Correlation Analysis. Each card, symbol, number, or stop position is independently chosen without regard to any other card, symbol, number or stop position, drawn within that game play. Each card, symbol, number, or stop position is considered random if it meets the 99 percent confidence level using standard correlation analysis.
Correlation Analysis. Shown is a scatterplot with histograms for the respective axes. Statistics and other plot elements adapt dynamically to certain user-‐triggered events.
Correlation Analysis. The coordinated nature of the comparison programme led to a dataset in which there are significant correlations between individual frequency ratio measurement results. Prior to this project, correlations had been essentially ignored by the joint Frequency Standards Working Group (WGFS) of the Consultative Committee for Time and Frequency (CCTF) and Consultative Committee for Length (CCL) in calculating optimised frequency values and uncertainties for secondary representations of the second, even though this can lead to biased frequency values and underestimated uncertainties. NPL and INRIM therefore collaborated to prepare guidelines on the evaluation and reporting of correlation coefficients between frequency ratio measurements, which are available on our project website. These guidelines discuss ways in which correlations between frequency ratio measurements may arise, and describe how they can be quantified. Worked examples are presented based on measurement data available in the published literature and include several examples of very significant correlations that were neglected in the 2017 update to the list of CIPM recommended frequency values. Suggestions are also presented as to how the information necessary to compute the correlation coefficients might be gathered from the groups performing such measurements, for future updates to the list. These guidelines were shared with the WGFS and strongly influenced the 2021 update to the list of recommended frequency values (section 4.4.1), ensuring that it was underpinned by a more robust analysis of the available data. The guidelines were also used by other members of the consortium to compute the correlation coefficients between the various frequency ratios measured in this project. In total 313 non-zero correlation coefficients were evaluated between pairs of frequency ratio measurements, of which 135 had a magnitude ≥ 0.1 and 40 had a magnitude ≥ 0.5. A graphical representation of the correlation coefficients between the 20 different remote ratios measured via satellite links in the 2022 campaign is shown in Figure 7.
