Common use of Statistical Analysis Clause in Contracts

Statistical Analysis. Standard statistical methods were used to calculate the means, standard deviations, and absolute and relative frequencies. The Kolmogorov-Smirnov and ▇▇▇▇▇▇ tests were used to assess the normality and homogeneity of the distributions respectively; data were analysed using parametric or non-parametric tests according to the results. A ▇▇▇▇- ▇▇▇▇▇▇▇ test or unpaired t-test was used to evaluate the differences between the Control and Panel Qualification and Final scores respectively. The reliability between E/A C&P-scores was calculated using a one way-random, absolute agreement Intraclass Coefficient of Correlation (ICC), because each routine was rated by judges randomly selected from a larger population of judges. ICC values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and greater than 0.90 are indicative of poor, moderate, good, and excellent reliability respectively (▇▇▇ & ▇▇, 2016). Validity was assessed by comparing the concrete judging (E/A P-scores) with the gold standard score (E/A C-Score). Systematic over- or under-rating of scoring, also known as bias (▇▇▇▇▇ et al., 2012) was also investigated as a further step in the analysis. The Execution/Artistic differences were computed as the differences between the two human scoring systems, which indicated bias, i.e. systematic under- or over-estimation of Execution/Artistic scores. These differences were defined as: E/A C-P bias = E/A C-Score – E/A P-scores. If the gold standard method (E/A C-Score) is sometimes higher, and sometimes the other method (E/A P-Score) is higher, the average of the differences will be close to zero. If it is not close to zero, this indicates that the two assay methods are systematically producing different results. Assuming that the E/A C-Scores, given by the highest category of judges, are accurate, the concordance value would show to what extent the scores assigned by the panel are correct. ▇▇▇▇▇-▇▇▇▇▇▇ plots (▇▇▇▇▇ & ▇▇▇▇▇▇, 1986) were used to assess and display agreement along the entire spectrum of scores and at each Qualitative Performance Range in Qualification and Final competition. Systematic C-P scores bias and the 95% limits of agreement (LoA = C-P scores bias ±1.96 SD) were calculated. Each ▇▇▇▇▇-▇▇▇▇▇▇ plot shows the limits of agreement (LoA), calculated by using the mean ±2 standard deviations of the differences between the two E/A C-P scores. The difference of the two paired measurements is plotted against the mean of the same two measurements, and 95% of the data points should lie within ±2 standard deviations of the mean differences. The maximum FIG allowed deviation was included in the ▇▇▇▇▇-▇▇▇▇▇▇ plot, in order to assess the findings for clinical significance for each Qualitative Performance Range. Non-parametric methods such as ▇▇▇▇▇▇-▇▇▇▇▇ survival-agreement plots (▇▇▇▇ et al., 2003) and the Log Rank Test were used to evaluate the probability of a certain magnitude occurring in the differences between C-P scores bias data in the selected Qualitative Performance Ranges in competitions and events. The ▇▇▇▇▇▇-▇▇▇▇▇ plots provided a graphical approach as a complement to the ▇▇▇▇▇-▇▇▇▇▇▇ method and allowed a simple interpretation of agreement, taking into account the “clinical” importance of the inter-score differences. ▇▇▇▇▇▇-▇▇▇▇▇ plots allow analysis of reliability or agreement by means of survival analysis techniques (▇▇▇▇ et al., 2003). On the ▇▇▇▇▇▇-▇▇▇▇▇ plot, the horizontal axis shows the absolute difference between two E/A C-P Score measurements for each routine and the vertical axis shows the proportion of cases in which the discrepancies equal at least each of the observed differences. The graph is thus constructed the same way as for a survival analysis, where the 0-difference values are removed, and the variable “time” is replaced by the absolute differences between the E/ A C-P Scores measurements. Significance was accepted at the P ≤ 0.05 level and all analyses were performed using SPSS software version 26.0 (IBM Corp., Armonk, NY, USA).

