Shoulder tremor in archery: Lin 2010 study

Ten novice men, mean age 21.9 years, hold six simulated shooting positions still for seven seconds each, with a twenty-six pound recurve bow. The six positions come from three arm elevation angles, ninety, one hundred and one hundred and ten degrees, by two draw positions, partial and full. No arrow is shot: these are isometric contractions held in a laboratory. What is recorded is the electrical activity of eight muscles, four that move the humerus and four that move the scapula, and the tremor, derived from the acceleration component of motion sensors placed on the sternum, the acromion and the distal humerus, analysed in two frequency bands, three to seven hertz and eight to twelve.

Two results emerge from the comparisons between positions. At full draw the muscles work harder than at partial draw, both those of the humerus and those of the scapula. And the tremor is greater at one hundred and one hundred and ten degrees of elevation than at ninety, in both bands; it is also greater at the humerus than at the scapula.

The part on the correlations is the one the abstract carries forward, and it needs reading with care. The authors compute twenty-four correlations between muscle activity and tremor power at full draw and another twenty-four at partial draw, one for each combination of muscle group, sensor, band and angle. The values run from minus 0.57 to plus 0.57, that is they change sign according to the angle and to the sensor: at one hundred and ten degrees, at the humerus, more activity goes with more tremor (plus 0.573), while at one hundred degrees the same pair gives minus 0.424. No p-value is reported for any of the correlations, and the asterisks in the tables do not mark significance but bands of magnitude, as the legend states.

The authors conclude that ninety degrees of elevation at full draw is the position suited to the demands of archery, and that the activity of the scapular muscles counts towards reducing humerus tremor. In their limitations, though, they write themselves that the largest correlation, minus 0.569, explains thirty-three per cent of the variation, and that the effect of tremor on performance was not studied.

A single test session, in a laboratory, on the drawing arm, right and dominant in all ten. Body mass index 22.6 ± 3.0. Some familiarisation practice before collection, then each position held for seven seconds, with the data taken from the middle five seconds. The elevation angle was monitored by the tracking system.

The tremor was captured with an electromagnetic position tracking system, sampled at one hundred and twenty hertz, with a stated accuracy of 0.15 degrees on orientation and between 0.3 and 0.8 millimetres on position. The sensors sat on the sternum, the superior surface of the acromion and the distal humerus between the two epicondyles; the scapular and humerus traces were analysed. From the time series of displacements the power spectral density of the acceleration component was computed by Fourier analysis in Matlab, and the power, normalised to the peak, was summed within the two bands.

For the electromyography, surface electrodes of silver and silver chloride, a recording diameter of ten millimetres and twenty millimetres between centres, skin lightly abraded and cleaned with alcohol, reference on the olecranon of the drawing arm, impedance kept below fifteen kilohms. Gain of one thousand, common mode rejection of 86 decibels at sixty hertz, bandwidth from ten to one thousand hertz, sampling at two thousand hertz per channel on a sixteen-bit converter.

The four humeral muscles are the middle deltoid, the biceps, the infraspinatus and the teres minor; the four scapular ones the upper trapezius, the serratus anterior, the rhomboid major and the latissimus dorsi, with the application points described one by one. The signal was reduced to root mean square envelopes at twenty samples per second. The mean amplitude of each muscle was normalised not to a maximum contraction but to the composite mean of its own group, then the four components of each group were summed: the values are therefore relative contributions within the group, not percentages of a maximal effort.

Synchronisation between the two systems ran through an acoustic signal and a switch operated by the investigator, which generated an electrical pulse collected by both.

The analysis uses two-way repeated measures analysis of variance, elevation by draw position, on the amplitude of the two muscle groups, and three-way, adding the sensor location, on tremor power, with pairwise comparisons Bonferroni-corrected where needed. Pearson correlations between amplitude and tremor power were computed separately for each angle, position and sensor. The authors state reading bands for the coefficients: above 0.75 a good to excellent relationship, between 0.5 and 0.75 moderate to good, between 0.25 and 0.5 fair, below 0.25 little or none.

None of the correlations the abstract carries forward is statistically significant, and this can be checked against a table. With ten participants, that is eight degrees of freedom, a Pearson correlation reaches the 0.05 threshold from 0.632 upwards. The largest in the whole full-draw table is 0.573, which corresponds to p equal to 0.083; the one the authors cite as the study's maximum, minus 0.569, sits at 0.10. The article reports no p-value for any correlation, although the methods say the correlations served to assess their significance, and the limitations nonetheless state that there are significant relationships between tremor and muscle activity.

