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Numeric Summary


This option is accessed from the Review's Numeric option. It is used to display all numerical peak analysis information. The Numeric Summary window is live and can remain up while different data sets are selected or deselected in the Review.

The View Numeric Summary for this Fit right click popup menu option opens the Numeric Summary with only the content for the specific fit where this right click popup was invoked. If the window is already open, it is updated with just this specific fit.

This numeric summary can consist of the following items, all selected from the Options menu:

· Fitted Parameters - goodness of fit and fitted parameter values

· Equivalent Parameters - for GenHVL and GenNLC models, the equivalent diffusion-kinetic parameters

· Measured Values - measured peak characteristics; also includes analytic areas if available

· Analytic Moments - the analytic moments of the model

· Deconvolved Moments - the moments of the deconvolutions inherent in a model

· Advanced Area Analysis - additional information in breakdown of components of areas

· Parameter Statistics - peak by peak parameter statistics

· Chromatography Analysis - theoretical plates and resolutions

· Overlap Areas - matrix of overlap areas for all peaks

· Analysis of Variance - ANOVA

· Details of Fit - Convergence State, Iterations, Fit Settings

· Average Multiple Fits - Averages of Coefficients of Variations of multiple similar fits

The Options menu also includes:

· Add Probabilities - adds probability values to the parameter statistics and analysis of variance table

· Add X Area Values - adds the x values at specific cumulative areas for supported models

· 90 %Confidence - uses 90% confidence levels for parameter statistics

· 95 %Confidence - uses 95% confidence levels for parameter statistics

· 99 %Confidence - uses 99% confidence levels for parameter statistics

· Specify Column Dead Time - offers input of dead-time for the specific retentions reported in chromatographic summary if x values were not transformed

The Options menu also includes menu options for selecting a predefined set of options:

· Select All - all sections will be included

· Select Only Fitted Parameters - only the Fitted Parameters section will be included

· Select Chromatography - Fitted Parameters, Equivalent Parameters, Measured Values, Analytical Moments, Deconvolved Moments, Advanced Area Analysis, Chromatography Analysis, Overlap Areas

· Select Statistical - Fitted Parameters, Measured Values, Analytical Moments, Parameter Statistics, ANOVA - Analysis of Variance, Add Probabilities

All elements of this Numeric Summary are computed when the Review is opened with the exception of Overlap Areas. Because this is a matrix of integrations, it can require a considerable time with a large number of peaks or with those that are particularly demanding to compute. Overlap Areas should not be routinely checked unless you really need this information.

The Numeric Summary is toggled on and off by the Numeric button in the Review. The window size and position you choose for the Numeric Summary is automatically saved across sessions. The Numeric Summary uses the PFChrom RTF Viewer to display, modify, and print the information.

Viewing/Averaging only Selected Fits

When multiple data sets are fitted, you can view (and average) only specific fits in the Numeric Summary. The selection process must be done in the Review window. It cannot be done directly within the Numeric Summary window.

Procedure in Review to Select Fits

These instructions apply to the Review window. If you wish to compare/average only certain fits in the Numeric Summary, select those you wish to review by clicking on the specific graph for that fit (the border will turn gray to indicate selection). You can also use the Select this Graph right click menu option for each fit. You can click again on a selected set to deselect it, or use Unselect this Graph from the right click popup menu. When the sets you wish to individually review are selected, select the Plot | Only Selected Fits from the right click menu. Only those data fits will be rendered in the Review graphs, in the Numeric Summary, in the Residuals, in the Explore option, and in the Export.

If you only wish to review one of the fits, you can double click that graph to open a review of just that fit. You can also choose Plot this Fit (or Plot Only this Fit) from the right click menu. When you are finished, and you wish to restore all of the fits, you can once more double click the graph or select Plot All Fits.

Averaging Different Fits without Refitting

If the data sets are identical in peak count, peak model, and in how they were fitted, the Average Multiple Fits will produce useful values for a standard. If you wished run a concentration series for a standard, for example, you can fit all of these data sets in one step and use this selection in the Review to have only those selected sets displayed in the Numeric Summary. The averages and CVs will be automatically updated to reflect those selections. There is no need to create different data files or execute separate fits. Simply select the fits you wish to view and these will be displayed and averaged in the Numeric Summary.

Fitted Parameters

The Fitted Parameters section begins with PFChrom's sum of squares based goodness of fit criteria. These are the rČ coefficient of determination, a degree of freedom adjusted rČ, the standard error for the fit, the F-statistic for the fit, and the ppm unaccounted variance. The summary then presents each function and its fitted parameter values. If a background was fitted, it is last in the function list.

