground, and Thomas 1997) are N, sis and other medical statistics, MONI• SHAZAM, STAT POWER, and TRUE TOR and TRENDS for population Literature cited EPISTAT. trend analysis. Bradley, D. R, R L. Helmstreet, and The inclusion of inappropriate The power analysis capabilities S. T. Zeigenhagen. 1992. A simu• methods in the general purpose pack• built into general purpose statistical lation laboratory for statistics. ages is distressing because these tend software are not currently adequate Behaviour Research Methods, In• to be used by statistically naive re• for most users. Of the programs we struments, and Computers 24: searchers. These packages should be reviewed, SIGMASTAT can handle the 190-204. modified so that the programs ask us• most tests but has no built-in features Bradley, D. R., R L. Russell, and C. ers for the alpha level of the test and to assist with the analysis (such as P. Reeve. 1996. Statistical power either: (1) calculate power for a tools to help calculate effect size or in complex experimental designs. specified effect size (or range of ef• sampling variance, produce tables or Behaviour Research Methods, In• fect sizes) thought to be the minimum graphs, or export the results to other struments, and Computers 28: for biological significance, or (2) cal• applications). JMP is relatively useful 319-326. culate detectable effect size for a for fixed-effect ANOV A designs, but Cohen, J. 1988. Statistical power specified minimum desired level of does nothing else. Unfortunately all analysis for the behavioral sci• power. Another useful addition of the programs that calculate retro• ences. Second edition. Lawrence would be the calCulation of confi• spective power (JMP, NCSS, and Erlbaum Associates, Hillsdale, dence intervals about power and de• SIGMASTAT) use the observed effect New Jersey, USA. tectable effect size estimates (Thomas size to calculate power by default, Ellison, A. M. 1992. Statistics for 1997). which produces uninformative re• pes. ESA Bulletin 73:74-87. sults. In all three programs the manu• ---.1997. Review ofnQuery Ad• Conclusions als do not clearly explain the implica• visor, version 1.0. ESA Bulletin Contrary to popular perception, tions of this approach. 78:66. there are many software packages More advanced users who already Erdfelder, E., F. Faul, and A. available to help researchers perform work with programmable statistics Buchner. 1996. GPOWER: a gen• statistical power analysis (Table 1). packages, especially those that have eral power analysis program. The packages vary in the scope of built-in noncentral distribution func• Behaviour Research Methods, In• their tests, their accuracy, ease of use, tions, should consider using one of struments, and Computers 28: I• and ease oflearning. the programs already available (Table ll. For beginner to intermediate level 4) or writing their own. For those Fairweather, P. G. 1991. Statistical use we recommend one of the com• without access to these packages, a power and design requirements mercial general purpose power pack• free alternative is POWERPACK. for environmental monitoring. ages NQUERY ADVISOR, PASS, or STAT At present, power analyses are Australian Journal of Marine and POWER. Of these our graduate student still rare in the ecological literature. Freshwater Research 42:555-567. class preferred PASS, although both Given the diversity of software avail• Gerrodette, T. 1987. A power analy• NQUERY ADVISOR and STAT POWER able there is no longer any reason to sis for detecting trends. Ecology perform some tests not available in ignore statistical power when plan• 68:1364-1372. PASS (Table 3). Note also that the ning studies and analyzing their re• ---. 1991. Models for power of software is constantly under develop• sults. In the near future we expect to detecting trends-a reply to Link ment: a new version of NQUERY ADVI• see an explosive increase in the use of and Hatfield. Ecology 72:1889- SOR is due to be released in the spring power analyses fueled by the kinds of 1892.

