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**Cualia Support Docs Definitions (Public)**

This is used for user documentation at docs.cualia.io
Name
Definition
Deming Variance Ratio (vr)

Quantifies the agreement between two measurement methods, considering measurement errors. A maximum allowable difference from 1 is standard. VR=Var(X)+Var(Y)Var(X−Y)VR = \frac{Var(X) + Var(Y)}{Var(X - Y)} Var(X)Var(X) = Variance of X Var(Y)Var(Y) = Variance of Y

Passing Bablok Correlation Coefficient (r)

Measures the strength and direction of the linear relationship between two measurement methods using Passing Bablok regression. A minimum absolute value of 0.95 is standard for strong correlation. r=Cov(X,Y)Var(X)+Var(Y)r = \frac{Cov(X, Y)}{Var(X) + Var(Y)} Cov(X,Y)Cov(X, Y) = Covariance of X and Y Var(X)Var(X) = Variance of X Var(Y)Var(Y) = Variance of Y

Spearman Rank Correlation Coefficient (p)

Measures the strength and direction of a monotonic relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation. p=1−6∑di2n(n2−1)p = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} did_i= Difference between ranks of X and Y nn = Number of pairs

Sample Correlation Coefficient (R)

The sample correlation coefficient (R) quantifies the strength and direction of the linear relationship between two variables based on sample data. A min value of 0.95 is standard. R=r2R = \sqrt{r^2} r2r^2 = Coefficient of Determination

Pearson Correlation Coefficient (r)

Measures the strength and direction of a linear relationship between two variables. A minimum absolute value of 0.95 is standard for strong correlation. r=Cov(X,Y)σXσYr = \frac{Cov(X, Y)}{\sigma_X \sigma_Y} Cov(X,Y)Cov(X, Y) = Covariance of X and Y σXσ_X = Standard Deviation of X σYσ_Y = Standard Deviation of Y Cov(X,Y)=1n−1∑i=1n(xi−xˉ)(yi−yˉ)Cov(X, Y) = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y}) nn = Number of data points xix_i = Individual data point of variable XyiXy_i = Individual data point of variable Y xˉ\bar{x} = Mean of variable X yˉ\bar{y} = Mean of variable Y

R-squared (R²) Coefficient

R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, with higher values indicating a better fit. Usually >0.95 is considered statistical correlation. R2=1−∑i=1n(yi−y^i)2∑i=1n(yi−yˉ)2R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}i)^2}{\sum{i=1}^{n} (y_i - \bar{y})^2} R2R^2 = Coefficient of determination yiy_i = Observed value y^i\hat{y}_i= Predicted value yˉ\bar{y} = Mean of observed values nn = Sample size