Method Comparison Regression Mode and Linearity Allow for 6 different Regression Measurements

Feature: Method Comparison and Linearity Allow for 6 different Regression Measurements

In experiment settings you may now select the type of regression analysis for your acceptance criterias. This allows for more advanced testing or when your analytical methods have an expected difference making Allowable Error testing inapplicable to the performance evaluation. See Quantitative Linearity and Quantitative Method Comparison for more information.

image
image

You may choose from the following regression types:

🗣️
**Cualia Support Docs Definitions (Public)**

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

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

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

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