# Validation and Application of Two New Core Stability Tests in Professional Football
## 2 Methods
### Statistical Analysis  
The SPSS statistical package (version 17.0.0.236; SPSS Inc. Chicago, IL, USA) was used to perform all the statistical analyses. All analyses assumed statistical significance at \(p\leq 0.05\). **Study I: (Cross-sectional study)**  
A total of 22 participants were evaluated for the intrasession, and intra- and inter-rater reliability analysis. Furthermore, a subset of seven subjects was randomly selected from the initial cohort and they repeated the whole examination at seven days for the test-retest reliability calculations. Descriptive statistics, including mean peak torque values with standard deviation, coefficient of variation (%) (expressed as the SD of the mean, multiplied by 100% and expressed as a percentage) and confidence intervals (95%), were calculated. The peak isometric force values obtained from each evaluator during the PPT and CCT were gathered for intra-rater (trial 1, trial 2), inter-rater (male tester, female tester) and intra-rater intersession (assessment day 1/day 2). Afterwards, a Paired \(t\)-test comparison and the corresponding non parametrical Wilcoxon Signed-rank test were run to primarily test whether the two sets of scores were significantly different from each other, before their test-retest reliability was analyzed [18]. The data was graphically examined using [PERSON] and [PERSON] [19] plots in, which the difference between test sessions was plotted against the mean of the two test sessions. Mean differences between test sessions with 95% CIs were calculated to determine whether there was any systematic bias. The relative reliability of the data was determined using a two-way random effect model intraclass correlation coefficient (2, k). Before calculating absolute reliability, [PERSON] and [PERSON] plots were generated to examine the correlation (R2) between the absolute differences and the mean values for each test, in order to detect the presence or absence of heteroscedasticity in the data [19]. If the random error increases as the measured values increase, the data is considered heteroscedastic. In contrast, when there is no relation between the error and the size of the measured value, the data is described as homoscedastic. With homoscedastic errors, providing that they are also normally distributed, the raw data can be analyzed with conventional parametric analyses, but heteroscedastic data should  
Figure 2: Core stability training program divided into 3 different training phases. The first column of the figure represents the 3 core exercises. The second and third columns exemplify the progression of each exercise, adding motor control difficulty, in ascending order. be transformed logarithmically before analysis, or investigated via an analysis based on ratio statistics. This comparison method is widely used to verify the reliability and reproducibility of the measurement, rather than the correlation coefficient (r) and regression techniques, which are inadequate and can be very misleading when assessing agreement, as they evaluate only the linear association of two sets of observations. With this graph, evaluation of the magnitude of the disagreement, identification of outliers and the observation of any bias are easily achieved [20]. Due to the simplicity and potential for the identification of pairs of observations whose differences reach beyond clinical tolerances, the [PERSON] and Altman approach is currently the preferred approach to evaluate agreement between two measurements [19]. If R2 was between 0 and 0.1, the data were considered homoscedastic; consequently, the absolute reliability was assessed by determining the SEM, which was calculated using the square root of the mean square error from the analysis of variance model, as recommended by [PERSON] and [PERSON] [21]. If R2 was greater than 0.1, the data was considered heteroscedastic; consequently, absolute reliability was determined by calculating the CV.