CGA FAQ, Statistics: What people said...

I just received this enquiry and was about to email my response when it occurred to me that this might be a good topic for discussion on CGA. Look forward to your comments!

We are a little green when it comes to the statistical interpretation of gait lab data. I have been attempting to look at the effects of two
  orthotic interventions on pathological gait. We have completed ANOVA analysis on 18 gait parameters so far. We were quite pleased
  with ourselves, until it was pointed out that our error level of 5%, effectively meant we had a 1 in 20 chance of interpreting a parameter as
  significantly different; when error was to true cause of the difference.

  It was suggested that it is possible to test the sensitivity of each parameter, although he was unable to shed any light on how this
  is accomplished.

  Could you provide any further enlightenment??


Well, I'm no stats expert either, I'm afraid. But there are basically two types of error:

Type I: when you conclude that the hypothesis is correct (that there is a difference between two groups, e.g. control vs. treated) when it's not. This is the commonest error - caused by chance, as you mention. You can reduce the chance of making your error by reducing alpha from 5% to 1%, but very few people do this in rehab research;

Type II: (also common but not as well recognized) when you conclude that the hypothesis is not proven (i.e. there's no difference between the two groups) but in fact there is a difference. This is usually caused by having insufficient subjects (i.e. low statistical power, or Beta) - very common in our field! Ther are ways to calculate the power needed (and therefore number of subjects needed if you know the "effect size" (the size of the difference that is considered clinically significant - usually derived from a pilot study).

My own personal view is that stats cause more problems that they are worth in rehab research. I'd far rather see people just present the data and let me make up my own mind. Unfortunately, stats have become expected (even though they are usually very dubious because of the small numbers of subjects). The risk is that people just look at the stats and don't look at the data.

Even when you have enough subjects for the various criteria to be satisfied (e.g. normal distributions) conventional (Fischer) statistics can still be quite misleading. If you speak to mathematicians these days they will often laugh when you mention Fischer and tell you that the only reason he did stats this way was because of the limitation in calculating power at the time. Modern statisticians are much more interested in computer simulation studies, which are apparently much more informative.

Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America
620 Michigan Ave NE, Washington, DC 20064
Tel. 202-319-6134,  fax 202-319-4287

ANOVA is the right test: it looks globally to see if there differences between the groups - if (and only if) there is you can now inspect your
individual groups to see which are different  - from the global mean.
From Dr Christopher Smith
Head of Biomedical Science BSc
Centre for Applied Biomedical Research, King's College London
4.1 Shepherd's House, Guy's Campus, London Bridge SE1 1UK
Phone/fax 020 7848 6301, Biomed Office 020 7848 6400
If need be, phone me on 0797 0713507

Just some food for thought:

 Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would
often apply with justice and force: "There are three kinds of lies: lies, damned lies and statistics.
                                                                                                                                                            - Autobiography of Mark Twain

Alan Lovejoy

There was a good editorial in this regard written by Jules Rothstein, the editor of the Journal of the American Physical Therapy Assoc, this past May.  Here is the hyperlink: .  Speak to everyone soon, John J Fraser, PT, MS

Greetings Chris et al:
I'm reminded of an epidemiologist citing Winifred Castle (a statistician) who, apparently, said:

We researchers use statistics the way a drunkard uses a lamp post - more for support than illumination.


Ted Stevenson

At least you are thinking about this issue. Its exceedingly common to see papers published who have investigated a statistical tests on
a thousand different parameters and find that 20 of them show "statistically significant results" at the 5% level. It's particularly
prevalent in gait analysis where there is no shortage of parameters to look at. There are various solutions. There is a related though
not identical phenomenon that the more parameters you look at the higher the percentage of statistically significant results will be the
product of random chance.

The most commonly used is called the Bonferroni correction which effectively says the more tests you do the lower the level at which
you should accept statistical significance. Any decent stats book will guide you through this process as its applied to multiple t-tests.
The principle is the same for ANOVA but I'm not sure whether the technical details are the same.

A much stronger method is to limit the number of parameters you look at before you start. Preferably nominate one key parameter in
advance and stick to this - what ever you do make sure you can count the number of parameters on one hand (and no polydactyly).
How you do this is up to you. You can either use you clinical skill and judgement to nominate these or do a pilot study, run tests on
all the variables, and use the data to nominate the top five variables for a definitive trial. The problem with this is that in the present
environment no-one will believe you. Running multiple statistical comparisons on data is so common that it will be assumed that
you've done all those tests  and just reported the good results. In big scale projects you can now actually pre-declare your primary
outcome measures with the Lancet before you start to ensure that you don't cheat. This is a little over the top for a most of us mere
mortals though.