Fitted Parameters

r2 Coef Det        DF Adj r2          Fit Std Err        F-value            ppm uVar

0.99991477         0.99991466         0.00968436         9,571,866          85.2295102

 Peak        Type                a0                a1                a2                a3                a4    

    1        GenNLC        2.01452745        3.05122094        0.00024861        -0.0031843        1.14665629  

    2        GenNLC        0.57304194        4.90636059        0.00030115        -0.0006486        1.14665629  

    3        GenNLC        0.66842649        5.89144460        0.00030732        -0.0004125        1.14665629  

    4        GenNLC        0.30453186        9.32507941        0.00047594        0.00031223        1.14665629  

    5        GenNLC        1.06248152        21.7583350        0.00119313        0.01094087        1.14665629  

    6        GenNLC        0.60317688        27.4861040        0.00143410        0.00832760        1.14665629  

If a peak parameter fails significance, the parameter and the model listed for that peak will be grayed. This furnishes immediate feedback that a model may be overspecified (that a more complex model has been fitted than the data can support).

Equivalent Parameters

For a GenHVL model, this section converts the parameters from a diffusion-based HVL model to a kinetics-based NLC, furnishing the equivalent parameters had you chosen to make a GenNLC fit. For a GenNLC model, this section converts the parameters from a kinetics-based NLC model to a diffusion-based HVL, furnishing the equivalent parameters had you chosen to make a GenHVL fit.

Equivalent Parameters

 Peak        Type                a0                a1                a2                a3                a4    

    1        GenHVL        2.01452745        3.05122094        0.03894996        -0.0031843        0.01463749  

    2        GenHVL        0.57304194        4.90636059        0.05436082        -0.0006486        0.01270456  

    3        GenHVL        0.66842649        5.89144460        0.06017585        -0.0004125        0.01171207  

    4        GenHVL        0.30453186        9.32507941        0.09421421        0.00031223        0.01158503  

    5        GenHVL        1.06248152        21.7583350        0.22786153        0.01094087        0.01200822  

    6        GenHVL        0.60317688        27.4861040        0.28077663        0.00832760        0.01171335  

 

Measured Values

The initial Measured Values section uses minimization and root-finding algorithms to report amplitude, center (mode or apex), full width at half-maxima (FWHM), asymmetry at half-maxima (Asym50), full width at 10% of maxima (FW Base), and asymmetry at 10% of maxima (Asym10) measured values.

The final Measured Values section first reports an integrated area and its percentages. The integrated area is computed from the minimum X of the fitted data to the maximum X of the fitted data. Note that the integrated area will be less than the analytic area if some portion of that peak is outside this X range of the data. The final four elements are the first, second, third, and fourth moments. The second moment is reported as an SD instead of a variance. The area and moment computations use an automated integration routine which uses a Gaussian Quadrature or Romberg method. Target precision is 1E-8.

Measured Values

 Peak        Type           Amplitude          Center             FWHM             Asym50           FW Base            Asym10    

    1        GenNLC        17.8716084        3.14096487        0.10664365        0.48899022        0.21451372        0.42773806  

    2        GenNLC        4.16502418        4.92863684        0.12935111        0.88416960        0.25864659        0.86456084  

    3        GenNLC        4.41042518        5.90649497        0.14244138        0.93009104        0.28489828        0.92035906  

    4        GenNLC        1.29103598        9.31113024        0.22152812        1.05741417        0.44380373        1.08094057  

    5        GenNLC        1.77954450        21.3677392        0.55844785        1.75524682        1.14463028        2.02141201  

    6        GenNLC        0.84359492        27.1673938        0.66972658        1.45557636        1.35828714        1.61026579  

 

 Peak        Type             Area             % Area             Mean             StdDev           Skewness          Kurtosis   

    1        GenNLC        2.01452745        38.5467988        3.11407765        0.04686849        -0.5508965        2.97230910  

    2        GenNLC        0.57304194        10.9648208        4.92282943        0.05490883        -0.1112859        2.99210316  

    3        GenNLC        0.66842649        12.7899480        5.90283072        0.06044843        -0.0589339        2.99493096  

    4        GenNLC        0.30453186        5.82703808        9.31637063        0.09421028        0.08095826        3.00760983  

    5        GenNLC        1.06248152        20.3299594        21.4872108        0.24940648        0.53909101        3.10909761  

