Test-retest reliability of each threshold, from your own repeated tests
Source:R/compare.R
lactate_reliability.RdThe typical error of each threshold, from athletes who did the same test two or more times while their fitness did
not change (e.g. a few days apart): the residual standard deviation of a two-way analysis of athletes and tests,
which leaves out the mean change from one test to the next (Hopkins, 2000). It is given in intensity units and as a
coefficient of variation, 100 * (exp(s) - 1), with s the typical error of the log intensities. Pass the result
to compare_tests(cv = ) so that its verdicts use the noise of your own protocol, analyzer and athletes rather than
the default values, from trained male cyclists.
Arguments
- x
The result of
lactate_threshold()with.by, one group per athlete and test (e.g..by = c("athlete", "test")).- athlete, test
The columns of
xthat name the athlete and the test (e.g. the test number or date). Tests are matched by their order within each athlete: first, second, and so on.
Value
a tibble with one row per method: method, n_athletes (with two or more tests), n_tests, bias
(the mean change from one test to the next, intensity units), typical_error (intensity units), cv (%) with
its 90% confidence interval (cv_low, cv_high), and the degrees of freedom of the typical error (df).
Methods with fewer than two such athletes get NA.
Details
A typical error from few athletes is itself uncertain: with 10 athletes and 2 tests (9 degrees of freedom) its 90%
confidence interval spans 0.73 to 1.65 times its value (from the chi-square distribution of a variance). The
result therefore gives the degrees of freedom (df) and that interval for the cv (cv_low, cv_high), as
reliability statistics should always come with one (Sainani, 2017), and compare_tests() widens its intervals for
a small df. Atkinson & Nevill (1998) recommend more than 40 athletes for a reliability study; with fewer, read
the interval.
The bias is the mean change from each test to the next, which the typical error leaves out. Report it beside the
random error (Atkinson & Nevill, 1998): a bias that is not near zero is a learning or order effect, or a change
in fitness between the tests. The cv assumes that the error grows with the intensity, as it usually does for
such measures; with athletes of a similar level the two cannot be told apart, and typical_error is the same
noise in intensity units.
References
Atkinson G, Nevill AM. Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine. Sports Medicine. 1998;26(4):217-238.
Hopkins WG. Measures of reliability in sports medicine and science. Sports Medicine. 2000;30(1):1-15.
Sainani KL. Reliability statistics. PM&R. 2017;9(6):622-628. doi:10.1016/j.pmrj.2017.05.001
Examples
## the same athlete tested twice, a few days apart (simulated here as small changes in lactate)
set.seed(1)
repeats <- do.call(rbind, lapply(1:4, function(a) do.call(rbind, lapply(1:2, function(t) {
transform(demo_data, athlete = a, test = t, intensity = intensity * (0.9 + 0.05 * a),
lactate = lactate * exp(rnorm(nrow(demo_data), 0, 0.05)))
}))))
results <- lactate_threshold(repeats, intensity, lactate, method = c("OBLA", "Dmax"), plot = FALSE,
.by = c("athlete", "test"))
reliability <- lactate_reliability(results, "athlete", "test")
reliability
#> # A tibble: 10 × 9
#> method n_athletes n_tests bias typical_error cv cv_low cv_high df
#> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
#> 1 OBLA 2.0 4 8 0.25 3.43 3.16 1.95 9.52 3
#> 2 OBLA 2.5 4 8 -0.25 2.97 2.39 1.47 7.13 3
#> 3 OBLA 3.0 4 8 0.25 3.08 2.28 1.41 6.8 3
#> 4 OBLA 3.5 4 8 0.5 2.61 1.8 1.11 5.35 3
#> 5 OBLA 4.0 4 8 0.5 2.12 1.38 0.85 4.08 3
#> 6 Dmax 4 8 1.25 3.39 2.5 1.54 7.48 3
#> 7 ModDmax 4 8 0 2.45 1.75 1.08 5.19 3
#> 8 Exp-Dmax 4 8 -0.25 1.86 1.29 0.8 3.82 3
#> 9 Log-Poly-M… 4 8 4.25 4.14 2.59 1.6 7.75 3
#> 10 Log-Exp-Mo… 4 8 4 3.87 2.39 1.48 7.15 3