From thDepartmenToronto, ONetwork; DCommunityInstitute; §DepartmenToronto, OnDivsion of OEpidemioloOntario, Ca

SubmitNo benReprint

Hospital, U1-439, Tor

© 20110883-5doi:10.1

The Journal of Arthroplasty Vol. 26 No. 5 2011

Incorrect Use of the Student t Test inRandomized Trials of Bilateral Hip and Knee

Arthroplasty Patients

Rajiv Gandhi, MD, MS, FRCSC,* Holly N. Smith,*Nizar N. Mahomed, MD, ScD, FRCSC,yz§ Randy Rizek, MD,* and

Mohit Bhandari, MD, MSc, FRCSCO

Abstract: The statistical analysis of a study's results is critical to its interpretation. Often confused,2 types of t tests exist for dependent or independent samples. We reviewed randomized controlledtrials that included patients undergoing bilateral total hip or knee arthroplasty (dependentsamples) that used the t test for analysis. Our inclusion criteria resulted in 40 studies for review, 10of which combined both unilateral and bilateral patients. Of the 30 studies that compared a puresample of only bilateral patients, 18 (60%) incorrectly used the independent t test. Of the 10studies with mixed samples, 8 (80%) used the independent t test. The extent to which theincorrect use of this statistical test led to misleading conclusions is uncertain; however, our findingshighlight the misuse of statistical tests in the arthroplasty literature. Keywords: arthroplasty,t tests, statistics, epidemiology.© 2011 Elsevier Inc. All rights reserved.

Evidence-based medicine suggests that medical decisionmaking should be based on the best available scientificevidence. A methodologically well-designed trial withthe appropriate statistical analysis and interpretationallows for strong conclusions to be drawn from a study.Conversely, simply applying an incorrect statistical testto a data set may lead to a biased analysis and anincorrect conclusion.In the comparison of 2 surgical treatment outcomes,

such as functional outcome scores, the t test is the mostcommonly used [1]. The t test is used for the comparisonof normally distributed, continuous data between 2groups. Two types of t test exist—one for independent

e *Division of Orthopaedic Surgery, University Health Network;t of Surgery, University of Toronto, University Health Network,ntario; yDivision of Orthopaedic Surgery, University Healthivision of Health Care and Outcomes; zResearch and ArthritisResearch and Evaluation Unit, Toronto Western Research

Department of Health Policy, Management and Evaluation andt of Surgery, University of Toronto, University Health Network,tario; and OCanada Research Chair in Musculoskeletal Trauma,rthopaedic Surgery, McMaster University, Department of Clinical

gy and Biostatistics, McMaster University Medical Center, Hamilton,nada.ted October 19, 2009; accepted June 9, 2010.efits or funds were received in support of this study.requests: Rajiv Gandhi, MD, MS, FRCSC, Toronto Westernniversity Health Network, 399 Bathurst Street, East Wingonto, Ontario M5T-2S8.Elsevier Inc. All rights reserved.

403/2605-0024$36.00/0016/j.arth.2010.06.007

811

samples and one for dependent samples. The choice ofthe appropriate statistical test is important because the ttest is very sensitive to data interdependence [2].Many studies in the total hip (THA) and total knee

arthroplasty (TKA) literature use a bilateral study designwhereby one side receives the therapy being investigat-ed, whereas the other side acts as the control. In thisdesign, the authors minimize confounding betweengroups by measuring 2 outcomes in the same patientand thereby ensuring that any differences in outcomesare more likely due to the intervention of interest. Forstudies of this design, the appropriate statistical test tocompare continuous data between groups is the depen-dent t test.Several authors [3-6] have documented that the

quality of methodology and reporting in the orthopedicliterature is inconsistent and inadequate. We performeda systematic review of the orthopedic literature toidentify randomized controlled trials (RCTs) relating tobilateral THA or TKA to evaluate appropriate use ofstatistical tests, namely the t test.

Materials and MethodsEligibility CriteriaWe included studies that met the following criteria: (1)

the study related to TKA or THA; (2) the study includedat least 1 bilateral patient (a patient enrolled in boththe intervention and control group); (3) the study wasan RCT; (4) the study was published or accepted for

812 The Journal of Arthroplasty Vol. 26 No. 5 August 2011

publication between 1998 and July 2009; and (5) thestudy performed a statistical comparison of continuousdata using a t test.