    6        GenNLC        0.60317687        11.5414348        27.2649660        0.29211223        0.40048612        3.07535479  

  All        Total         5.22618613        100.000000  

 

Analytic Moments

An analytic moment is one which has a closed form solution. PFChrom has closed form analytic moment formulas for many of its peaks functions. Unfortunately, we do not have formulas for the GenHVL and GenNLC families of models. When an analytical moment is not available, the analytic moments will be given for the ZDD (zero-distortion density) of the GenHVL or GenNLC model:

Analytic Moments

 Peak        Type                FnArea           % FnArea           FnMean           FnStdDev         FnSkewness        FnKurtosis  

    1        GenNorm[m]        2.01452745        38.5467987        3.05122094        0.03895622        0.04391796        3.00342915  

    2        GenNorm[m]        0.57304194        10.9648208        4.90636059        0.05436740        0.03811728        3.00258309  

    3        GenNorm[m]        0.66842649        12.7899480        5.89144460        0.06018204        0.03513903        3.00219519  

    4        GenNorm[m]        0.30453186        5.82703806        9.32507941        0.09422369        0.03475781        3.00214782  

    5        GenNorm[m]        1.06248152        20.3299594        21.7583350        0.22788617        0.03602769        3.00230764  

    6        GenNorm[m]        0.60317688        11.5414351        27.4861040        0.28080552        0.03514286        3.00219567  

  All        Total             5.22618614        100.000000  

In this case, the moments for the generalized normal with a1=mean, the ZDD, are given. When the Measured Values and Analytic Moments section use the same model, unless some portion of a peak extends beyond the X-range of the data, the analytic and numeric integration areas will be essentially equivalent.

The baseline is not included in this option.

Deconvolved Moments

A given model will have its own specific deconvolutions or simplifications. If an <irf> instrument response function model is fitted, the first deconvolution will be the peak absent this IRF. There will then be a succession of up to two additional deconvolutions. In this example where the IRF was presubtracted and a GenNLC fitted, the moments are for the pure NLC, the peak absent the ZDD adjustments for nonideality, and the Giddings, the peak absent all chromatographic distortion, the expected peak at infinite dilution.

Deconvolved Moments

 Peak        Type               Area              Mean             StdDev           Skewness          Kurtosis   

    1        NLC             2.01452745        3.11359553        0.04638333        -0.5754550        3.01434309  

    2        NLC             0.57304194        4.92280794        0.05481415        -0.1327280        2.99963882  

    3        NLC             0.66842649        5.90282199        0.06038679        -0.0787251        2.99874389  

    4        NLC             0.30453186        9.31636798        0.09424530        0.06134788        3.00315182  

    5        NLC             1.06248152        21.4859511        0.25094228        0.51874259        3.07620833  

    6        NLC             0.60317687        27.2643081        0.29324707        0.38067153        3.05177301  

 

 Peak        Type               Area              Mean             StdDev           Skewness          Kurtosis   

    1        Giddings        2.01452745        3.05122094        0.03894996        0.01914805        3.00048886  

    2        Giddings        0.57304194        4.90636059        0.05436082        0.01661949        3.00036828  

    3        Giddings        0.66842649        5.89144460        0.06017585        0.01532116        3.00031298  

    4        Giddings        0.30453186        9.32507941        0.09421421        0.01515497        3.00030623  

    5        Giddings        1.06248152        21.7583350        0.22786153        0.01570857        3.00032901  

    6        Giddings        0.60317685        27.4861040        0.28077641        0.01531470        3.00027213  

These are also numeric integrations similar to those used in the Measured Values section. Again, the integrated area will be less than the analytic area if some portion of that peak is outside this X range of the data, and the second moment is reported as an SD instead of a variance.

Advanced Area Analysis

In most cases, this Advanced Area Analysis section will furnish a measure of the deviation from the non-ideality furnished by the ZDD's higher moment parameters. This is especially useful for higher overload peaks or in instances where you would like to quantify these deviations.

Advanced Area Analysis

 Peak        Type                   Area              % Area            ApexAsym          NonOverlap1       % PkArea        NonOverlap2       % PkArea  

    1        GenHVL[Yp2]<e2>        323.654533        100.000000        0.47529501        225.535354        69.6839781        53.8177535        16.6281476  

The Apex Asym furnishes the area asymmetry relative to apex or mode of the peak, the area to the right of the apex divided by the area to the left.

