Ring test parameters

The aim of the analysis step is to specify the basic ring test parameters such as the overall mean and the precision measures (repeatability and reproducibility standard deviation). The-se are then uThe-sed to determine the assigned value and target standard deviation, the two quantities on the basis of which the evaluation step is performed. Even if these two quantities are determined independently of the ring test parameters ( e.g. when reference samples are used), these ring test parameters must nevertheless be computed so that at least the overall mean is available for the evaluation step.

Under Statistics – Ring test parameters the following statistical methods are available:

- ISO 5725-2

- Nested Design 2x2 (ISO 5725-3/5)

- Nested Design (ISO 5725-3)

- Q method and Huber estimate

The statistical method according to ISO 5725-3/5 (nested design 2 x 2) is a combination of the two guidelines. On the one hand, the calculations are performed according to the ISO 5725-3 guideline for nested design, but on the other hand, the rules for robust calculations according to ISO 5725-5 are implemented. At the moment, this combination is only available for a 2 x 2 nested design. The statistical method according to ISO 5725-3, however, can be applied to all nested designs with one factor. The kind of design must have been previously defined in the Basic tables, and the measurement values must have been entered in a spe-cific order (see section 7.7).

Figure 60: Statistics – Ring test parameter

Having selected a method, click on the Computation button to start the calculation for all se-lected data.

The evaluation results depend on the calculation method selected. For the statistical meth-ods ISO 5725-2, DIN 38402-A42 and ISO 5725-3 an outlier detection is carried out before the actual calculation of the ring test parameters. More specifically: the Cochran test is ap-plied for the analysis of variance, and the Grubbs test is apap-plied for the analysis of mean val-ue deviations. For the outlier detection according to ISO 5725-3, a distinction is drawn be-tween the variability of the measurement values within one factor level ( e.g. measurements performed on one particular day) and between different factor levels ( e.g. measurements performed on different days). Accordingly, the outlier detection window for the ISO 5725-3 method reflects this distinction by means of the separate displays Cochran test within and between.

The outlier tests are carried out automatically via the button Detect outlier. A distinction is drawn between outliers (at the significance level 1 %) and stragglers (at the significance level 5 %). By squares, circles and, additionally, in ISO 5725-3, by diamonds, it is indicated which of the tests showed a significant result: circle and diamond stand for the Cochran test, while the square stands for the Grubbs test. If a symbol is completely grey, the corresponding la-boratory proved to be an outlier lala-boratory, if the sign is half white and half grey, the

corre-sponding laboratory is a straggler.

Figure 61: Legend to ISO 5725-2 (top) and ISO 5725-3 (bottom)

Outlier laboratories are marked by a red cross. The corresponding measurement values will be excluded from all further calculations. However, it is possible to correct the outlier status manually with the right mouse button. Furthermore, for the outlier detection according to ISO 5725-2 and ISO 5725-3 the outlier detection tests may be repeated, whereas according to DIN 38402 A42 this is not allowed and, hence, not possible in ProLab Plus.

The example below shows the results of the outlier detection according to ISO 5725-2 after activating the button Detect outliers. Laboratory L003 is an outlier according to Cochran, i. e.

with a significantly differing mean value. It is marked in red in the chart. Laboratory L025 is a straggler according to Cochran. Only values of laboratory L003 will be excluded from further calculations.

If you close the window immediately after the calculations have been completed, the empiri-cal values for the mean value and the reproducibility s.d. will be used for the assigned value and the target standard deviation, respectively.

Figure 62: Ring test parameters – ISO 5725-2

At this point a check for outliers of type E is not carried out. Outliers of type E are defined as values that lie outside the tolerance limits which are calculated during the Z score computa-tion. Outliers of type E will never automatically be eliminated from the calculation of ring test parameters by ProLab, as they are not classical outliers.

10.2.1 Option for DIN 38402 A 45: logarithmic calculation

If the box for Logarithmic calculation is checked, ProLab Pluscalculates the mean, standard deviations and tolerance limits using the logarithmized test results, but always reverts to non-logarithmic values for the display of results. Moreover, the option is added to the method name, e.g. in report 34 (Charts and tables – Further reports – Tolerance limits, methods of analysis and results). Please note that relative standard deviations are meaningless when computed on the basis of logarithmic data, and that they are accordingly automatically con-verted using the following formula:

approximate absolute standard deviation of non-logarithmic data

= calculated standard deviation based on logarithmized test results * mean value of the nonlogarithmic data

If you prefer a logarithmic scaling of the axes in charts, e.g. in the Summary results, you can adjust the settings in the chart editor (right click on chart area, menu item Axis).

Please note that the only score-type that can be computed when using logarithmic calcula-tion are Z scores.

An overview of the measurements, laboratory means and standard deviations or of the eval-uation results can be obtained by clicking on one of the report buttons for either laboratory data or results.

After finishing the calculations the assigned value and target standard deviation need to be defined. If no further data is input, ProLab Plus uses the empirically determined values (overall mean and reproducibility standard deviation). If you wish to use a different definition for these quantities, e.g. reference value and the standard deviation according to Horwitz (Horwitz s.d.), click the buttons for Assigned value and target s.d.

