A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

We give a formal definition of a representative sample, but roughly speaking, it is a scaled-down version of the population, capturing its characteristics. New methods for selecting representative probability samples in the presence of auxiliary variables are introduced. Representative samples are needed for multipurpose surveys, when several target variables are of interest. Such samples also enable estimation of parameters in subspaces and improved estimation of target variable distributions. We describe how two recently proposed sampling designs can be used to produce representative samples. Both designs use distance between population units when producing a sample. We propose a distance function that can calculate distances between units in general auxiliary spaces. We also propose a variance estimator for the commonly used Horvitz-Thompson estimator. Real data as well as illustrative examples show that representative samples are obtained and that the variance of the Horvitz-Thompson estimator is reduced compared with simple random sampling.

We propose a novel one-leg standardised rebound side-hop test (SRSH) specifically designed for detailed analysis of landing mechanics. Anterior cruciate ligament reconstructed persons (ACLR, n = 30) and healthy-knee controls (CTRL, n = 30) were tested for within-session and test-retest (CTRL only, n = 25) reliability and agreement. Trunk, hip and knee angles and moments in sagittal, frontal, and transversal planes during landing, including time to stabilisation (TTS), were evaluated using intra-class correlations (ICCs), average within-person standard deviations (S W) and minimal differences. Excellent within-session reliability were found for angles in both groups (most ICCs > 0.90, S W ≤ 5°), and excellent to good for moments (most ICCs > 0.80, S W ≤ 0.34 Nm/kg). Only knee internal rotation moment showed poor reliability (ICC < 0.4). Test-retest results were excellent to fair for all angles and moments (ICCs 0.47-0.91, S W < 5°and ≤ 0.25 Nm/kg), except for peak trunk lateral bending angle and knee internal rotation moment. TTS showed excellent to fair within-session reliability but poor test-retest results. These results, with a few exceptions, suggest promising potential of evaluating landing mechanics during the SRSH for ACLR and CTRL, and emphasise the importance of joint-specific movement control variables in standardised tasks.

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Motivated by the analysis of the dependence of knee movement patterns during functional tasks on subject-specific covariates, we introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed effects. The procedure does not only test the global hypothesis on the entire domain but also selects the intervals where statistically significant effects are detected. We prove that the proposed tests are provided with an asymptotic control of the intervalwise error rate, that is, the probability of falsely rejecting any interval of true null hypotheses. The procedure is applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals (two injured groups with different treatments and one group of healthy controls), taking individual-specific covariates into account.