NonOverlap1 is the area of non-overlap between the peak with the ZDD non-ideality and the pure ZDD (the HVL or NLC deconvolved peak). In an overload peak, this is the difference between the peak with the overload shape (minus the IRF) and the deconvolved HVL, the peak that would theoretically exist if there were no overload or any other deviation from this ideality. For analytic peaks, this will be the difference between the GenHVL and HVL, or GenNLC and NLC, and in general, the removal of the ZDD non-idealities will result in only a small amount of non-overlap. In the example below, the non-overlap area is close to 70%. Only 30% of the deconvolved HVL's area is contained in the overload shape.

NonOverlap2 is the area of non-overlap between the peak with and without the IRF removed. In the example below, the area without overlap is 16.6%. One sixth of the overall area of the peak is without overlap between the two peaks.

If the fit is for an experimental two-state model, such as the GenHVL[Z|E], where there are two-components to the ZDD each of which contributes a portion to the overall area of a peak, the state 1 values will consist of the area for the D1 primary component in the (D1|D2) density, where state 2 will the the area for the secondary D2 density, the one adding the anomaly to the overall shape.

For certain models, you will also see a table similar to the following:

 Peak        Type                x0.005            x0.01             x0.025            x0.05             x0.25             x0.50     

    1        GenHVL_C          4.46650032        4.54866980        4.67067048        4.77669246        5.09764104        5.29247708  

 Peak        Type                x0.50             x0.75             x0.95             x0.975            x0.99             x0.995    

    1        GenHVL_C          5.29247708        5.44831575        5.62480580        5.67771494        5.73919823        5.78142930  

 Peak        Type                 xwa50             xwa90             xwa95             xwa98             xwa99    

    1        GenHVL_C          0.35067472        0.84811334        1.00704446        1.19052843        1.31492898  

 

 Peak        Type                x0.005            x0.01             x0.025            x0.05             x0.25             x0.50     

    1        HVL_C             4.48743900        4.56215809        4.67519812        4.77555231        5.09223273        5.29474252  

 Peak        Type                x0.50             x0.75             x0.95             x0.975            x0.99             x0.995    

    1        HVL_C             5.29474252        5.46283811        5.66029357        5.72103970        5.79256978        5.84230132  

 Peak        Type                 xwa50             xwa90             xwa95             xwa98             xwa99    

    1        HVL_C             0.37060538        0.88474126        1.04584158        1.23041170        1.3548623

If the model is a GenHVL, or Gen2HVL, the Advanced Area Analysis will evaluate the roots of the GenHVL and HVL cumulatives to get the x values at .5%, 1%, 2.5%, 5%, 25%, 50%, 75%, 95%, 97.5%, 99%, and 99.5% area. If the model is the HVL, only the HVL cumulative is evaluated. The xwa50 through xwa99 values are the peak widths for areas of 50%, 90%, 95%, 98%, and 99%. Note that the xwa50 width will likely be very different from the FWHM (full width at half-maximum, 50% of the peak's amplitude) and the xwa90 width will likely be very different from the FW Base (width at 10% of the peak's amplitude).

If the model is a GenNLC or Gen2NLC, the GenNLC and NLC cumulatives will be evaluated. For the NLC, only the NLC cumulative is evaluated.

The x0.005-x0.995 values will only be shown if the Add X Area Values is checked in the Options menu.

Note that this Advanced Area Analysis only exists for these specific closed form cumulatives. If an <irf> version of one of these models is fitted, you will see these cumulatives absent the IRF, and those will represent the IRF Deconv. and Partial Deconv. deconvolution levels in the Review.

A center of mass is not reported for the model with the <irf> (a peak model that is itself not of a closed-form solution will not a have a closed-form cumulative). You can still manually get this center of mass of the eluted peak with the IRF present by using the Evaluate Fit Model right click menu option in the Review to integrate from a baseline x position prior to the peak to various x positions within the peak, seeking a value where exactly half the reported area is found.

If the peak area is proportional to mass, the mean or first moment of an asymmetric peak will not be the center of mass. You will need to use the x0.50 values from this Advanced Area Analysis for center of mass retention values.

For the GenHVL, Gen2HVL, GenNLC, and Gen2NLC models, a1 is the mean of the ZDD zero distortion density (either a generalized normal or generalized error model). This reflects a concentration independent location of the retention absent the a3 chromatographic distortion (the retention at infinite dilution), but it includes the deviation from theoretical ideality which is present in the ZDD. In the Measured Values section, the Center is the mode or apex of the peak as fitted, and the Mean is the first moment of the actual fitted peak. In the Deconvolved Moments section, the mean or first moment is given for the different deconvolutions.

