calibração método - spectraplus v 1.6-1.7 calibration part ii

SPECTRAplus

Calibration in detail

Part 2: Regression Analysis and corrections

Calibration

� Determine relationship between the measured intensities and the known concentrations from the set of calibration standards that we have previously measured

� It may be necessary to apply corrections to the measured data to make it fit a straight line

• Line overlap correction

• Matrix correction

• Quadratic correction

� Might want to use a non-mathematical approach to correct for Matrix effects by using an Internal Standard technique

� Might want to determine if the measurement of a particular background intensity is really necessary

Calibration End Plan (1)

� When we have finished working with all of the data that was measured we should:

• Save our calibration coefficients (line slope, line offset, line overlap factors, matrix correction terms, quadratic factor)

• Validate the calibration by measuring samples with known concentrations that were not part of the Standards set

• Validate the Drift Correction if implemented

• Document our calibration by making printouts of the data(calibration curve, table of results, summary with measurement conditions)

• Document the expected accuracy for this method(Std.Dev. of calibration line)

Calibration End Plan (2)

� When we have finished working with all of the data

that was measured we should (continued):

• Document the LLD (Lower Limit of Detection) for

each constituent with low concentrations

• Calculate the LOQ (Lower Limit of Quantification)

for each constituent with low concentrations (3 to

10 times the LLD)

• Document the valid calibration range for each

constituent

(lowest standard or LOQ to highest standard)

• MAKE A NEW BACKUP of the Databases and

Libraries folders

Notes on Mathematical Corrections (1)

Corrections used in the calibration can be Empirical or Theoretical

� Empirical corrections

• Calculated from the data (intensity & concentration) using multiple linear regression

• These are simply numbers (factors) that make the data fit better

• Software does not test these factors to ensure they make sense

o e.g. Line Overlap correction may increase instead of decrease an intensity

• Must be re-calculated any time a change is made

o Delete standard

o Apply another correction


� Empirical corrections (continued)

• If we re-measure the same set of standards the software

will calculate different factors

• Requires a well characterized set of standards

o Must have random element concentrations

o Must have larger number of standards then when using

theoretical corrections (2*n + 1, where n = number of

calculated degrees of freedom)

• All Empirical factors SHOULD be carefully evaluated to

ensure they make sense

o Magnitude should be inline with expectations

o Direction (sign) should be appropriate for type of effect

the factor is correcting for


� Theoretical corrections

• Based on Science – Physical properties of the elements, X-ray tube output, absorption edges, fluorescent yield, etc. = Fundamental Parameters

• Assumes all samples are infinitely thick and homogeneous

• Require less standards than Empirical corrections

• Are correction factors that can be trusted (accepted at face value)

• Require that all standards be fully defined

o Σ of concentrations ≥ 95%

o Any constituent defined as Trace has a concentration close to zero


� Types of Mathematical Corrections

• Line Overlap correction

o Either purely Empirical or has an Empirical part

• Quadratic correction

o Always Empirical

• Matrix correction

o Can be Empirical or Theoretical

Notes on Calibration (1)

� Recommended number of standards to define a calibration:

• S = 2n + 1

• where:

o S = minimum number of standards

o n = the number of calculated (Empirical) corrections

» Calibration Line Slope

» Calibration Line Offset

» Line Overlap correction

» Matrix correction

» Quadratic correction

• Standards with very similar concentrations only count as one

Notes on Calibration (2)

� Number of standards to define a calibration (continued):

• S = 2n + 1

� To define a straight line without any corrections:

• n = 2 (slope & offset)

• S = 5 standards

� To apply one line overlap correction and two matrix

corrections:

• n = 5 (slope, offset, 1 calculated line overlap correction,

2 calculated matrix (absorption) corrections)

• S = 11 standards

� Note that S increases 3 times as much as n

Calibration -Calibration Method

� Select Calibration Methodfrom the explorer window

� Make sure Material and Preparation are correct

� Calibration should normally be referenced to the Standards

• Start new reference point for drift (intensities to correct back to)

• Library is used for special circumstances

� After modifications have been done in an analytical method click Reinitialize; the previous calibration is canceled

Calibration -Standard Samples (1)