Study IdentificationTwo of us completed a computerized search of the

online databases OVID MEDLINE (1998 to July 2009)and EMBASE (1998 to 2009) with the following searchterms (total knee arthroplasty OR total knee arthro-plasty OR total hip arthroplasty OR total hip arthro-plasty) AND (bilateral) AND (randomized controlledtrial OR RCT). We also searched the Cochrane Database

Table 1. Summary Data for RCTs Included in Systematic Review

Journal Year t Test Used Study Results

Acta OrthopaedicaCarlsson et al 2005 [27] D SKim et al 2007 [38] I NClinical Orthopaedics and Related ResearchKim et al 2001 [11] I SRees et al 2005 [30] D SJournal of ArthroplastyKim et al 1998 [9] I SLau et al 2001 [13] B SKomatsu et al 2003 [20] D SMaruyama et al 2004 [25] U SSharrock et al 2005 [31] D SKim 2006 [8] I SLee et al 2007 [42] D SBerth et al 2007 [37] D SDalury et al 2008 [43] I NKim et al 2008 [44] I NRama et al 2009 [47] I SJournal of Bone and Joint Surgery (Am)Meding et al 2000 [10] I SWood et al 2002 [15] I SKim et al 2003 [17] I NKim et al 2003 [19] I NKim et al 2003 [16] I NWaters et al 2003 [22] U SKim et al 2004 [23] I NWon et al 2004 [26] I NYamasaki et al 2005 [33] D SKim et al 2005 [28] D SKim 2005 [29] I SDalury et al 2009 [45] D NKim et al 2009 [46] D NJournal of Bone and Joint Surgery (Br)Kim et al 2001 [12] I NKim et al 2002 [14] I NPrice et al 2003 [21] D SKim et al 2003 [18] I NLachiewicz et al 2004 [24] I SWalmsley et al 2005 [32] I SVendittoli et al 2006 [35] I NKim et al 2007 [39] I NKim et al 2007 [41] I SKim et al 2007 [40] I SOrthopedicsSong et al 2006 [34] U SThe KneeBeard et al 2007 [36] D N

D indicates dependent t test; I, independent t test; U, unspecified t test

of Systematic Reviews and the Cochrane CentralRegister of Controlled Trials. We reviewed the bibliog-raphy of each study to identify further relevant studies.

Data ExtractionRelevant data were extracted from each eligible study

by 2 of the authors. This included authors, publishingjournal, total number of patients enrolled, number ofbilateral patients, type of surgery (hip versus knee),details of statistical analysis, and whether the testresulted in a significant finding (ie, P b .05). Year ofpublication was also extracted as we hypothesized a

TKA (K)/THA (H) Total Number of Patients Bilateral Only

K 30 YK 21 Y

K 116 YK 7 Y

H 48 YK 43 NK 10 YK 20 YH 19 YH 70 YH 20 YK 20 YK 20 YK 60 YH 187 N

K 39 YK 201 NH 98 NH 156 NH 50 YK 390 NK 190 YH 17 YH 21 YK 50 YH 52 YK 37 YK 250 Y

H 70 YK 227 NK 40 YH 100 YK 423 NH 552 NH 194 NK 174 YK 100 YK 120 Y

K 42 Y

K 33 Y

; B, both t tests; S, significant results; N, nonsignificant results.

Fig. 1. Graphical depiction of the studies comparing onlybilateral patients for the use of the correct and incorrect t testby year of publication.

Use of Student t Test in Randomized Trials � Gandhi et al 813

priori that the studies using the correct test may be of amore recent publication date.

Study AppraisalWe applied the Detsky scale to all included studies to

evaluate the methodology of each RCT [7]. This scaleassesses the quality of a study with respect to itsrandomization, outcome measures, inclusion/exclusioncriteria, intervention description, and the statisticalanalysis [5]. The statistical analysis portion contains anextra question for negative trials of “Were confidenceintervals or post hoc power calculations performed?”Thus, the total possible scores for positive and negativetrials are 20 and 21, respectively. Studies with a scoregreater than or equal to 16 points were classified as high-quality clinical trials.

Statistical AnalysisAnalyses consisted of descriptive statistics including

frequencies, whereas means and ranges were used tosummarize our continuous variables. Statistical signifi-cance was set at a level of 5%.