Parameter Statistics

The Parameter Statistics section is a peak by peak display of parameter statistics, which include each parameter's value, standard error, t-value (parameter value/std error), and confidence limits. The confidence level is set in the Options menu. Note that these standard errors and confidence limits assume normal (Gaussian) errors. If you plan to use these statistics, you should confirm normal errors using a Residuals Graph, inspecting both a distribution and SNP plot.

Parameter Statistics

Peak 1 GenNLC

 Parameter           Value             Std Error         t-value           95% Conf Lo        95% Conf Hi        P>|t|

         Area        2.01452745        0.00018515        10880.4555        2.01416454         2.01489036         0.00000

       Center        3.05122094        2.9614e-5         1.0303e+5         3.05116290         3.05127899         0.00000

        Width        0.00024861        2.764e-7          899.444774        0.00024806         0.00024915         0.00000

     Distortn        -0.0031843        1.764e-6          -1805.1787        -0.0031877         -0.0031808         0.00000

      NLCasym        1.14665629        0.01514743        75.6997452        1.11696604         1.17634653         0.00000

If a peak parameter fails significance, the parameter row for that peak will be grayed. You will be able to see the t-values used to test the significance. For a reasonably-sized chromatographic data set, 90% significance occurs around |t|=1.65, 95% significance occurs around |t|=1.96, and 99% significance occurs around |t|=2.58.

Chromatography Analysis

The Chromatography Analysis section furnishes two computations of the theoretical plate count. The N-model uses the moments formula and the N-Gauss uses the more familiar Gaussian approximation. For the HVL and NLC based generalized and native models, the N-model uses the second moment estimated from the underlying zero-distortion density a2 value. This means distortion resulting from the IRF, the chromatographic fronting and tailing, and the zero-distortion density asymmetry, are not represented in the theoretical plate estimate. The N-model estimate will thus be IRF, zero-distortion density, and concentration independent.

For the NLC-based models, the equivalent parameters computations are used to convert the NLC's kinetic width to a statistical standard deviation. The GenHVL and GenNLC models will thus produce equivalent N-model values for identical goodness of fit. For models that are not HVL or NLC based, the full second moment is used, and the IRF, zero-distortion density asymmetry, and concentration-dependent tailing-fronting will be reflected in the N-model theoretical plate estimate. If the IRF fits to a significant tailing, the N in this instance may be substantially smaller since those tails can appreciably increase the second moment.

The next columns are the full width at the base (extrapolated from a straight line between 90% and 10% of peak maximum) and the asymmetry at 10% of peak maximum.

The retention column contains the thermodynamic capacity factor. This will be the a1 value of the fitted peaks. If the x-values were not transformed for dead-time in a transform applied prior to fitting, you can still report the k' capacity factor by using the Specify Column Dead Time in the Options menu. The Retention value is adjusted for this dead time. If you have pre-transformed the data for a Retention scale, do not enter a dead time in the Numeric Summary Options menu since the a1 parameter values will already reflect the capacity factor values. Also note that this specification of a column dead time in this Numeric Summary only impacts the values reported in the Retention column. An untransformed time-scale fit is in no way altered.

The last column contains the resolution between adjacent peaks.

Chromatographic Analysis

 Peak      Type       N-model       N-Gauss       FW Base       Asym10       Retention      Resolution

    1      Gen2HVL      57679.1140      56136.3646      0.10176837      0.93309755      5.22305252      

    2      Gen2HVL      1.5477e+05      1.4743e+05      0.08624138      0.95535694      7.36217776      22.7332895

    3      Gen2HVL      1.9469e+05      1.8843e+05      0.08546698      0.96455364      8.10223725      8.61919513

    4      Gen2HVL      2.2587e+05      2.175e+05      0.08037897      0.95103106      8.22879149      1.52937238

    5      Gen2HVL      2.2187e+05      2.1644e+05      0.08261828      0.97540720      8.32501136      1.17322212

    6      Gen2HVL      1.8381e+05      1.8287e+05      0.09665338      1.05168122      8.81928515      5.48184226

    7      Gen2HVL      2.6423e+05      2.5414e+05      0.08259916      0.96918000      9.15917776      3.82454840

    8      Gen2HVL      2.8145e+05      2.589e+05      0.07907287      0.95585499      9.32551187      2.05525673

    9      Gen2HVL      2.7702e+05      2.57e+05      0.08234331      1.00088992      9.57605326      3.09087461

  

Overlap Areas

The Overlap Areas section consists of a square matrix whose size is the peak count. This option can be quite time consuming with a large number of peaks or with peaks whose functions are computationally demanding. To find the overlap area between any two peaks simply find the desired position in the matrix. The computations use an automated integration routine which uses a Gaussian Quadrature or Romberg method. Target precision is 1E-8.