� Select Standard Samplesfrom the explorer window

� The list of Standards will be shown in upper window

• File column should show Exist

• If File column shows Missing then raw intensity file (*.ssd) was not found

• Move samples up and down by clicking the arrows

• Delete samples by clicking red cross

• Uncheck any standard that should not be used


� In special cases it may be

necessary to highlight

Standards in the lower

window and use the Import

button to move them to the

top window

• Example:

o A Calibration was

previously completed

and saved

o In FQUANT this

calibration is opened

o New Standards are

added and measured


� Under normal circumstances

• Select Calibration from the text menu at the top of the window

o Check Material Specific Lines Only

o Check Enable Line Position Checking

o Uncheck Disable Automatic Regression

Calibration -Compute Coefficients (1)

� Select Compute Coefficientsfrom the Explorer window

• The raw intensity data files (*.ssd) and concentrations will be read into memory

Calibration –Compute Coefficients (2)

� A warning is displayed if the sum of the concentrations for all standards is not between 95% and 105% (the sum can be adapted)

• Theoretical matrix corrections (variable alpha’s) will be disabled

Calibration -Compute Coefficients (3)

� The actual display may

differ from that shown, but

will typically show:

• A Tabular display

• A Graphics window

• A Calibration Toolbox

• A Summary window

Calibration Toolbox -Displaying

� If the Calibration Toolbox is

not shown:

• Click the “Toggle

Calibration Toolbox” icon

• Or use the <F2> key to

toggle it on and off

� Use this control to expand

and collapse the “Additional

Tools” part of the

Calibration Toolbox.

Calibration Toolbox –Element Control

� Element / Compound control shows element or compound being calibrated

� Brings up periodic table to switch between elements

� Moves to next higher Element / Compound that can be calibrated

� Moves to next lower Element / Compound that can be calibrated

Calibration Toolbox –Line Control

� Moves to next higher Line that can be calibrated

� Moves to next lower Line that can be calibrated

� Brings up list of lines that can be calibrated

� Line Control shows

current line being

calibrated

� Designates “Primary”,

“Secondary” and

“Tertiary” line

� NOTE: The “Primary” line will be used to report the concentration

Calibration Toolbox –Element/ Compound

� Switch display of concentrations

between:

• Elements on a “prepared

specimen” basis

• Compounds on an “original

sample” basis

� Does not effect the way the

calibration is stored, or the way

concentrations will be calculated

Calibration Toolbox –Concentration Units

� Switches the units used to display the concentrations:

• Weight-%

• PPM

� Does not effect the way the calibration is stored, or the way concentrations will be calculated

Calibration Toolbox –Compute and Refresh

� Compute and Refresh button

• Recalculates calibration data

• Updates display of calibration data

� This is normally not necessary unless Disable Automatic Regression was selected before doing Compute Coefficients

Calibration Toolbox –Standard Deviation

� Displays the Standard Deviation (1-σ) of the calibration line in concentration units

1

)(..

2

−

−=∑

n

CCDevStd allstds

chemcalc

� Estimator of accuracy of calibration

� Includes all errors associated with measurement process

• Errors in the standards concentrations

• Errors in the measurements

• Errors in sample preparation

Calibration Toolbox –Regression Weighting

� You can weight the regression in 3 different ways

[ ] Minimumallstd

XRFChem CC ⇒−∑2

Minimumallstd Chem

XRFChem

CCC ⇒

−∑

2

( )Minimum

allstdChem

XRFChem

CCC ⇒

−∑

2

Abs olute:

Relative:

Stat istical:

� Abs = Weight on High Conc.

� Rel = Used for wide ranges of concentrations

� Stat = No weighting

Calibration Toolbox –Offset (1)

� Change how the Offset of the calibration line is determined

• Fixed on (0,0) per default

• Active

o Comp (Offset is calculated from the regression)

o Fixed (Offset is a known value)

� It is normally best to use an Active - Comp Offset when possible

• i.e. when the matrix is roughly constant

• When no background is measured


� The calibration line will pass through the origin if:

