Overview

The purpose of this analysis was to example the association between accumulated training load and the associated training response in female, university level hockey players.

In your observational design, players (n = 9) recorded repeated measures (k = 4) of training load (independent variables) which were paired with measures of the training response (dependent variables). Training loads derived from heart rate and Global Positioning Systems were accumulated in the the 3 (‘acute) and 7 (’week’) days prior to measurement of the training response, which included the Short Recovery Stress Scale (SRSS) and countermovement jump height (CMJ).

Examining The Data

Before we get going, lets take a look at what we are dealing with:

Dataset (scrollbox)
ID week_adj CMJ O_Stress_m O_Recovery_m G_Stress_m G_Recovery_m S_Stress_m S_Recovery_m gen_stress emo_stress soc_stress pressure fatigue lack_energy som_complaints success soc_relax som_relax wellbeing sleep breaks burnout_ee injury fitness burnout_pa efficacy regulation Week_dur Week_B1 Week_B2 Week_B3 Week_B4 Week_B5 Week_B6 Week_TD Week_HR Week_TRIMP Days3_dur Days3_B1 Days3_B2 Days3_B3 Days3_B4 Days3_B5 Days3_B6 Days3_TD Days3_HR Days3_TRIMP
1 1 42.5 7.8 11.000000 8.142857 10.6 7.000000 11.50 7 8 7 15 9 5 6 11 9 12 11 10 1 8 12 13 9 10 14 464.26667 648.39 10865.31 6380.75 4906.15 3110.27 952.90 26864.706 61.32621 579.54499 236.50000 318.07 5632.90 3373.47 2245.08 1311.56 524.87 13406.827 61.09581 294.77747
1 2 41.2 5.6 11.111111 6.285714 10.6 4.000000 11.75 4 5 7 10 8 6 4 10 13 10 11 9 1 5 6 12 7 13 15 391.76667 612.05 9336.22 5402.73 3914.59 2683.80 1730.22 23683.457 64.49210 566.96078 187.68333 299.64 4851.58 2939.04 2033.29 1201.47 780.15 12105.399 66.65720 304.55006
1 3 39.7 7.6 11.000000 8.142857 9.4 6.333333 13.00 3 8 10 14 9 7 6 7 10 9 10 11 1 6 12 14 9 12 17 528.36667 751.23 13463.69 8674.73 5818.47 3399.45 1408.91 33517.147 67.08676 953.67105 210.61667 313.04 5716.53 3708.12 2755.56 1224.95 517.88 14236.275 70.05896 485.82685
1 4 43.1 6.3 14.555556 6.428571 15.2 6.000000 13.75 3 5 4 10 7 9 7 14 16 15 18 13 3 3 12 14 9 14 18 175.83333 339.41 3971.22 1235.45 794.69 392.69 207.50 6942.019 55.45785 138.93430 83.28333 159.80 1720.69 807.66 573.03 256.36 200.24 3718.231 66.48040 128.72697
3 1 22.8 10.3 12.555556 10.142857 14.8 10.666667 9.75 7 8 8 13 13 13 9 16 17 17 15 9 9 12 11 10 10 9 10 459.78333 663.86 10091.81 7607.94 5154.42 2515.22 542.32 26578.723 65.08797 733.00800 236.50000 329.62 5243.85 3860.04 2597.41 1104.94 341.76 13480.922 64.77750 399.06082
3 2 20.6 10.0 13.111111 10.142857 14.4 9.666667 11.50 9 8 9 14 12 10 9 14 18 14 14 12 8 11 10 12 11 11 12 391.76667 562.10 9517.02 6819.90 4505.76 1970.31 1118.38 24493.770 69.72022 801.16348 187.68333 249.31 4604.10 3559.16 2401.54 848.19 376.02 12038.417 69.19230 392.49398
3 3 NA 12.5 11.444444 12.428571 12.6 12.666667 10.00 12 9 11 14 15 13 13 12 16 10 11 14 10 13 15 7 12 10 11 528.36667 700.42 12254.24 9530.65 6135.27 2407.73 988.38 32017.530 69.21081 1021.81735 210.61667 335.38 5545.83 4307.70 2997.18 1017.35 306.63 14510.554 73.04635 539.53284
3 4 21.4 10.7 12.555556 11.000000 13.0 10.000000 12.00 9 9 8 16 15 10 10 12 17 9 15 12 8 11 11 10 13 13 12 175.83333 325.95 4020.10 1490.51 760.81 314.21 75.62 6988.656 58.80690 128.72213 83.28333 142.97 1531.36 698.59 467.23 248.00 73.22 3161.768 64.76740 96.85408
