Interpreting magnitude of change in strength and conditioning: Effect size selection, threshold values and Bayesian updating

Figures & data

Table 1. Distribution (percentiles) of study characteristics and overview of outcome domains.

Study characteristic	0%	10%	20%	30%	40%	50%	60%	70%	80%	90%	100%
Participants per study	4	14	17	19	21	24	28	32	37	51	177
Participants per group	4	7	8	9	10	11	12	14	16	21	72
Mean Age	14.0	16.7	18.9	20.0	20.4	21.0	22.0	23.0	23.8	25.0	60.0
Publication Year	1962	1996	2005	2008	2010	2012	2014	2015	2016	2017	2018
Intervention duration (weeks)	4	5	6	6	8	8	8	10	12	14	520
Outcome domain			Number of studies (%)					Number of effects (%)
Maximum strength			419 (65.2)					2588 (39.4)
Jump			379 (58.2)					1552 (23.6)
Sprint			254 (39.5)					1251 (19.0)
Power			203(31.6)					1183 (18.0)

Table 2. Direct calculation of largest and smallest 1%, 2% and 5% of effect sizes across outcome types.

Outcome	Statistic	0.005-Quantile	0.0125-Quantile	0.025-Quantile	0.5-Quantile	0.975-Quantile	0.9875-Quantile	0.995-Quantile
All	SMDpre	−0.86	−0.55	−0.32	0.49	3.2	4.8	8.6
	%Improve	−15.0%	−7.3%	−4.1%	6.9%	45.9%	59.6%	88.2%
Maximum Strength	SMDpre	−0.84	−0.43	−0.23	0.62	4.0	6.0	8.6
	%Improve	−17.0%	−9.2%	−5.0%	12.4%	59.9%	84.2%	113.9%
Jump performance	SMDpre	−0.75	−0.38	−0.25	0.47	2.5	3.3	8.0
	%Improve	−11.2%	−5.9%	−3.5%	6.3%	27.6%	34.8%	42.2%
Sprint Performance	SMDpre	−0.90	−0.71	−0.51	0.38	3.1	5.3	11.2
	%Improve	−5.3%	−3.4%	−2.6%	2.1%	19.4%	40.5%	60.8%
Power	SMDpre	−0.78	−0.58	−0.32	0.36	2.2	4.0	8.9
	%Improve	−17.1%	−11.3%	−5.0%	6.6%	38.8%	45.9%	53.9%

Figure 1. Empirical distribution and modelled outcome-specific standardised mean difference effect size thresholds.

(Below): Black curve is a density plot of the directly calculated empirical effect size values across all outcomes. Small, mid, and large thresholds represent the 0.25, 0.5 and 0.75-quantiles of predicted draws. Black diamonds are based on direct calculation and red intervals illustrate uncertainty in estimates through the median value (circle) and 95% credible interval.

Figure 2. Empirical distribution and modelled outcome-specific percentage improvement effect size thresholds.

(Below): Black curve is a density plot of the directly calculated empirical effect size values across all outcomes. Small, mid, and large thresholds represent the 0.25, 0.5 and 0.75-quantiles of predicted draws. Black diamonds are based on direct calculation and red intervals illustrate uncertainty in estimates through the median value (circle) and 95% credible interval.

Table 3. Mean and standard deviations of prior distributions for standardised mean difference (SMD_pre) and log transformed relative ratio (RR) effect sizes statistics across outcome domains.

		Prior mean	Prior standard distribution
Outcome	Statistic
All	SMDpre	0.50	0.44
	Log(RR)	0.081	0.083
Maximum Strength	SMDpre	0.62	0.53
	Log(RR)	0.128	0.105
Power	SMDpre	0.39	0.41
	Log(RR)	0.074	0.079
Jump performance	SMDpre	0.45	0.40
	Log(RR)	0.066	0.060
Sprint Performance	SMDpre	0.38	0.47
	Log(RR)	0.026	0.034