• All instrument effects have been perfectly removed:

o Background Intensity

o Line Overlap contributions

o System contributions

• All matrix effects have been corrected for

• There are calibration standards with low concentrations


� Corrected Intensity Offset

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� Offset on Intensity axis

Calibration Toolbox –Intensity

� Select intensity to use for a

calibration

• Net = Peak - Bkgd Intensity

• Gross = Peak Intensity

� Do not use the Gross intensity,

unless the background is the same

for every standard and unknown

sample. In this case, time can be

saved not measuring a background

The offset has to be activated

Calibration Toolbox –Icons (1)

� Use these Icons to open

various windows which give

• Different Views of the data

• Allow different Corrections

to be applied to the data

Calibration Toolbox –Icons (2)

� Calibration Chart

� Standards Table

� Comparison Table

� Line Overlap Corrections

� Internal Standard

� Matrix corrections

� Calibration Summary

Calibration – Summary (1)

� Summary of Calibration

• Line with conditions

• # of Standards used

• Intensity model

• Std Dev of calibration line

• Calibration line slope

• Calibration line offset

� Note pad

• Can be used to write reminder notes

• Saved in FQN document

Calibration – Summary (2)

� Icons can be used to transfer the data

� Clipboard Copy

� Rich Text Format file

� Text file

Calibration – Plot (1)

� Plots Chemical Concentration on the x-axis in ppm or %

� There are two y-axis

• Right y-axis plots one of:

o Corrected Intensity

o Chemical Concentration

• Left y-axis plots any of:

o Net Intensity

o Gross Intensity

o Background Intensity

� Note: It is typical to plot the Corrected Intensity versus the Chemical Concentration


� Zoom operations are

performed by defining an

area while the left mouse

button is held down

� The “Fit to current points”

button scales the plot so

all data points are visible

� Use these icons to zoom

by steps

• Hold the mouse pointer

over one of the icons to

see a “tool tip”

describing its function


� Use these icons to control the display of certain data points

• Enabled Standards

• Missing Standards

• Disabled Standards


� Placing the mouse pointer over one of the data points, then holding it still brings up a small window that gives information about the Standard

• Name

• Corrected Intensity

• Chemical Concentration

• XRF Concentration

• Other Major Elements


� Single-Clicking a data point selects it

� The data point will blink in the Graphical display

� The data point will be highlighted in the Tabular display


� Double-Clicking one of the data points causes it to be removed from the regression

• The data point will be displayed in red when not used

• Double-Click on a red data point to re-use it in the regression

• This icon controls whether or not the Red data point will be visible

Calibration – Standards Table (1)

� Displays calibration data in tabular format

� Use “eye-glass” icon to choose and arrange the columns that are displayed

� Click on one of the column headers to change sort order of list


� List of columns displayed is on right side of window

� List of columns not displayed is on left side of window

� Move items between lists using the Add and Removebuttons

� Change the display order using the Move Up and Move Down buttons

� Using the “eye-glass” icon


� Meaning of the columns displayed (1-4)

Number Number of the standard in the listStandard Name Name of the standardGross Intensity (1) Intensity at the peak angle in kCPSBackground (1) Weighted intensity at the background angle(s) in kCPSNet Intensity (1) When Net Intensity is selected

Peak - Background Intensity in kCPS

When Gross Intensity is selected Gross Intensity in kCPS

(1) Corrected for absorption by film and drift if applicable



Ref. Intensity Net Intensity in kCPS without any corrections applied Absorption correction for film Drift correction

Corrected Intensity Corrected Net Intensity in kCPS matrix effects line overlap effects quadratic term

Ratio Ratio of analytes intensity to Internal Standards IntensityPeak Counts Total accumulated counts at the peak angle

= IGross * TPeak

Bkg Counts Total accumulated counts for the background = IBkgd * TpeakNOTE: Background counting is not saved in the SSD file



Chemical Concentration Certified concentration (Chem)XRF Concentration XRF concentration calculated from the calibration line (XRF)Absolute Deviation Absolute difference between XRF and Certified concentrations

= XRF - ChemRelative Deviation Relative % difference between XRF and Certified concentrations

= 100% * (XRF - Chem) / Chem

Count. Stat. Abs. Error from counting statistics expressed in concentration unitsThis can be compared to Abs Dev column to determine if thecounting time was long enough

Count. Stat. Rel. Error from counting statistics expressed as a relative %This can be compared to Rel Dev column to determine if thecounting time was long enough