ResultsLiterature SearchWe identified 146 potentially relevant studies. Appli-

cation of our eligibility criteria resulted in 39 papers forinclusion. We eliminated 95 studies based on abstract ortitle, 8 did not use the t test, and 4 did not provide anydetails of their method of analysis. One additional studywas identified through a review of the bibliographies ofrelevant publications, for a total of 40 randomized trialsfor systematic review [8-47]. All studies were publishedin English and represented a broad spectrum oforthopedic journals (Table 1).

Study CharacteristicsOf 40 included trials, 30 (75%) evaluated only bilateral

patients, whereas 10 (25%) included a combination ofunilateral and bilateral patients in each group. The meannumber of study subjects was 165 (range, 14-577).Twenty-nine studies (73%) reported nonsignificantfindings for the outcome measures analyzed using thet test (P N .05). Common outcomes reported included theKnee Society Scores, Harris Hip Scores, Western OntarioMcMaster University Osteoarthritis Index scores, rangeof motion, and alignment in degrees. Fifteen studies(37.5%) achieved high-quality reporting (Detsky score =16 or higher).

Correct Use of Statistical TestsOf the 30 studies evaluating only bilateral patients, 12

(40%) correctly used the dependent t test, whereas 16(53%) incorrectly used the independent t test. Twostudies (7%) only described using a t test without givingfurther details. Of the 10 studies that included bothunilateral and bilateral patients, 8 (80%) used theindependent t test, 1 (10%) did not specify which type

of t test was used, and 1 (10%) used both theindependent and dependent t tests. For the latterstudy, the authors reported a single P value with nodiscussion of how the results from separate t tests werecombined. We did not identify a significant correlationbetween the year of publication and the use of thecorrect test (Fig. 1).

Impact on Study ResultsOf the 24 studies that did not use a dependent t test, the

3 forwhichwe are unsure, and the 1 study that used bothtests, 12 provided sufficient data to calculate their effectsizes. Nine (75%) reported effect sizes of 0.6 or less, 1(8%) reported an effect size of 0.6 to 0.8, and 2 (17%)reported effect sizes of 1.0 or greater. Without the rawdata from each study, we cannot reliably conclude whenthe use of the dependent t test would have resulted in achange from nonsignificant to significant P value.

DiscussionWe conducted a systematic review of statistical tests

used in 40 RCTs of bilateral TKA or THA. Twenty-eight(70%) of 40 articles reviewed used the incorrectstatistical test or did not adequately report on the t testused. It should be noted that 17 of the studies reviewedwere published by the same author across 4 orthopedicjournals (Table 1). Fifteen of their publications used theincorrect independent t test, whereas the other 2 usedthe correct dependent test. Of the 24 studies incorrectlyusing the independent t test in our review, 15 were fromthis single author. Our findings are meant to highlightfor future authors and journal readers the importance ofmethodologic vigor in performing and analyzing RCTs ofthis design.

Strengths and LimitationsOur study has several strengths. First, we conducted a

thorough search of the literature in duplicate to limit any

814 The Journal of Arthroplasty Vol. 26 No. 5 August 2011

selection bias. Second, we used a validated checklist toevaluate the methodologic quality of the studies.There are also several potential limitations of our

systematic review. First, only studies that were pub-lished or accepted for publication were identified. Wedid not include any unpublished abstracts because theygenerally do not provide sufficient detail on statisticalanalysis performed. Second, our study looked exclu-sively at RCTs, and as discussed, matched case-controlstudies may be prone to the same error. Finally, we wereforced to exclude RCTs that made no mention of theirmethods of statistical analysis.

Relevant LiteratureThe t statistic for 2 independent samples is equal to the

observed difference between the sample means dividedby the standard error of the difference between themeans (x − μo/SEx), as compared with the meandifference divided by the standard error of the meandifference for 2 paired samples. When samples arematched, there is less variability in the samplingdistribution of difference scores, resulting in a smallerpooled standard deviation. The outcome is a smallerstandard error of the difference (denominator). Conse-quently, if the difference between the means (numer-ator) is the same, the t value for a dependent samplest test will be larger than that of an independent samplest test. A larger t value (for a consistent degrees offreedom) is more likely to attain statistical significanceby deviating farther from the mean of the normaldistribution [48].Incorrect use of an independent t test for a dependent

sample results in a smaller than expected t value [48].The comparison is less likely to achieve statisticalsignificance, resulting in a greater probability of a typeII error (failing to reject the null hypothesis when it is infact false). Of the 16 studies that incorrectly used theindependent t test for a purely dependent sample, 14reported findings that were not statistically significant.Table 2 demonstrates the relationship between effectsizes and the P values generated using the independentand dependent t tests for 2 hypothetical data sets.A smaller effect size results in a greater difference in

