F-test (hypothesis test)

Add one or several F-tests to your assay.

Important: Test definitions are ignored without notification if the Type of test you select results in invalid test definitions (for example, if a test cannot be performed for the model you use).

The following table lists all F-tests we recommend for new assay development and indicates which models they support:


F-tests on the significance of:	Support the following models:	Scope of the test¹
regression non-linearity (lack of fit)	Linear parallel-line Slope ratio 4-parameter logistic 5-parameter logistic 3-parameter logistic with fixed lower or upper asymptote	Group 1
non-parallelism	Linear parallel-line 4-parameter logistic 5-parameter logistic 3-parameter logistic with fixed lower or upper asymptote	Group 1
non-similarity	Slope ratio	Group 1
the slope² the square coefficient³	Linear parallel-line Slope ratio	Group 2

¹ The tests of Group 1 and 2 differ in how the Scope of the test affects inclusion of various assay elements. The groups are explained in the Scope of the test section.

² Corresponds to 'test of slope' in PLA 2.0.

³ Corresponds to 'test of linearity' in PLA 2.0.

Important: Test definitions are ignored without notification if the scope you select results in invalid test definitions (for example, if a test cannot be performed for the assay element type you select).

The following table indicates how the scope of the test affects inclusion of various assay elements in tests without simultaneous regression:


Scope of the test	Calculations by tests of Group 1	Calculations by tests of Group 2
All assay elements	The test is computed for each Test-vs-Standard and for each Control-vs-Standard comparison.	The test is computed by fitting the data of each sample separately.
Standard only	No test is computed.	The test is computed by only fitting the data of the Standard sample.
Test samples only	The test is computed for each Test-vs-Standard comparison.	The test is computed by only fitting the data of each Test sample.
Control samples only	The test is computed for each Control-vs-Standard comparison.	The test is computed by only fitting the data of each Control sample.

Note: With simultaneous regression (formerly called multiplex assay), all samples are regarded as one single dataset and are tested together (not as individual samples or pairwise comparisons).

The following table indicates how F-values are calculated:


Test type	Description	Calculation of F-value
F-test on the significance of regression	Tests for the significance of the regression term. The test is passed if F ≥ F_critical.	If Pure-error ANOVA is selected: F = MS_Regression / MS_PureError. If Residual-error ANOVA is selected: F = MS_Regression / MS_{ResidualError}. Where: MS is the mean squared error.
F-test on the significance of non-parallelism	Tests for the significance of the non-parallelism term. The test is passed if F ≤ F_critical.	If Pure-error ANOVA is selected: F = MS_{Non-Parallelism} / MS_PureError. If Residual-error ANOVA is selected: F = MS_{Non-Parallelism} / MS_{ResidualError}. Where: MS is the mean squared error.
F-test on the significance of non-linearity (lack of fit)	Tests for the significance of the non-linearity term. The test is passed if F ≤ F_critical.	For both ANOVA methods: F = MS_{Non-Linearity} / MS_PureError. Where: MS is the mean squared error.
F-test on the significance of non-similarity	Tests for the significance of the non-similarity term of the Slope ratio model. The test is passed if F ≤ F_critical.	If Pure-error ANOVA is selected: F = MS_{Non-Similarity} / MS_PureError. If Residual-error ANOVA is selected: F = MS_{Non-Similarity} / MS_{ResidualError}. Where: MS is the mean squared error.
F-test on the significance of the slope	This test corresponds to the 'test of slope' in PLA 2.0. The test is passed if F ≥ F_critical.	F = MS_Model / MS_{ResidualError}. Where: MS is the mean squared error.
F-test on the significance of the square coefficient	This test corresponds to the 'test of linearity' in PLA 2.0. The test is passed if F ≤ F_critical.	F is calculated as: $F = \frac{\sum {(f_{q u a d r} (x_{i j k}) - \overline{y})}^{2} - {(f_{l i n} (x_{i j k}) - \overline{y})}^{2})}{\sum {(f_{q u a d r} (x_{i j k}) - y_{i j k})}^{2}}$ Where f_lin is the fit for one assay element of a linear model, and f_quadr is the fit for one assay element of a quadratic model.

The following table lists all custom F-tests.

Note: We do not recommend these tests for new assay development. They are not standard tests and were introduced to replace outdated custom software.


F-tests on the significance of:	Support the following models:	Scope of the test¹
the square coefficient (assay scope) the difference of the quadratic full vs. restricted (assay scope)	Linear parallel-line Slope ratio	Group 1
preparation	Supports all models except: Slope ratio 4-parameter logistic with Control line included	Group 1

¹ The tests of Group 1 and 2 differ in how the Scope of the test affects inclusion of various assay elements. The groups are explained in the Scope of the test section.

The following table indicates how F-values are calculated for custom F-tests:


Test type	Description	Calculation of F-value
F-test on the significance of the square coefficient (assay scope)	The test is passed if F ≥ F_critical.	The test statistic is calculated by dividing $\sum {(f (x_{i j k}) - \overline{y})}^{2}$ by MS_PureError if Pure-error ANOVA is selected. If Residual-error ANOVA is selected, the term is divided by MS_{ResidualError} instead. Here MS is the mean squared error, and f is the fit corresponding to the model: a₀ + b ⋅ log (x) + c ⋅ ( log (x) )² with parameters a₀ depending only on the defined assay element and b and c depending on the Standard sample and the defined assay element.
F-test on the significance of the difference of the quadratic full vs. restricted (assay scope)	The test is passed if F ≤ F_critical.	The test statistic F is calculated by performing a model comparison between an unrestricted quardatic model with six parameters and a quadratic model with five parameters where the coefficent of the quadratic term is identical for test and standard sample. The denominator is MS_PureError if Pure-error ANOVA is selected. If Residual-error ANOVA is selected, MS_{ResidualError} is used as the denominator instead.
F-test on the significance of preparation	The test is passed if F ≤ F_critical.	If Pure-error ANOVA is selected: F = MS_Preparation / MS_PureError. If Residual-error ANOVA is selected: F = MS_Preparation / MS_{ResidualError}. Where: MS is the mean squared error.


Data type	Multiplicity	Usage	Default value
Node	0...unbounded	optional	none

/Quantitative response assay/Analysis/Suitability tests/Assay suitability tests/alternatives/

/Quantitative response assay/Analysis/Suitability tests/Sample suitability tests/alternatives/

/Test system definition (Quantitative response assay)/Suitability tests/Assay suitability tests/alternatives/

/Test system definition (Quantitative response assay)/Suitability tests/Sample suitability tests/alternatives/

F-test (hypothesis test)

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