LLD (PPM) Lower-Limit-of-Detection calculated by converting 3-standarddeviations of the background intensity into a concentration



Sum (%) Sum of the concentrations in the prepared specimenOriginal Sum (%) Sum of the concentrations in the original sampleChem. Dev. Abs. Not used at this timeChem. Dev. Rel. Not used at this time


� Disable / Enable a standard by double-clicking on it

� Disable all standards with Trace concentrations, and concentrations flagged as Uncertain

� Disable all standards with an invalid sum

� Relax limits for invalid sum

Calibration – Line Overlap (1)

� Ii = Analyte intensity

� IOL = Overlapping-line

� Ik = Intensity contribution to theanalytes intensity from theOverlapping-Line

� Need to remove the contribution from the Overlapping-Line from the Analyte Lines Intensity

� Line-Overlap Correction

• Intensity based (fully empirical)

• Concentration based (fully empirical)

• Theoretical (partly empirical)

2-theta

I

Ii

IOL

Ik

Calibration – Line Overlap (2)

� General form of Line-Overlap Correction

Icorr = Imeas + L

Where:

Icorr = Analyte intensity corrected for line-overlap effects

Imeas = Measured analyte intensity

L = Correction for all line-overlap effects

� Since ALL line-overlap corrections have an empirical part these must be validated before being accepted

• Direction: L must be a negative number

• Magnitude: L must be in line with what was observed from a scan, or expected from the circumstances

Line OverlapIntensity Correction

� Icorr = Imeas + Σ Lij Ij

• Icorr = Analyte intensity corrected for line-overlap effect (Ii – Ik)

• Imeas = Measured analyte intensity before correction

• Lij = Line-overlap factor for effect of element jon the analyte (i)

• Ij = Intensity of undisturbed line for interfering element (j)

2-theta

I

Ii

IOL

Ik

Ij

� Lij can be determined:

• Empirically (regression)

• Experimentally (measurement)

� Doesn’t work when absorption edge for some element lies on Ii or Ij

Line Overlap Concentration Correction

� Icorr = Imeas + Σ Lij Cj


• Imeas = Measured analyteintensity before correction

• Lij = Line-overlap factor for effect of element j on the analyte (i)

• Cj = Concentration of interfering element (j)

� Lij can be determined:

• Empirically (regression)

• Experimentally (measurement)

� Works better when absorption edge for some element lies on Ij

• Cj can be corrected for absorption

2-theta

I

Ii

IOL

Ik

Ij

Line Overlap Theoretical Correction

� Icorr = Imeas + Σ Lij IOL(theoretical)


• Imeas = Measured analyte intensity before correction

• Lij = Scaling factor for element j on the analyte (i)

o Scale Theoretical I to Meas I

o Scale IOL to Ik

• IOL(theoretical) = Theoretical intensity of interfering element (j) line (IOL )

2-theta

I

Ii

IOL

Ik

� Lij is determined Empirically (regression)

� Works for very wide composition changes with complicated absorption effects

Line Overlap Selecting Overlapping Line

� Select an overlapping line to correct for

� Filter for displaying possible overlaps

Line Overlap Applying Overlap Correction

� Select type of correction

• Meas = Intensity

o Must also choose line to base the correction on

• Calc = Theoretical

• Conc = Concentration

� Select Fixed or Calculated coefficient

• If Fixed, enter coefficient

• If Calculated coefficient will be displayed

Line Overlap Validating Overlap Correction

� Standard deviation of calibration line should have significantly improved

� Direction of the correction must be negative

• Sign of correction factor is negative

� Can sometimes estimate magnitude of overlap from a scan (e.g. ~ 0.268 kCPS)

� Can calculate magnitude of overlap correction from data

+

Validating Intensity based Line Overlap Corrections

� Intensity correction (Meas)

• SD before = 59 ppm

• SD after = 29 ppm

• IMoKA1 = 67.542

• LSMo = -2.605e-03

� SD got significantly better

� Direction of correction is appropriate (negative)

� OL = -2.605e-03 * 67.542= -0.176 kCPS

This is in-line with observation (0.268 kCPS)

+

Validating Concentration based Line Overlap Corrections

� Concentration correction (Conc)