The asterisks in the two tables are not p-values. The legend says so: they mark bands of coefficient magnitude, one asterisk between 0.25 and 0.5, two between 0.5 and 0.75. A table of correlations with asterisks is read by habit as a table of significance, and this one is not: it is a reading trap, and it deserves naming.

The correlations number forty-eight in all, twenty-four for each draw position, and they change sign. At the humerus in the low band they go from minus 0.424 at one hundred degrees to plus 0.573 at one hundred and ten; at the scapula in the high band from plus 0.492 at ninety degrees to minus 0.261 at one hundred. The abstract reports the positive subset, from 0.43 to 0.57, as though it were the result. Read in full, the table says that the link between how hard a muscle works and how much the limb trembles depends on position in a way these data do not explain, and not that more activity means more tremor.

The degrees of freedom do not add up with ten participants. In the two-way analysis the effect of draw position is reported as F on 1 and 16 degrees of freedom and that of elevation as F on 2 and 16: in a repeated measures design on ten people the error would be 9 for the first and 18 for the second, and in no case does a one-degree-of-freedom effect take 16. In the three-way analysis the error is 28, which corresponds to neither 9 nor 18. And within one sentence the elevation effect, which has three levels and therefore two degrees of freedom, is reported as F on 1 and 28 for one band and on 2 and 28 for the other. These are reporting inconsistencies, and they leave a reader without knowing how many people the comparisons ran on.

In the partial-draw table a value of minus 0.920 appears with no asterisk at all, while the legend would assign three asterisks to anything above 0.75. The authors write in their limitations that the study's maximum correlation is minus 0.569, so that number is not a result of the study but an error, of printing or of text extraction.

There is a flaw too in the passage that defines what is being measured. The introduction explains that the two components of tremor come one from the stretch reflex, given as eight to twelve hertz, and the other from the supraspinal system, given also as eight to twelve hertz: the same band twice, where one of the two should be the low band. The following sentence clarifies that the reflex component falls from eight to twelve down to three to seven as contraction increases, so the intention is clear, but the definition the whole analysis rests on is written in a way that does not hold.

On the sample and the task, the limit is large and only partly declared. These are ten novices, not archers, and all of them hold the same twenty-six pound bow, so full draw is a different relative effort for each and no normalisation to individual strength is described. No arrow is shot, there is no clicker, no release and no score: these are positions held still for seven seconds. The authors write that the effect of tremor on performance was not studied, and then conclude that ninety degrees at full draw is the position suited to the demands of archery. That recommendation does not come from the data, because the data contain no measure of performance.

Finally the electromyography is normalised not to a maximum contraction but to the composite mean of its own muscle group. The numbers are therefore shares within the group: they say which muscle of the group contributes most, not how hard it is working, and they do not compare between people or against the values of other studies.

Two things in this study rest on the comparisons between positions rather than on the correlations, and those are the ones to keep. The first is that at full draw the shoulder muscles work harder than at half draw, both those moving the humerus and those moving the scapula: obvious to say, useful to have measured. The second is that tremor grows when the bow arm rises above the line, that is at one hundred and one hundred and ten degrees of elevation compared with ninety, and that it is larger at the humerus than at the scapula. Put in the terms of a shooting hall: the higher the arm is held, the more the structure oscillates, and the oscillation comes from the arm rather than from the scapula.

From this the authors conclude that ninety degrees at full draw is the suitable position. It is plausible and consistent with what is taught, but the study contains no arrow and no score, so that sentence is an inference rather than a measurement: these are ten novices holding a position for seven seconds in a laboratory with the same twenty-six pound bow.

The part on the correlations, which is the one the abstract carries forward, cannot be used. With ten people a correlation becomes significant from 0.632 upwards, and the study's largest is 0.573: none reaches the threshold, and the article publishes no p-value. The asterisks in the tables, which suggest significance, mark bands of magnitude instead. And the signs change with the angle, so the data yield neither that more activity means more tremor nor the opposite.

One indication of direction remains worth knowing, with that caution: at some angles more work from the scapular muscles goes with less tremor of the humerus. It is the same reasoning behind teaching an archer to carry with the scapula rather than hold with the arm, and here it appears as a trace, not as evidence.

The registry keeps this work as a laboratory measurement on ten novices in static positions, for the comparison between elevation angles and between full and partial draw, and not for the correlations between muscle activity and tremor.