Statistical Analysis. Standard statistical methods were used to calculate the means, standard deviations, and absolute and relative frequencies. The Kolmogorov-Smirnov and ▇▇▇▇▇▇ tests were used to assess the normality and homogeneity of the distributions respectively; data were analysed using parametric or non-parametric tests according to the results. A ▇▇▇▇- ▇▇▇▇▇▇▇ test or unpaired t-test was used to evaluate the differences between the Control and Panel Qualification and Final scores respectively. The reliability between E/A C&P-scores was calculated using a one way-random, absolute agreement Intraclass Coefficient of Correlation (ICC), because each routine was rated by judges randomly selected from a larger population of judges. ICC values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and greater than 0.90 are indicative of poor, moderate, good, and excellent reliability respectively (▇▇▇ & ▇▇, 2016). Validity was assessed by comparing the concrete judging (E/A P-scores) with the gold standard score (E/A C-Score). Systematic over- or under-rating of scoring, also known as bias (▇▇▇▇▇ et al., 2012) was also investigated as a further step in the analysis. The Execution/Artistic differences were computed as the differences between the two human scoring systems, which indicated bias, i.e. systematic under- or over-estimation of Execution/Artistic scores. These differences were defined as: E/A C-P bias = E/A C-Score – E/A P-scores. If the gold standard method (E/A C-Score) is sometimes higher, and sometimes the other method (E/A P-Score) is higher, the average of the differences will be close to zero. If it is not close to zero, this indicates that the two assay methods are systematically producing different results. Assuming that the E/A C-Scores, given by the highest category of judges, are accurate, the concordance value would show to what extent the scores assigned by the panel are correct. ▇▇▇▇▇-▇▇▇▇▇▇ plots (▇▇▇▇▇ & ▇▇▇▇▇▇Almant, 1986) were used to assess and display agreement along the entire spectrum of scores and at each Qualitative Performance Range in Qualification and Final competition. Systematic C-P scores bias and the 95% limits of agreement (LoA = C-P scores bias ±1.96 SD) were calculated. Each ▇▇▇▇▇-▇▇▇▇▇▇ plot shows the limits of agreement (LoA), calculated by using the mean ±2 standard deviations of the differences between the two E/A C-P scores. The difference of the two paired measurements is plotted against the mean of the same two measurements, and 95% of the data points should lie within ±2 standard deviations of the mean differences. The maximum FIG allowed deviation was included in the ▇▇▇▇▇-▇▇▇▇▇▇ plot, in order to assess the findings for clinical significance for each Qualitative Performance Range. Non-parametric methods such as ▇▇▇▇▇▇-▇▇▇▇▇ survival-agreement plots (▇▇▇▇ et al., 2003) and the Log Rank Test were used to evaluate the probability of a certain magnitude occurring in the differences between C-P scores bias data in the selected Qualitative Performance Ranges in competitions and events. The ▇▇▇▇▇▇-▇▇▇▇▇ plots provided a graphical approach as a complement to the ▇▇▇▇▇-▇▇▇▇▇▇ method and allowed a simple interpretation of agreement, taking into account the “clinical” importance of the inter-score differences. ▇▇▇▇▇▇-▇▇▇▇▇ plots allow analysis of reliability or agreement by means of survival analysis techniques (▇▇▇▇ et al., 2003). On the ▇▇▇▇▇▇-▇▇▇▇▇ plot, the horizontal axis shows the absolute difference between two E/A C-P Score measurements for each routine and the vertical axis shows the proportion of cases in which the discrepancies equal at least each of the observed differences. The graph is thus constructed the same way as for a survival analysis, where the 0-difference values are removed, and the variable “time” is replaced by the absolute differences between the E/ A C-P Scores measurements. Significance was accepted at the P ≤ 0.05 level and all analyses were performed using SPSS software version 26.0 (IBM Corp., Armonk, NY, USA).