Table 2. Comparison of Dependent and Independent t Tests fo20 Patients

Effect SizePower % of

Independent t Test

10 pairs or 10 in each of 2 groups 0.4 140.6 250.8 401 56

20 pairs or 20 in each of 2 groups 0.4 230.6 460.8 691 87

P values from the independent and dependent t tests.Simply put, the dependent t test has more statisticalpower and is more likely to correctly reject the nullhypothesis when a true significant difference exists [48].

t Test for Studies With Bilateral andUnilateral PatientsOf the articles included in our review, 10 compared the

pooled outcomes of patients undergoing both unilateraland bilateral surgeries. In such cases, statistical analysismust be performed with caution. Some advocate for useof the dependent t test considering the presence of thepaired samples and that the randomized design likelybalanced all potential confounders between groups.Others advocate for use of the independent t testbecause it is a more conservative approach and thereforeless likely to result in a type I error (incorrectly rejectingthe null hypothesis when it is in fact true). Calculating aP value for the paired and unpaired samples individuallyand combining those into one final result must beavoided. The most appropriate analysis would be someform of clustered regression, or random effects approachto account for the dependencies in the data.

t Test for Other Study TypesOur review focused only on RCTs; however, other

study designs represent paired data and should beanalyzed with paired tests. Case-control studies ofteninvolve tightly matched groups to control for confound-ing. Longitudinal studies comparing results taken fromthe same patients at different time points; for example, apredesign-postdesign also represents an example ofpaired data. In a crossover study, one group of patientsreceives the treatment, whereas another group receivesa placebo or control. After a period of time withouttreatment (washout period), the groups exchangetreatments, so that both have undergone treatmentand control states. In the first design, the selection of onestudy group directly determines the other group,whereas in the latter 2 designs, both therapies are testedin the same patient. The dependent t test is one possiblemethod of analysis in all of these situations.It is important to choose the appropriate statistical test

from the outset of the study, because it will affect the

r Various Effect Sizes for a Hypothetical Dataset of 10 and

Power % ofDependent t Test

Independent t Test,P Value (T Statistic)

Dependent t Test,P Value (T Statistic)

20 0.58 (0.56) 0.24 (1.25)40 0.48 (0.73) 0.11 (1.78)62 0.12 (1.6) 0.03 (2.6)80 0.01 (2.8) 0.01 (3.3)39 0.19 (1.3) 0.08 (1.9)72 0.09 (1.8) 0.02 (2.7)92 0.07 (1.9) 0.004 (3.3)99 0.008 (2.8) b0.001 (4.7)

Use of Student t Test in Randomized Trials � Gandhi et al 815

sample size required. Because dependent samples haveless variance in the data, the sample size required toshow a specified difference will be less.Our findings support previously published reviews

that have questioned the quality of reporting inorthopedic trials [3-6]. Randomized controlled trialsare the best method of scientific testing because theyprovide the strongest evidence for concluding a rela-tionship between an intervention and an outcome [49].However, the results of methodologically well-designedstudies can be compromised when the wrong statisticalanalysis is used. When planning a study, it is essential toconsider the sampling distribution for the patientsbecause this will guide the statistical test that shouldbe used. Our findings also highlight the importance forthe reader to critically appraise the methodologic vigorof a study to determine the scientific merit of theconclusions presented.

References1. Gehlbach SH. Interpreting the medical literature: practical

epidemiology for clinicians. 5th ed. USA: McGraw-HillMedical; 2006; p. 166.

2. Livingston EH. Who was student and why do we care somuch about his t-test. J Surg Research 2004;118:58.

3. Chan S, Bhandari M. The quality of reporting oforthopaedic randomized trials with use of a checklist fornonpharmacological therapies. J Bone Joint Surg Am2007;89:1970.

4. Rama KRBS, Poovali S, Apsingi S. Quality of reporting oforthopaedic diagnostic accuracy studies is suboptimal. ClinOrthop Relat Res 2006;447:237.

5. Bhandari M, Richards RR, Sprague S, et al. The quality ofreporting of randomized trials in the Journal of Bone andJoint Surgery from 1988 through 2000. J Bone Joint SurgAm 2002;84:388.

6. Dulai SK, Slobogean BLT, Beauchamp RD, et al. A qualityassessment of randomized clinical trials in pediatricorthopaedics. J Pediatr Orthop 2007;27:573.