• CMo = 1.0%

• LSMo = -17.68



� OL = -17.68 * 0.01= -0.177 kCPS


+

Validating Theoretical Line Overlap Corrections

� Theoretical correction (Calc)



• LSMo = -13.42

• Inet-S = 0.8312 kCPS

• Icorr-S = 0.6553



� OL = 0.8312 – 0.6553= 0.176 kCPS


� NOTE: This only works if no other corrections are applied

+

Calibration – AlphasGeneral Description

� The term Matrix adjusts Intensities as if

absorption / enhancement had not occurred

� Keep in mind that not only the Intensities

(Ij) are multiplied by the Matrix term, but

also the error (±σ) associated with these

Intensities

� Should only apply corrections when they

improve the calibration fit (Std Dev)

� Otherwise only increasing the errors

without obtaining any benefit (better fit)

Ci = ai + bi Ii (Matrix)

Calibration – AlphasWarning on Empirical Models

� In reality the term Matrix is actually:

Matrix = (1 + Matrix)

� Must take care that Matrix term does not

become too large

• Otherwise:

o Concentration of analyte (Ci) is

being calculated mostly from Matrixterm (other elements intensities

and/or concentrations)

o So concentration of analyte (Ci) has

little to do with intensity (Ii)measured from analyte


Calibration – AlphasEmpirical Intensity Correction

� Lucas-Toothe-Price Model

� Correction based on Ij

� Ij can suffer absorption & enhancements effects

� Does not fit as wide a concentration range as the other models

� Don’t need to know 100% sample composition

� Need sufficient number of standards

� Standards must have random concentrations

Intensity

(1 + Σ kij Ij )

Empirical


Calibration – Alphas Empirical Concentration Correction

Concentration

(1 + Σ αij Cj )

Empirical


� Lachance-Traill Model

� Correction based on Cj

� Cj can be corrected for absorption & enhancement effects

� Fits wider concentration range than Intensity model

� Don’t need to know 100% sample composition

� Need sufficient number of standards

� Standards must have random concentrations

Calibration – Alphas Theoretical Concentration Correction

Concentration

Theoretical


� Lachance-Traill Model

� Correction based on Cj

� Cj can be corrected for absorption & enhancement effects

� Fits wider concentration range than Intensity model

� Need to know 100% sample composition

� No extra standards needed

� No restriction on Standards concentrations

α+∑

≠ijij jC1

Calibration – Alphas Fixed Alphas Calibration Model

Concentration

Theoretical

Fixed α’s


� α’s calculated from average composition

Σ [ (Ci (max) + Ci (min) ) / 2 ] normalized to 100%

� α’s are then fixed

• Fixed α’s applied to each standard in the calibration

• Fixed α’s applied to each unknown sample measured with this calibration

� Can handle fairly wide concentration ranges

• One or two elements changing by 30 wt-%

α+∑

≠ ijij jC1

Calibration – Alphas Variable Alphas Calibration Model

Concentration

Theoretical

Variable α’s


� α’s calculated individually for each standard using its composition

� Applies a more exact matrix correction during the calibration phase

� α’s are calculated iteratively when an unknown sample is measured

• In the end the α’s applied to the unknowns data are based on its reported composition

� Can handle very wide concentration ranges

• Many elements changing by 100 wt-%

α+∑

≠ ijij jC1

Calibration – AlphasMixing Calibration Models

IntensityConcentration

(1 + Σ kij Ij )(1 + Σ αij Cj )

EmpiricalEmpiricalTheoretical

Fixed α’sVariable α’s


These models can be used

togetherStands Alone

Calibration – Alphas Window (1)

Calibration Line Slope Corrected Intensity OffsetSame function as in Toolbox

Quadratic TermCan be used when one element is predominate absorber and other elements have trace levels

Calibration – Alphas Window (2)

Element concentration range in

prepared specimens

Relative influence of each Element

on the current line

Theoretical Fixed α’s

(Only if Sum near 100%)

Range of Variable Fixed α’s

(Only if Sum near 100%)

Calibration – Alphas No Corrections (straight-line)

� Click the No Correct button

• Switches to Fixed alphas (concentrations)

• All α’s are set to Fixed 0

Calibration – AlphasFixed Theoretical Alphas

� All α’s are set to Theoretical

(1) Make sure Fixed alphas (concentrations) button is pressed

(2) Click Select All Elements icon

(3) Click Copy icon (>>)