Another approach which I've heard proposed recently from a visiting lecturer  from the UK (Dr Jonathan Sterne, University of
Bristol, UK - I gather he's just brought a new book out which it may be worth looking for) is to move away from assuming that
anything below 5% is significant and anything above is not. Clearly there's little difference between p=0.0499 and p=0.0501 and its
daft to have a precise cut-off. Sterne would have you look at the p-values as indicating comparative levels of confidence in results.
This then forms the basis for a balanced assessment of the data and suggestion of probable explanations (which may include the
suggestion that any particular result is a chance finding). In biomechanics it is rare that your parameters are ever fully independent and
finding patterns within your significance values amongst related parameter can be powerful evidence of a real effect rather than an
aberration. Using 5% as a clear cut-off makes the process of science appear objective but this is a lie. We should accept that the
interpretation of results is subjective and get down to the nitty-gritty of doing this honestly and intelligently.

Another hang-up of Stern's, which is partially related, and reasonably well supported in the literature is to focus more on confidence
limits in interpretting data rather than p-values.

I find Martin Bland's An introduction to medical statistics to be an excellent guide to these issues (although it is a little superficial in its
treatment of ANOVA). Bland (mostly with Doug Altman) has also written a number of articles on related issues for the BMJ which
can be accessed easily through his web-site (

This whole area is a can of worms but you've got no option but to get to grip with it if you want to valid science.

Hope this is useful.

Richard Baker

Gait Analysis Service Manager, Royal Children's Hospital
Flemington Road, Parkville, Victoria 3052
Tel: +613 9345 5354, Fax +613 9345 5447

Adjunct Associate Professor, Physiotherapy, La Trobe University
Honorary Senior Fellow, Mecahnical and Manufacturing Engineering, Melbourne University

Living With Error (from Physical Therapy May 2003)

            Even as we mourn the tragic end of the shuttle Columbia, we can marvel at NASA's
            incredible history of 10 successful manned Apollo missions and more than 100 successful
            shuttle missions. In addition to highly trained personnel, spaceflight requires highly reliable
            technology. When NASA talks about reliability, the agency ultimately is talking about how
            long parts function before they are likely to fail. Consider the Apollo space program:
            Some experts have suggested that there were a total of about 2,000,000 functional parts
            in the Saturn V rocket, lunar module, and command module. How much error could have
            been tolerated in this complicated array? Even if the reliability for each part had been
            99.9% for its contribution to the mission, the potential existed for about 2,000 parts to
            fail—in which case, the command module almost certainly would not have made it to the
            moon and back!

            When we physical therapists talk about reliability, of course, we're talking about the error
            associated with a measurement. Reliability of 99.9% for a measurement used in physical
            therapy would almost always be astoundingly good! We could only dream….

            Reliability can be a critical issue in the planning of a study. It also is a critical issue in
            clinical practice. The Journal has found that, regardless of whether authors are describing
            research or a patient case, the reason why a measurement was used cannot always be
            discerned in the submitted manuscript. Some authors do discuss the selection of
            measurements; other authors have to be asked to do so during revision. Either way,
            however, authors rarely clarify their clinical decision making—clarification that would
            enhance an otherwise superb article.

            The truth is, no measurement is perfect. Whether physical therapists are making a
            diagnosis or determining a change in impairment or disability, all measurements have some
            error associated with them. All of our decisions can be error ridden! And errors are not
            eliminated or minimized by ignoring their presence.

            Authors often try to justify the use of tests with the statement, "The reliability and validity
            of the measurements have been established." Even with a supporting reference, that
            statement is untenable. Reliability isn't like pregnancy. You can say that a woman is either
            pregnant or not pregnant—but you can't say that a measurement is either reliable or
            unreliable. Not only does error always exist, it is context dependent, and it relates to how
            the measurement will be used.

            Is the error so large that using the measurement would be unlikely to provide useful
            information? Both in research and in routine practice, we have to consider whether the
            error could interfere with understanding the results of research or practice. Unlike
            statements of pregnancy, estimates of reliability lie along a continuum, and we need to
            know where along the continuum they lie and what that means for how the measurement
            can be used.