Overlap Areas

 Peak        Type           Peak 1            Peak 2            Peak 3            Peak 4            Peak 5            Peak 6     

    1        GenNLC        2.01452745        5.1385e-87        4.973e-178        0.00000000        0.00000000        0.00000000  

    2        GenNLC        5.1385e-87        0.57304194        6.3064e-18        4.86e-202         0.00000000        0.00000000  

    3        GenNLC        4.973e-178        6.3064e-18        0.66842649        1.606e-113        0.00000000        0.00000000  

    4        GenNLC        0.00000000        4.86e-202         1.606e-113        0.30453186        0.00000000        0.00000000  

    5        GenNLC        0.00000000        0.00000000        0.00000000        0.00000000        1.06248152        1.1842e-29  

    6        GenNLC        0.00000000        0.00000000        0.00000000        0.00000000        1.1842e-29        0.60317687  

In the diagonals of the matrix are the actual areas of the peaks.

Analysis of Variance

The Analysis of Variance section includes a standard ANOVA table and also reports the rČ coefficient of determination, the degree of freedom adjusted rČ, and the standard error for the fit (the square root of the Mean Square Error).

Analysis of Variance

r2 Coef Det        DF Adj r2          Fit Std Err

0.99991477         0.99991466         0.00968436

Source         Sum of Squares          DF                Mean Square              F Statistic            P>F

Regr           21545.171207352         24                897.71546697301          9571866.1517028        0.0000000000

Error          1.8364409071549         19581             9.37868805e-5  

Total          21547.007648259         19605

   

Details of Fit

The Details of Fit section is helpful for subsequently referencing how a fit was made, and its success or failure relative to convergence. Also reported are the number of parameter constraints violated on the final iteration. Many of the items summarize the current Fit Preferences since these can significantly affect the results of any given fit.

Details of Fit

Set Convergence        State         Iterations       Minimization       Curvature Matrix      GA Prefit      GA Conv

    1E-6             Converged            10         Least Squares           Sparse-Roots           None         6   

Constraint      a0           a1           a2           a3           a4           a5           a6           a7           a8           a9           Fail

  Local         25.00        5.00         50.00        None         None         None         None         None         None         None           0

  Global        None         None         None         None         None         None         None         None         None         None   

 

Average Multiple Fits

The Average Multiple Fits section is only available where there are multiple fits and those can averaged. All must have exactly the same peak count and use the same model, and there must be no customizations, as in locking a parameter in one fit but not another.

When this option is selected, and averaging is permitted, you will see two separate numeric summaries at the end of summaries for the individual data sets. The first will contain the averages, there will be no data set information, and a title similar to "Average for 12 Fits" will precede a summary where every value is an average of the values from all of the individual summaries. You will need to use caution with respect any value arising from a parameter in one data set that happens to fit to a wild value that severely distorts the average.

The second numeric summary at the end of the individual data set summaries will contain the CV% (coefficient of variation percentages), there will again be no data set information, and a title similar to "CV Percent for 12 Fits" will precede a summary where every value in that summary is a CV% from the averages of the individual summaries. A CV is simply the SD/mean, here expressed as a percent. You will need to be cautious here since these will be CV percentages whose values will look strange inserted into the same exact Numeric Summary format. When averaging multiple analyses, this format allows you to see all of the variability in one view. It may take some getting used to, but we have found it helpful to see with effortless immediacy which parameters within an average are most tightly determined and which are more variable, and in a % format where everything is comparable.

This averaging can be useful for creating standards. In the example that follows, we took a standard run at three different times with varying columns and column age, and at various concentrations, and fit these in a single step. Using the fit selection described at the beginning of this topic, we automatically averaged the three sets at three different concentrations to see if the variability was lessened at higher sample concentration.