7. Detsky AS, Naylor CD, O'Rourke K, et al. Incorporatingvariations in the quality of individual randomized trialsinto meta-analysis. J Clin Epidemiol 1992;45:255.

8. Kim YH. Comparison of primary total hip arthroplastiesperformed with a minimally invasive technique or astandard technique: a prospective randomized study. JArthroplasty 2006;21:1092.

9. Kim YH, Cho SH, Kim RS. Drainage versus nondrainage insimultaneous bilateral total hip arthroplasties. J Arthro-plasty 1998;13:156.

10. Meding JB, Keating EM, Ritter MA, et al. Total kneearthroplasty after high tibial osteotomy. J Bone Joint Surg2000;82-A:1252.

11. Kim YH, Kook HK, Kim JS. Comparison of fixed bearingand mobile bearing total knee arthroplasties. Clin OrthopRelat Res 2001;392:101.

12. Kim YH, Kim JS, Cho SH. A comparison of polyethylenewear in hips with cobalt-chrome or zirconia heads: aprospective, randomised study. J Bone Joint Surg Br 2001;83-B:742.

13. Lau SKK, Chiu KY. Use of continuous passive motion aftertotal knee arthroplasty. J Arthroplasty 2001;16:336.

14. Kim YH, Kim JS. Incidence and natural history of deep-vein thrombosis after total knee arthroplasty: a prospective,randomised study. J Bone Joint Surg Br 2002;84-B:566.

15. Wood DJ, Smith AJ, Collopy D, et al. Patellar resurfacing intotal knee arthroplasty: a prospective, randomized trial.J Bone Joint Surg Am 2002;84:187.

16. Kim YH, Kim JS, Oh SH, et al. Comparison of porous-coated titanium femoral stems with and without hydroxy-apatite coating. J Bone Joint Surg Am 2003;85:1682.

17. Kim YH, Oh SH, Kim JS, et al. Contemporary total hiparthroplasty with and without cement in patients withosteonecrosis of the femora head. J Bone Joint Surg Am2003;85:675.

18. Kim YH, Oh SH, Kim JS. Incidence and natural history ofdeep-vein thrombosis after total hip arthroplasty: aprospective and randomised clinical study. J Bone JointSurg Br 2003;85-B:661.

19. Kim YH, Oh SW, Kim JS. Prevalence of fat embolismfollowing bilateral simultaneous and unilateral total hiparhtroplasty performed with or without cement: aprospective, randomized clinical study. J Bone Joint SurgAm 2003;84:1372.

20. Komatsu T, Ishibashi Y, Otsuka H, et al. The effect ofsurgical approaches and tourniquet application on patel-lofemoral tracking in total knee arthroplasty. J Arthro-plasty 2003;18:308.

21. Price AJ, Rees JL, Beard D, et al. A mobile-bearing totalknee prosthesis compared with a fixed-bearing prosthesis:a multicentre single-blind randomised controlled trial.J Bone Joint Surg Br 2003;85-B:62.

22. Waters TS, Bentley G. Patellar resurfacing in total kneearthroplasty: a prospective, randomized study. J BoneJoint Surg Am 2003;85:212.

23. Kim YH, Kim JS. Comparison of anterior-posterior-glideand rotating-platform low contact stress mobile-bearingtotal knee arthroplasties. J Bone Joint Surg Am 2004;86:1239.

24. Lachiewicz PF, Kelley SS, Haden LR. Two mechanicaldevices for prophylaxis of thromboembolism after totalknee arthroplasty: a prospective, randomised study. J BoneJoint Surg Br 2004;86-B:1137.

25. Maruyama S, Yoshiya S, Matsui N, et al. Functionalcomparison of posterior cruciate-retaining versus posteri-or stabilized total knee arthorplasty. J Arthroplasty 2004;19:349.

26. Won YY, Dorr LD, Wan Z. Comparison of proximalporous-coated and grit-blasted surfaces of hydroxyapa-tite-coated stems. J Bone Joint Surg Am 2004;86:124.

27. Carlsson A, Björkman A, Besjakov J, et al. Cemented tibialcomponent fixation performs better than cementlessfixation. Acta Orthop 2005;76:362.

28. Kim YH, Sohn KS, Kim JS. Range of motion of standardand high-flexion posterior stabilized total knee prostheses;a prospective, randomized study. J Bone Joint Surg Am2005;87:1470.