7 1 30.3 6.0 9.444444 6.714286 10.8 4.333333 7.75 3 8 6 9 5 9 7 10 14 10 11 9 1 4 8 9 7 7 8 459.78333 651.38 9262.47 6499.52 5932.66 2625.72 116.82 25088.925 68.43369 772.25127 236.50000 289.89 4464.45 3366.61 3172.59 1054.54 47.70 12396.169 69.90392 414.44587
7 2 31.8 6.3 8.555556 7.000000 9.2 4.666667 7.75 2 6 3 12 9 8 9 9 12 8 9 8 2 5 7 8 8 6 9 391.76667 575.86 8946.56 5906.42 5076.97 2111.24 689.64 23308.059 69.83350 697.43186 187.68333 280.46 4084.67 3267.48 2893.05 971.37 173.65 11671.697 70.95850 383.03388
7 3 33.4 7.1 9.000000 6.857143 9.6 7.666667 8.25 2 6 7 9 9 7 8 8 14 9 10 7 9 6 8 8 9 7 9 528.36667 711.34 11544.47 7715.76 6190.34 2618.80 612.04 29394.462 68.41722 837.32394 210.61667 291.07 4563.45 3045.63 2757.55 998.46 110.44 11767.586 68.65950 311.12999
7 4 33.4 5.2 8.666667 6.000000 9.4 3.333333 7.75 4 5 4 6 8 9 6 9 14 7 10 7 3 3 4 9 7 7 8 175.83333 274.84 3973.92 1426.28 809.93 412.54 53.41 6951.099 64.11529 197.22528 83.28333 104.03 1686.40 748.76 554.42 342.57 53.41 3489.591 70.41276 146.89355
9 1 32.0 8.6 15.444444 9.000000 15.0 7.666667 16.00 4 9 8 12 11 11 8 14 15 15 18 13 6 9 8 16 17 15 16 459.78333 767.84 9723.36 5240.13 4110.20 1777.40 169.79 21791.793 70.98106 905.45521 236.50000 420.91 4823.57 2313.14 1956.12 762.18 115.46 10394.065 68.56146 394.45629
9 2 32.4 8.9 16.555556 9.285714 16.2 8.000000 17.00 6 7 9 14 10 12 7 18 14 17 19 13 6 8 10 19 19 15 15 391.76667 592.32 8389.78 4263.64 3329.55 1985.60 366.69 18928.151 74.69649 985.13211 187.68333 285.33 3803.56 2296.61 1863.56 746.23 138.63 9133.929 73.89063 463.01407
9 3 NA 8.6 16.111111 9.000000 14.6 7.666667 18.00 7 9 10 10 10 8 9 16 15 17 14 11 6 7 10 16 18 17 21 409.55000 637.88 9461.60 5223.92 3605.94 1435.64 498.95 20864.464 74.23502 995.83809 91.80000 167.70 2155.30 833.72 649.26 198.85 33.27 4038.204 70.15690 152.15770
9 4 NA 8.7 12.777778 9.857143 14.8 6.000000 10.25 7 9 8 5 13 13 14 12 18 11 14 19 0 4 14 11 13 7 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
10 1 29.7 7.1 14.000000 6.714286 15.0 8.000000 12.75 5 4 5 7 8 10 8 14 16 13 20 12 3 7 14 13 14 12 12 463.50000 677.43 10720.36 5047.12 4931.78 2691.30 341.09 24409.054 73.47818 1101.99058 236.50000 349.35 5618.94 2500.24 2231.30 1208.95 212.82 12121.657 72.37112 527.02642
10 2 30.5 7.6 14.444444 7.285714 16.6 8.333333 11.75 4 5 7 9 10 6 10 19 17 14 19 14 2 11 12 14 10 13 10 391.76667 560.78 9205.87 4357.01 4023.77 1977.17 690.37 20815.314 77.02251 1116.38883 187.68333 279.25 4645.33 2295.81 2286.27 1008.52 403.35 10918.550 77.11554 549.65535
10 3 NA 7.4 14.111111 7.571429 16.0 7.000000 11.75 6 6 5 13 10 7 6 18 15 13 19 15 11 5 5 16 12 12 7 528.36667 836.00 12435.40 5653.03 4858.48 3228.51 1013.10 28028.072 75.88619 1411.91490 210.61667 349.89 4736.98 2217.88 2191.29 1447.05 199.66 11144.360 76.01313 536.70074
10 4 NA 8.0 8.444444 10.000000 13.0 3.333333 2.75 9 10 9 8 14 11 9 12 12 11 14 16 1 3 6 1 10 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
12 1 32.9 12.1 9.444444 11.285714 9.4 14.000000 9.50 9 14 16 8 5 11 16 12 9 9 9 8 9 17 16 9 13 9 7 459.78333 691.01 10852.08 5556.69 3886.55 1998.09 420.35 23404.954 76.36112 1274.87809 236.50000 324.68 5177.63 2554.68 1689.18 759.21 192.66 10698.130 75.35232 613.48843