5ppm
Average for 3 Fits

 

Fitted Parameters

r2 Coef Det        DF Adj r2          Fit Std Err        F-value            ppm uVar

0.99999176         0.99999174         0.00361099         50,008,399         8.23618667

 Peak        Type                    a0                a1                a2                a3                a4                a5                a6                a7    

    1        GenNLC<ge>        1.77357298        2.33640185        0.00024239        -0.0022886        1.17011522        0.00659790        0.04324097        0.61185853  

    2        GenNLC<ge>        0.49582206        3.79381822        0.00027024        -0.0003633        1.17011522        0.00659790        0.04324097        0.61185853  

    3        GenNLC<ge>        0.57367978        4.56474247        0.00026385        -0.0001801        1.17011522        0.00659790        0.04324097        0.61185853  

    4        GenNLC<ge>        0.25930420        7.26517653        0.00038954        0.00029395        1.17011522        0.00659790        0.04324097        0.61185853  

    5        GenNLC<ge>        0.43847415        11.9222856        0.00081624        0.00281495        1.17011522        0.00659790        0.04324097        0.61185853  

    6        GenNLC<ge>        0.89753559        13.5566498        0.00087205        0.00617092        1.17011522        0.00659790        0.04324097        0.61185853  

 

CV Percent for 3 Fits

 

Fitted Parameters

r2 Coef Det        DF Adj r2          Fit Std Err        F-value            ppm uVar

4.5945e-5          4.6074e-5          3.31584855         5.75911264         5.57691676

 Peak        Type                    a0                a1                a2                a3                a4                a5                a6                a7    

    1        GenNLC<ge>        0.93704162        0.44733312        1.61674263        0.80244269        14.7176342        14.9444496        1.35253140        1.76572075  

    2        GenNLC<ge>        1.10525181        0.10674379        0.75401308        4.10251401        14.7176342        14.9444496        1.35253140        1.76572075  

    3        GenNLC<ge>        1.59853985        0.14221774        0.10465515        6.83408844        14.7176342        14.9444496        1.35253140        1.76572075  

    4        GenNLC<ge>        1.18375811        0.49254277        0.39443729        7.51451576        14.7176342        14.9444496        1.35253140        1.76572075  

    5        GenNLC<ge>        1.00553087        0.61434321        0.73820553        2.05882070        14.7176342        14.9444496        1.35253140        1.76572075  

    6        GenNLC<ge>        1.24164589        0.77370110        0.65903115        1.76584386        14.7176342        14.9444496        1.35253140        1.76572075  

 

 

10ppm
Average for 3 Fits

 

Fitted Parameters

r2 Coef Det        DF Adj r2          Fit Std Err        F-value            ppm uVar

0.99999203         0.99999201         0.00675034         51,723,654         7.97274523

 Peak        Type                    a0                a1                a2                a3                a4                a5                a6                a7    

    1        GenNLC<ge>        3.53790243        2.32065496        0.00022910        -0.0044989        1.25254712        0.00867667        0.04331777        0.62286980  

    2        GenNLC<ge>        0.98894059        3.78785288        0.00027418        -0.0006667        1.25254712        0.00867667        0.04331777        0.62286980  

    3        GenNLC<ge>        1.14553797        4.56064618        0.00026515        -0.0002762        1.25254712        0.00867667        0.04331777        0.62286980  

    4        GenNLC<ge>        0.51944067        7.26246876        0.00039374        0.00083459        1.25254712        0.00867667        0.04331777        0.62286980  

    5        GenNLC<ge>        0.87895741        11.9127144        0.00081961        0.00583762        1.25254712        0.00867667        0.04331777        0.62286980  

    6        GenNLC<ge>        1.80027348        13.5676007        0.00089807        0.01258912        1.25254712        0.00867667        0.04331777        0.62286980  

 

CV Percent for 3 Fits

 

Fitted Parameters

r2 Coef Det        DF Adj r2          Fit Std Err        F-value            ppm uVar

5.7016e-5          5.7197e-5          3.14069349         7.03282761         7.15684149

 Peak        Type                    a0                a1                a2                a3                a4                a5                a6                a7    

    1        GenNLC<ge>        1.19031673        0.40975167        0.65897871        0.40864655        3.91202616        5.40931380        0.48895763        1.56800196  

    2        GenNLC<ge>        1.37221451        0.08045825        0.77476572        2.92067435        3.91202616        5.40931380        0.48895763        1.56800196  

    3        GenNLC<ge>        1.55592047        0.14689382        0.28231932        8.19606519        3.91202616        5.40931380        0.48895763        1.56800196  

    4        GenNLC<ge>        1.35544799        0.52143216        0.32934378        2.95440225        3.91202616        5.40931380        0.48895763        1.56800196  

