Arm endurance and shooting: Nusufi 2017 study

Twenty-four archers from the provincial federation of Aceh were measured once on three things: a push-and-pull dynamometer test, which the author calls arm muscle endurance, arm length with a tape measure, and an accuracy score over 36 arrows shot at 10, 20 and 30 yards. The correlations reported are very high: r = 0.897 between the dynamometer and the score, r = 0.871 between arm length and the score, and r = 0.958 between the two predictors. The author turns the first two values into percentage contributions, 80.46% and 75.86%, by squaring them.

This is where the arithmetic fails, and the failure sits at the centre of the result. If two measures each account on their own for 80% and 76% of the variation in the score, together they cannot account for less; yet the multiple correlation reported is R = 0.816, that is 66.6%, less than either one taken singly. The statistical check does not add up either: the printed formula starts from R = 0.816 and arrives at F = 33, whereas the same calculation carried through gives about 21, and the critical value appears twice on the same page with two different figures, 3.44 and 3.47.

The paper's conclusion, that the two measures contribute significantly to shooting accuracy, therefore rests on numbers that do not hold together.

The author describes the study as descriptive and correlational, on a single group measured in the field. The push-and-pull dynamometer test runs like this: the athlete presses the device with both hands as hard as possible, then pulls it in opposite directions, with two attempts at each. It is a measure of maximal force in two brief efforts, not of endurance, despite the name the paper gives it; the reference table reproduced, from a 1996 Indonesian ministry manual, grades males from below 29 to above 51 without stating the unit.

Arm length is measured with a tape, standing with the arms by the sides, from the outer edge of the shoulder to the tip of the middle finger.

The accuracy test comes from a 1993 American teaching manual: men shoot 36 arrows in all, starting at 10 yards, then 20, then 30, on a 48-inch face, with four practice shots, any technique allowed, bows between 15 and 40 pounds and arrows between 24 and 48 inches; an archer who fails to score 10 points at one distance does not move to the next. The scoring scale attached sets 100% at a total of 270 points and steps down to 65. The calculations reported are the three simple correlations and a multiple correlation checked with an F test.

The figures are not consistent with each other, and that weighs more than any other limitation. The multiple correlation, 0.816, is lower than the two simple correlations, 0.897 and 0.871, which cannot happen algebraically; the F value written in the text, 33, does not match the formula printed just above it, which gives about 21; the critical value is given first as 3.44 and then as 3.47 in the same sentence.

Almost everything needed to judge the study is missing. The abstract states that means and standard deviations were computed, but the paper contains no mean, no standard deviation and no score: for the twenty-four people there is no age, sex, level or draw weight, and no indication of how many got through all three distances despite the rule that stops an archer below 10 points. No p value is given for either simple correlation.

There is also a problem of interpretation. The two predictors correlate with each other at 0.958, that is, they measure nearly the same thing, and with that much overlap there is no telling which of them has anything to do with the score. That a length measured with a tape from the shoulder to the middle finger should account for three quarters of the variation in the score is far higher than the values other studies of the same measure report. The data were collected in 2015 and the journal issue is dated January to June 2016; the text is in Indonesian.

An archer takes nothing usable from this record, and it is better to say so plainly. The correlations reported are among the highest to be found in the archery literature, but the arithmetic around them does not hold together: the contribution of the two measures taken jointly comes out lower than that of either taken alone, and that alone is reason enough not to lean on those values.

Even taken as written, the two predictors are not alike. Arm length cannot be changed, so any relation it has with the score would at most concern equipment choice and how draw length is handled, neither of which the paper measures. Push-and-pull force on a dynamometer is a two-handed effort with little resemblance to drawing a bow, and it is called endurance while being measured over two brief attempts.

Then there is the setting of the test: 36 arrows at 10, 20 and 30 yards on a 48-inch face, any technique allowed and bows between 15 and 40 pounds. That is closer to a physical education lesson than to a qualification round, and a score collected that way separates archers who can shoot from archers still learning, not one competitive archer from another.