12 2 34.0 12.5 14.000000 12.000000 14.4 13.666667 13.50 11 12 13 13 12 12 11 14 16 12 17 13 15 12 14 13 13 14 14 296.90000 536.33 7646.70 3488.74 2397.69 1183.24 451.10 15704.152 79.42422 851.40800 187.68333 303.66 4579.60 2446.24 1693.97 814.22 344.66 10182.588 78.37101 509.82333
13 1 36.7 5.5 10.666667 6.142857 12.4 4.000000 8.50 1 5 4 13 7 8 5 10 12 13 16 11 1 2 9 12 5 9 8 317.25000 444.47 7874.85 5829.23 3719.67 1395.93 524.40 19789.272 78.91602 1045.18092 113.20000 151.63 3687.00 2954.95 1865.75 681.77 281.33 9622.504 87.02074 515.75345
13 2 39.3 7.8 12.222222 8.857143 13.0 5.333333 11.25 2 9 7 16 9 12 7 13 11 14 15 12 1 4 11 13 12 12 8 335.41667 474.93 7466.73 5763.32 4496.44 2612.73 1608.24 22422.805 77.13007 980.49924 111.55000 149.03 2733.94 2107.00 1617.46 797.52 587.94 7993.249 82.46223 417.59732
13 3 NA 7.9 11.444444 9.000000 11.8 5.333333 11.00 5 8 6 15 9 12 8 11 10 11 13 14 4 4 8 13 10 13 8 422.65000 557.40 10029.85 7705.11 4857.76 1933.30 1354.68 26439.782 76.15047 1192.14298 210.61667 300.26 6042.65 4272.84 2676.08 922.98 485.54 14700.637 78.94224 694.42960
13 4 39.3 6.3 10.222222 8.142857 12.2 2.000000 7.75 7 4 8 14 8 11 5 11 12 11 16 11 0 0 6 13 7 8 3 83.28333 97.69 988.04 647.18 268.24 142.38 128.61 2272.185 75.05696 126.59226 83.28333 97.69 988.04 647.18 268.24 142.38 128.61 2272.185 75.05696 126.59226
14 1 26.8 13.2 12.111111 14.428571 10.8 10.333333 13.75 17 21 10 22 9 15 7 7 20 7 13 7 11 11 9 18 15 12 10 463.50000 602.37 10131.73 6945.02 5693.17 3200.42 558.95 27133.009 68.08356 804.16308 236.50000 307.76 5439.93 3748.04 3054.26 1461.58 308.62 14320.828 69.02373 441.41078
14 2 27.2 13.0 15.000000 13.714286 15.8 11.333333 14.00 13 13 9 21 18 11 11 18 17 14 19 11 14 15 5 21 12 9 14 296.90000 400.02 6164.80 4110.56 3419.18 1517.09 436.69 16048.447 69.78215 594.39978 187.68333 220.14 3687.67 2631.22 2346.55 1100.75 356.38 10342.699 68.96503 360.93639
14 3 32.5 17.6 12.555556 15.428571 12.8 22.666667 12.25 15 10 15 21 21 18 8 8 14 8 17 17 24 22 22 15 13 10 11 528.36667 689.91 11790.48 8892.92 7527.74 3416.37 1042.46 33360.627 72.14374 1219.45830 210.61667 283.39 4635.19 3130.42 3021.74 1441.80 244.18 12757.464 71.26352 422.23451
14 4 30.4 11.9 15.222222 12.285714 15.4 11.000000 15.00 16 10 4 18 18 14 6 21 16 15 16 9 13 10 10 21 16 8 15 175.83333 295.15 3767.68 1416.30 698.27 382.71 37.35 6597.518 64.34072 188.91125 83.28333 117.63 1430.18 620.79 419.88 229.09 29.81 2847.391 71.41411 132.62357
17 1 30.6 5.4 16.666667 6.000000 16.8 4.000000 16.50 4 5 4 9 6 9 5 15 20 19 18 12 5 2 5 19 14 16 17 440.55000 670.96 8948.28 5604.37 4168.84 2022.06 570.03 21985.058 66.40104 694.23677 236.50000 345.37 4530.29 2710.87 2274.69 1270.21 418.45 11550.384 65.47243 369.66087
17 2 27.2 4.5 16.777778 4.428571 16.0 4.666667 17.75 4 4 4 8 4 4 3 16 16 17 19 12 3 3 8 20 15 16 20 410.60000 638.36 8250.84 5693.62 4755.11 2776.89 1182.37 23297.526 68.87203 716.13278 187.68333 282.88 3503.01 2658.55 2223.86 1184.10 544.52 10396.884 68.85390 335.58361
17 4 27.4 4.9 15.000000 6.142857 14.2 2.000000 16.00 3 4 7 9 9 9 2 13 16 17 16 9 0 0 6 16 16 14 18 92.55000 170.95 1924.11 614.69 422.07 138.45 38.48 3309.375 61.21334 69.99502 NA NA NA NA NA NA NA NA NA NA