29. Kim YH. Comparison of polyethylene wear associated withcobalt-chromium and zirconia heads after total hipreplacement; a prospective, randomized study. J BoneJoint Surg Am 2005;87:1769.

816 The Journal of Arthroplasty Vol. 26 No. 5 August 2011

30. Rees JL, Beard DJ, Price AJ, et al. Real in vivo kinematicdifferences between mobile-bearing and fixed-bearingtotal knee arthroplasties. Clin Orthop Relat Res 2005;432:204.

31. Sharrock NE, Go G, Mayman D, et al. Decrease inpulmonary artery oxygen saturation during total hiparthroplasty. J Arthroplasty 2005;20:499.

32. Walmsley PJ, Kelly MB, Hill RMF, et al. A prospective,randomised, controlled trial of the use of drain in total hiparthroplasty. J Bone Joint Surg Br 2005;87-B:1397.

33. Yamasaki S, Masuhara K, Fuji T. Tranexamic acid reducespostoperative blood loss in cementless total hip arthro-plasty. J Bone Joint Surg Am 2005;87:766.

34. Song EK, Seon JK, Yoon TR, et al. Functional results ofnavigated minimally invasive and conventional total kneearthroplasty: a comparison in bilateral cases. Orthopedics2006;29:S145.

35. Vendittoli PA, Lavigne M, Girard J, et al. A randomisedstudy comparing resection of acetabular bone at resurfa-cing and total hip replacement. J Bone Joint Surg Br 2006;88-B:997.

36. Beard DJ, Pandit H, Price AJ, et al. Introduction of a newmobile-bearing total knee prosthesis: minimum three yearfollow-up of an RCT comparing it with a fixed bearingdevice. Knee 2007;14:448.

37. Berth A, Urbach D, Neumann W, et al. Strength andvoluntary action of quadriceps femorismuscle in total kneearthroplasty with midvastus and subvastus approaches.J Arthroplasty 2007;22:83.

38. Kim KJ, Iwase M, Kotake S, et al. Effect of bone marrowgrafting on the titanium porous-coated implant in bilateraltotal knee arthroplasty. Acta Orthop 2007;78:116.

39. Kim YH, Kim DY, Kim JS. Simultaneous mobile- and fixed-bearing total knee replacement in the same patients: aprospective comparisonofmid-termoutcomesusing a similardesign of prosthesis. J Bone Joint Surg Br 2007;89-B:904.

40. Kim YH, Kim JS, Kim DY. Clinical outcome and rate ofcomplications after primary total knee replacement per-formed with quadriceps-sparing or standard arthrotomy.J Bone Joint Surg Br 2007;89-B:467.

41. Kim YH, Kim JS, Yoon SH. Alignment and orientation ofthe components in total knee replacement with andwithout navigation support; a prospective, randomisedstudy. J Bone Joint Surg Br 2007;89-B:471.

42. Lee JM, Lee CW. Comparison of hydroxyapatite-coated and non-hydroxyapatite-coated noncementedtotal hip arhtroplasties in same patients. J Arthroplasty2007;22:1019.

43. Dalury DF, Snow RG, Adams MJ. Electromyographicevaluation of the midvastus approach. J Arthroplasty2008;23:136.

44. Kim YH, Kim JS, Yoon SH. A recession of posterior cruciateligament in posterior cruciate-retaining total knee arthro-plasty. J Arthroplasty 2008;23:999.

45. Dalury DF, Mulliken BD, Adams MJ, et al. Early recoveryafter total knee arthroplasty with and without patellareversion and tibial translation: a prospective randomizedstudy. J Bone joint Surg Am 2009;91:1339.

46. Kim YH, Choi Y, Kwon OR, et al. Functional outcome andrange of motion of high-flexion posterior cruciate-retain-ing and high-flexion posterior cruciate- substituting totalknee prostheses; a prospective, randomized study. J BoneJoint Surg Am 2009;91:753.

47. Rama KRBS, Vendittoli PA, Ganapathi M, et al. Hetero-topic ossification after surface replacement arthroplastyand total hip arthroplasty; a randomized study. J Arthro-plasty 2009;24:256.

48. Corty EW. Using and interpreting statistics: a practical textfor the health, behavioural, and social sciences. Missouri:Mosby, Elsevier: 2007; p. 296,431,443.

49. Dawson B, Trapp RG. Basic and clinical biostatistics.4th ed. McGraw-Hill Companies Inc; 2004; p. 7.