    5        GenNLC<ge>        1.13461344        0.54187712        0.44634291        1.39547291        3.91202616        5.40931380        0.48895763        1.56800196  

    6        GenNLC<ge>        1.18984591        0.70939707        0.37598270        1.49405036        3.91202616        5.40931380        0.48895763        1.56800196  

 

 

25ppm

Average for 3 Fits

 

Fitted Parameters

r2 Coef Det        DF Adj r2          Fit Std Err        F-value            ppm uVar

0.99999225         0.99999223         0.01434474         61,756,358         7.74812769

 Peak        Type                    a0                a1                a2                a3                a4                a5                a6                a7    

    1        GenNLC<ge>        8.83233211        2.29415896        0.00025133        -0.0109638        1.15099760        0.00881069        0.04291114        0.62827947  

    2        GenNLC<ge>        2.46684920        3.77587739        0.00028988        -0.0017208        1.15099760        0.00881069        0.04291114        0.62827947  

    3        GenNLC<ge>        2.86442829        4.55441389        0.00027141        -0.0007872        1.15099760        0.00881069        0.04291114        0.62827947  

    4        GenNLC<ge>        1.29272307        7.26904435        0.00039498        0.00231398        1.15099760        0.00881069        0.04291114        0.62827947  

    5        GenNLC<ge>        2.19303204        11.8787540        0.00081253        0.01410057        1.15099760        0.00881069        0.04291114        0.62827947  

    6        GenNLC<ge>        4.48819833        13.5868866        0.00092725        0.03086562        1.15099760        0.00881069        0.04291114        0.62827947  

 

CV Percent for 3 Fits

 

Fitted Parameters

r2 Coef Det        DF Adj r2          Fit Std Err        F-value            ppm uVar

0.00040330         0.00040432         26.2107987         40.9118570         52.0513290

 Peak        Type                    a0                a1                a2                a3                a4                a5                a6                a7    

    1        GenNLC<ge>        0.94020389        0.47187826        2.62482703        0.02801510        0.63021840        4.51584163        0.41439057        1.10829081  

    2        GenNLC<ge>        0.96980623        0.10394166        0.84639105        1.46689038        0.63021840        4.51584163        0.41439057        1.10829081  

    3        GenNLC<ge>        0.88288359        0.14607492        0.12781207        5.09615289        0.63021840        4.51584163        0.41439057        1.10829081  

    4        GenNLC<ge>        1.14343169        0.49102902        0.37273890        3.52361828        0.63021840        4.51584163        0.41439057        1.10829081  

    5        GenNLC<ge>        0.79244735        0.56182612        0.54549374        1.47090685        0.63021840        4.51584163        0.41439057        1.10829081  

    6        GenNLC<ge>        0.82300983        0.72613558        0.92480419        1.54897793        0.63021840        4.51584163        0.41439057        1.10829081  

 

The advantage of our unusual layout should be more apparent in this example. The test was done at three different concentrations, 5ppm, 10ppm, and 25ppm.

The a0 areas have a slightly better CV% at the higher concentration. The a1 average center values and CV% are little impacted by concentration nor are the averaged a2 time constants. The CV% for a2 looks better at the 10ppm concentration. The a3 distortion is close to linear with concentration. The a3 CV% improve with concentration.

The a4 higher moment ZDD parameter CV% is significantly improved at higher concentration (the greater the strength of the intrinsic chromatographic asymmetry arising from a3, the better a4 is estimated). Here we see that the half-Gaussian component of the IRF, a5, is somewhat impacted by concentration, and it also improves in its CV% with higher sample concentration. The exponential component of the IRF, a6, also becomes less variable with concentration, but here we can see in one quick look that the 'g' component of the <ge> IRF is about 10x more variable than the 'e' component. We can also note that we are computing the shared exponential width in the IRF almost as accurately as the a1 center values of the peaks. The area fraction of the 'g' component of the IRF, a7, is also close to constant in its averages, but the CV improves somewhat with higher concentration. If we look at the goodness of fit averages, there is only the slightest improvement with concentration, and the variability worsens.

While there might be many ways to interpret the information, the improved CV percentages with concentration are clearly apparent. If the a4 higher order ZDD parameter, and the a5 and a6 IRF parameters, were tied to column/instrument health, the reduction in variability in these higher concentration estimates would be important.

Database/Excel Export

The File menu of the numeric summary contains a Save Extract for Database option. This will write the numeric summary to a CSV format suitable for database or Excel import.



c:\1pf\v5 help\home.gif Deconvolution Levels Deconvolved Moments