Most, if not all of your independent and dependent variables can be classed as continuous (ratio) level data. There’s an argument to say we should treat items of the SRSS different, but we’ll take an ‘innocent until proven guilty’ approach in the first instance.

We are dealing with a fair few variables here—more than the number of players and observations, which is always a bit of a warning sign. Before we start number crunching, lets see if we can make informed decisions to trim the independent and dependent variables down, to reduce the amount of univariate associations (and, hopefully, the risk of making a Type I error!).

Training Response Measures

In a recent systematic review, we found a lack of evidence for face and content validity of all current Athlete Reported Outcome Measures (AROMs) of the training response. But, the good news is… the SRSS, along with the Acute Recovery Stress Scale, came up trumps on most of the other key measurement properties:

“…Among these AROMs, a few have been developed specifically for athletic populations, such as MTDS, RESTQ-Sport, ARSS, and SRSS, with some showing good evidence, at least in some measurement properties (e.g.,, ARSS and SRSS). The main area requiring improvement is certainly the content validity, in which all studies were rated inadequate.”

We have to remember the purpose of the SRSS a proxy of the training response is to capture the potential consequences of training stress on the body’s systems. I think the best approach when applying this tool in the context of training dose-response is to select the physical sub-domains (those with a more likely causal link to training load), and omit the other domains:

“With that being said, we remind that, within sport science, AROMs should be implemented to quantify physical symptoms of the training response as opposed to psychological aspects (where psychology experts should be consulted). Coaches and practitioners might therefore consider restricting domains of the RESTQ-S, ARSS, SRSS and MTDS to physical symptoms only.” McLaren et al. (2021), p. 247

This logic leaves with us Recovery (overall, sport-specific and general), Fatigue and (probably) Fitness. CMJ height can be retained as it is—that’s an obvious one!