            We also benefit from knowing something about how other authors have studied the
            reliability of the measurement being used. Did other authors study subjects who are similar
            to those currently being described? Did the physical therapists who took the
            measurements in those other studies have training and experience similar to the physical
            therapists taking the measurements in the current study? Were the procedures similar?
            Was the research sufficiently robust in terms of numbers of subjects and methods that the
            estimated error can be accepted as an excellent approximation of the true error? These
            are not esoteric issues. They relate to the practical world in which we live. And they are
            the basis on which clinicians should choose the measurements they use with patients.

            Unless authors share their thinking about the measurements they used, the concepts in an
            article cannot be developed, and readers are left to imagine what they should actually
            have been told. Instead of saying that reliability "was established," careful authors say,
            "We believe that the measurement was sufficiently reliable to be used because…,"
            followed by a logical argument, references, and details. In the Journal's experience, it
            takes only a few sentences to do this right. When the issue requires more than a few
            sentences, that usually means there is complexity, and the paper therefore will be made
            better by addressing the issue and the complexities forthrightly.

            In characterizing estimates of error—specifically, statistics that describe reliability—many
            authors cite experts such as Landis and Koch,1 who contended that values of kappa
            above 80% indicated excellent agreement, values above 60% indicated substantial levels
            of agreement, values of 40% to 60% indicated moderate agreement, and values below
            40% indicated poor to fair agreement. Other authors discuss other statistics.
            Unfortunately, what they have in common is an arbitrary method of judgment that does
            not relate to how a measurement will be used.

            For authors, the convenience of being able to "classify" reliability estimates and then give
            them value-laden names is clear. By naming reliability estimates, authors can discuss them
            quickly and "be done with it," claiming that their measurements have been blessed by the
            well-respected authors of the original papers (if those measurements, for example, reach
            excellent levels). The problem is that we have no basis for the classification. If we were
            considering the diagnostic accuracy of two surgeons, for instance, would we find it
            acceptable that there was a 20% chance of disagreement when it came to the decision to
            perform life-threatening surgery? On the other hand, that level of disagreement about the
            necessity to remove a lipoma wouldn't (in my view) be so bad.

            Can we tolerate having the same amount of error in all of our measurements? If we use a
            measurement that has a possible 30% error to determine whether there is normal
            accessory motion at the glenohumeral joint, can we consider that measurement to be as
            useful as a measurement with a possible 30% error that is used to determine whether we
            should refer a patient to a physician in an effort to ward off possible permanent
            neurological damage due to disc disease?

            Authors and clinicians have an obligation to provide an argument as to why any problems
            with a measurement are not sufficiently large to be consequential, and the amount of error
            that we can tolerate depends on what we are measuring and how a measurement will be
            used. The Landis and Koch approach has no context and does not take into account the
            nature of the measurement and the decisions that might be made based on the use of the
            measurements. Context and use are critical issues for both authors and clinicians, the
            difference being that authors must discuss these issues explicitly in submitted papers,
            whereas clinicians must consider these issues in patient management.

            Measurements are not equivalent to aerospace parts, of course, but there is something
            that the Apollo space program can teach us about reliability. Because NASA could not
            reduce the error level to "acceptable," they adopted an alternate strategy: planned
            redundancy, usually triple redundancy. They developed so many backup systems that a
            catastrophic failure could occur only when there were multiple failures of the same system.
            When our clinical measurements have more error than we want, the Apollo example
            should remind us that alternate strategies can be developed—but authors need to explain
            these strategies, and, if they did not use any, authors should explain why.

            Journal authors work hard in conducting studies and documenting practice, and harder
            still at preparing and revising their papers. They do their own work a disservice when they
            fail to share their thought process in choosing measurements and other aspects of their
            research methods. The same is true of clinicians who do not elaborate on why they chose
            measurements and interventions in case reports or who practice without regard to the
            quality of their measurements. Ignorance about the error level associated with
            measurements or dogmatic refusal to consider research evidence is poor practice.

            Please don't view this Note as a statement that reliability is more important than other
            measurement properties—it is not! Validity, specificity, sensitivity, and a host of other
            properties—as well as related topics such as receiver operating characteristics (ROC
            curves)—are equally, if not more, important. The issue for all of these topics is the use,
            and the usefulness, of measurements. We need to justify and explain what we do, thereby
            achieving better articles, better practice, and, in the long run, better physical therapists.

            Jules M Rothstein, PT, PhD, FAPTA
            Editor in Chief


            1 Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics. 1977;33:159–174.


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