138 Bulletin of the Ecological Society of America Goldstein. R. 1989. Power and O'Brien, R. G. 1988. Statistical com• Thomas, L., and F. Juanes. 1996. The sample size via MSIPC-DOS puting software reviews: Power• importance of statistical power computers. American Statistician Pack (Version 2.22). American analysis: an example from Animal 43:253-260. Statistician 42:266-270. Behaviour. Animal Behaviour Greenland, S. 1988. On sample-size Peladeau, N., and Y. Lacouture. 52:856-859. and power calculations for studies 1993. SIMSTAT: bootstrap com• Toft, C. A., and P. J. Shea. 1983. De• using confidence intervals. puter simulation and statistical tecting community-wide patterns: American Journal of Epidemiol• program for IBM personal com• estimating power strengthens sta• ogy 128:231-237. puters. Behaviour Research Meth• tistical inference. American Natu• Kraemer, H. C., and S. Thiemann. 'ods, Instruments, and Computers ralist 122:618-625. 1987. How many subjects? Sage, 25:410-413. Zar, J. H. 1996. Biostatistical analy• London, UK. Peterman, R. M. 1990. Statistical sis. Third edition. Prentice-Hall, Krebs, C. J. 1989. Ecological meth• power analysis can improve fish• Upper Saddle River, New Jersey, odology. Harper Collins, New. eries research and management. USA. York, New York, USA. Canadian Journal of Fisheries and Link, W. A., and J. S. Hatfield. 1990. Aquatic Sciences 47:2-15. Reviewed by Len Thomas Power calculations and model se• Rotenberry, J. T., and J. A. Wiens. Centre for Applied Conservation lection for trend analysis: a com• 1985. Statistical power analysis Biology ment. Ecology 71:1217-1220. and community-wide patterns. Faculty of Forestry Lipsey, M. W. 1990. Design sensitiv• American Naturalist 125: 164- University of British Columbia ity: statistical power for experi• 168. #270-2357 Main Mall mental research. Sage, Newbury Taylor, B. L., and T. Gerrodette. Vancouver Park, California, USA. 1993. The uses of statistical power British Columbia, Canada V6T 1Z4 Muller, K. E., and V. A. Benignus. in conservation biology: the [email protected] 1992. Increasing scientific power Vaquita and Northern Spotted with statistical power. Neuro• Owl. Conservation Biology and Charles 1. Krebs toxicology and Teratology 14: 7:489-500. Department of Zoology 211-219. Thomas, L. 1996. Monitoring long• University of British Columbia Nemac, A. F. L. 1991. Power analysis term population change: why are 6270 University Blvd handbook for the design and there so many analysis methods? Vancouver analysis of forestry trials. Biomet• Ecology 77:49-58. British Columbia, Canada V6T 1Z4 rics Information Handbook 2. ---. 1997. Retrospective power [email protected] Ministry of Forests, Victoria, Brit• analysis. Conservation Biology ish Columbia, Canada. 11, in press.

DRAGONDICTATE 2.0 front of the computer, as I suspect pause briefly between each word. The many of you do too, I've begun to program does have a built-in set of DragonDictate 2.0 for Windows. worry about potential problems re• Sentence Commands that let you Dragon Systems, Inc., 320 sulting from repetitive stress syn• speak naturally for some basic tasks, Nevada Street, Newton, MA drome. The advent of speech recogni• like turning the microphone off tem• 02160. (800) 825-5897, (617) tion programs for personal computers porarily ("go to sleep") and reactivat• 965-5200, fax (617) 527-0372. is in part a result of this kind of con• ing it ("wake up"), switching between List price $395, $695, $1,695 for cern, and DragonDictate is an ex• command mode ("command mode") versions with 10,000, 30,000, or ample of such a program. The pro• and dictate mode ("dictate mode"), 120,000 word dictionaries. gram comes with a headset micro• getting help ("get help"), and exiting phone that you plug into your sound the program ("voice menu, close"). Last year my department's busi• card, and once you've turned on your There are also sentence commands ness manager required surgery on computer and started the program you for editing in a word processing pro• both of her wrists because of prob• can use the microphone to accom• gram and for use with a spreadsheet, lems with carpal tunnel syndrome, plish a lot of what you'd otherwise do which allow you to move around the probably resulting from years of work with a keyboard. screen or file, select, cut, delete, for• on a keyboard. She is still unable to DragonDictate, as is true for most mat, print, etc. Beyond these continu• work a year later. Now that I find my• speech recognition programs, re• ous commands, the program relies on self spending most of my workday in quires discrete speech; you must training to match your voice with its

April 1997 139