Training Load Measures

The training load measures are a bit more straightforward. We can keep TRIMP as the sole measure of internal load and total distance (TD) as one external load measure. We’ll also take a look at a measure of high-speed running distance, but for that we’ll need to sum the banded distances above whatever threshold we set. We can chat about this to determine which you feel are the most appropriate for your population.

OK, enough talk, lets check some distributions!

Distribution Checks

Most of the training response measures look OK. One or two outliers at the extremes and we might consider removing General Recovery. There seems to be a bit of a skew in the training load data. Looks like there was a particularly ‘low’ week (including the 3 days of that week) which is creating a bimodal distribution. We’ll keep this in mind going forward. I’m reluctant to remove at the moment because we’re already dealing with a very small sample. Once we’ve fit our models we can check the distribution of their residuals.

For the remainder of this analysis, I’ll retain Overall Recovery as the dependent variable, just for exploration purposes. We can then apply the full strategy to all our dependent variables once we’ve chatted through things.

Going back to our aims, we need to build a model that plots the load~response relationship on an individual level, then combines the fit of all individuals to give us an overall model. Before we do this, lets have a look at whats going on at an individual level. We’ll fit individual linear models with TD as the independent (x) variable and Overall Recovery as the dependent (y) variable.

Fairly interesting! So, taking things with a pinch of salt, we’ve got quite a mixed bag here. First, there seems to be stronger associations to Overall Recovery with Week TD when compared to all other training load measures. But this relationship is fairly representative of all the others: we can see its a bit of a mixed bag between the 9 players. Looking into a bit more detail:

The process we are going through here is really good practice to help inform our model selection and how we best deal with the data going forward. Using Overall Recovery vs Week TD as an example, I think we can expect some negative, but small/weak associations between the two constructs. The other training load measures seem to render a ‘flatter’ (null or trivial) relationship and therefore these may not have a clear or substantial association.

In an ideal world, we would have our model consider each participant as fully independent from one another. That is, their modeled parameters (the intercept and the slope) would be allowed to vary, best fitting their own data. Visually and conceptually, this would be analogous to stacking all 9 charts from above on top of one another. The only issue here is it requires lots of degrees of freedom (both n and k), which we don’t have.

So lets try a random intercept model. We will build a linear regression where each participant has their own line through their own data. The y intercept of this line is allowed to cross wherever is best for the player. The slope of their relationship, however, has to be fixed, meaning it takes the value that is ‘the best for everyone’. This is sometimes called a parallel slopes model.

Repeated Measures Correlation

Lets run the repeated measures correlation see what we are dealing with. I’ll also plot these models so we have a better idea of what the statistical estimates are telling us. I’ll tidy these plots up (unlike the previous, which are sloppy!) so we can have a look at how this might present in your results section.

Our analyses confirm earlier thoughts—there is a small, negative, within-player association between training load and Overall Recovery. This time, our conclusions are supported by overall, pooled estimates (r values) and their associated 90% confidence limits (CL) as markers of uncertainty. Our CL are somewhat wide… at least wider than we would like to make inference on the true effect. Take 3-day TD with Overall recovery, for example. The correlation is moderate (-0.38) but the CL span from trivial (-0.03) to very large (-0.70). Of course, we could speculate as to reasons why this might be the case and I would edge my bets on the sample size.

If these associations were more pronounced (for example, the lower CL being < -0.10 to suggest the true relationship is at least small and negative) then we might consider running the full linear model to determine the regression coefficients, which can be really useful in giving practical interpretation to the outputs (e.g., what change in training load is associated with a 1 unit reduction in Overall Recovery). But, given what we know about the size and uncertainty of the correlations, we could make a reasonable assumption that we wouldn’t find any useful information here (we would need unrealistically large changes to see a meaningful change in Overall Recovery).

Nonetheless, running these models will let us check the model diagnostics and in particular, the distribution of model residuals. If these are normal then we know the above plot and r values are a good representation of the data.

Check Model Residuals

Really promising! These residuals look well behaved enough to suggest that the models we ran give an accurate description of our data.

Next Steps

I would love to hear what you think of the above and how you think we can best move forward with the results. I can show you how to run all of the above analyses in SPSS, R or SAS—whichever you prefer!