10.2.2 Determine assigned value

Activating the button Assigned value opens a window where the assigned value may be de-fined for each combination of sample and measurand.

You can choose between the following options for determining the assigned value:

R = reference mean the reference mean value as specified under Characteristics of measurands

M = mean the empirically determined value without considering results below the detection limit and the limit of determination

lM = lower mean like M = mean, except that all values below the detection limit and the limit of determination are set to zero

uM = upper mean like M = mean, except that all values below the detection limit and the limit of determination are set to the median of these limits Mo = mode main mode of kernel density estimation

Ma = manually the desired value is entered manually

Please note that by selecting M = mean the assigned valued is defined as the empirical mean value as computed in accordance with the selected statistical method. If for example ISO 5725-2 has been selected, the mean value is the arithmetic mean excluding outliers, while for Q method and median the mean value is defined as the median.

Figure 63: Statistics – Ring test parameter – Assigned value

In the column Mode the current selection, i. e. one of the possibilities R, M, lM, uM, Mo or Ma is displayed. The default setting is M. To change the mode, click on the mode field of the rel-evant row, and select the desired assigned value definition. If you choose the option manual-ly, you can change the value in the Assigned Value column.

To change the mode of all combinations at the same time, open the drop-down menu on the upper toolbar and select one of the options. The change will become effective upon clicking on the red check mark.

Figure 64: Determination of assigned value

10.2.3 Determine target s.d.

Activating the button Target s.d. opens a window where the target standard deviation value can be defined for each combination of sample and measurand.

You can choose between displaying the relative or absolute standard deviations (as a re-minder: the relative s. d. is defined as follows: (s. d. / mean value) x 100). Furthermore, the following options are available for the definition of the target standard deviation:

R = reference s.d. the reference standard deviation as specified under Database - Characteristics of measurands

L = limited s.d. if the empirical standard deviation is greater than the upper limit (assigned value _* rel. s.d. max / 100) then the target s.d. is set to this upper limit; if the empirical standard deviation is less than the lower limit (assigned value _* rel. s.d. min / 100) then the target s.d. is set to this lower limit; otherwise the target s.d.

is set equal to the reproducibility s.d. Use the option L in order to prescribe bounds for the range of acceptable empirical standard deviations, e.g. to prevent the target standard devia-tion from varying too much from one ring test to the next.. If the range of tolerance is defined by |Z| < 2 and all results in a range of +/- 10% of the mean are to be accepted, the value of rel. s.d.

min must be 5. The values of rel. s.d. min and rel. s.d. max are specified under Database – Characteristics of measurands.

S = reproducibility s.d. empirical s.d. (the empirically determined reproducibility stand-ard deviation without considering results below the detection limit and the limit of determination)

eH = empirical Horwitz empirical Horwitz (standard deviation determined on the basis of an empirically adapted Horwitz function; the assigned value established in the previous step is used for the calculation; the use of an empirically adapted Horwitz function is only recom-mended if at least three or four different levels have been ana-lysed)

kH = classical Horwitz classical Horwitz (standard deviation determined on the basis of the Horwitz function; the assigned value established in the previous step is used for the calculation)

tH = truncated Horwitz standard deviation determined on the basis of the Horwitz func-tion; the assigned value established in the previous step is used for the calculation; if the relative Horwitz-s.d. is greater than 22 %, the target standard deviation is set to 22 %.

Ma = manually if this option is selected, any value can be entered in the target s.d. field. That value may be a relative or absolute figure, de-pending on the view with which you are working in the table.

Vf = variance function the target s.d. is defined as the result of the calculation of the variance function

SM = s.d. of lab means standard deviation of the laboratories’ mean values

Figure 65: Statistics – Ring test parameters – Target s.d.

In the column Mode the current selection is shown. The default setting is S, that is the target s.d. equals the empirical reproducibility s.d.

To select a target s.d. mode for any particular sample-measurand combination click the Mode field in the relevant row to open a drop-down list box with the options. To change the mode of all combinations at the same time, open the drop-down list box in the upper part of the window and select one of the options. The mode change will become effective upon clicking on the check mark.

10.2.4 Variance function

If you want to use the variance function according to DIN 38402 A 45 as standard deviation, it has to be calculated beforehand.

By clicking on the Variance function button, the method described below is used to define the reproducibility standard deviation as a function of the concentration and to check that this function is sufficiently precise. The method can be used if interlaboratory test results are available for at least four samples with different concentrations per measurand.

Step 1: Identification of gross outliers – gross outliers can be identified when 4 to 15 samples are tested

Step 2: Determination of variance function – after the gross outliers have been eliminated, the final variance function is determined.

Step 3: Testing the variance function for adequate precision – it may be determined that the variance function is sufficiently precise. If this is not the case, it is checked whether other fac-tors exert an influence on the variance or whether the functional relationship is more com-plex.

Step 4: Testing the concentration dependence for significance.