If a significant decrease in Std.Dev. is not observed, then one should go back to No Corrections

Calibration – Alphas Variable Alphas

� All α’s are set to Variable

� Click the Variable alphas button� Variable alphas should

only be chosen if:

• Fixed alphas improved the Std Dev, but not enough

• The displayed variable alphas show a change in their values

• All concentrations can be determined with a fair degree of accuracy

� If Variable alphas does not significantly improve the Std Dev, Fixed alphas should be used

Calibration – AlphasFixed Empirical Concentration

(3) Click the Computed button

� Selected α’s will be computed

(1) Click the Fixed alphas (concentrations) button

(2) Highlight the elements to calculate

� Need sufficient standards with random concentrations

� Only calculate α’s that make sense - don’t use “shot-gun” approach

� Validity of individual α’sshould be verified

• Enhancement should have negative α

• Absorption should have positive α

• Values depend on matrix

Calibration – Alphas Remove Fixed Concentration Correction

� Selected α’s will be Fixed 0.000

2) Highlight the elements to remove

(3) Click Fixed buttonEnter 0

(4) Press <Enter> key

(1) Click the Fixed alphas (concentration) button

Calibration – AlphasFixed Empirical Intensity

(3) Click the Computed button

(1) Click the Fixed alphas (int) button

(2) Highlight the elements to calculate

� Need sufficient standards with random concentrations

� Only calculate α’s that make sense - don’t use “shot-gun” approach

� Validity of individual α’sshould be verified

• Enhancement should have negative α

• Absorption should have positive α

• Values depend on matrix

� Selected α’s will be computed

Calibration – Alphas Remove Fixed Intensity Correction

� Selected α’s will be Fixed 0.000

2) Highlight the elements to remove

(3) Click Fixed buttonEnter 0

(4) Press <Enter>

(1) Click the Fixed alphas (int) button

Calibration – Alphas Mixing Calibration Models

� Can inter-mix

• Theoretical Fixed

Concentration α’s

• Computed Fixed

Concentration α’s

• Computed Fixed

Intensity α’s

� Variable α’s must

stand alone

Calibration – Internal Standard (1)

� An Internal Standard can be added to each sample to address matrix effects in a non-mathematical way

• Viable for liquids, fusions (where addition is possible)

• Internal Standard (IS) is close in energy to Analyte AND not present in the sample

o Matrix effects on IS are the same as on Analyte

o By taking the ratio of the Analyte Intensity to the IS Intensity these effects will wash out

� The Compton line of the X-ray tube can sometimes be used as an internal standard

• When energy of Analyte is close to energy of Compton

o Ex: Rb to Mo with Rh tube in Geological samples

Calibration – Internal Standard (2)

� Select Internal Standard line

• Theoretical matrix corrections will be disabled

• Calibration Plot can only be done as CChem

vs CXRF

Calibration – Comparison

� Keeps history of what has been done in the calibration

� To re-load previous set:

• Click

• Select to restore as Line 1, Line 2, or Line 3

Documenting the Calibration (1)

� Use the Print icon to print current element or compound

� Use the Print Preview icon to preview the output before printing it


� Printout is pre-formatted

� First page has:

• Summary of Calibration(with any notes entered)

• Calibration Plot


� Second page and subsequent pages has Calibration Table

Saving the Calibration (Normal)

� Click File – Save or File – Save As to save the calibration

� In most cases the name should be same as Material name

• Creates FQN and FCL files

o FCL is calibration coefficients(needed to calculate unknown samples)

o FQN is “style sheet” needed to view calibration in FQuant

� Save directory should be:

C:\SPECplus\Libraries\Calibrations

Saving the Calibration

� To save the calibration of current to Line Library for use in a Standardless Program:

• Do Calibration – Save Current Line To Library

� Restrictions:

• Cannot do Ratio method

• Must use Net Intensity model

• Must use Variable Alphas if E > 2.06 keV

• Library Line must be unprotected

Testing the Calibration

� Measure some known samples against the calibrations

• Should not be part of Calibration Standard set

� If drift correction was set up

• Do a drift correction

• Re-measure some of the known samples to test drift correction

calibração método - spectraplus v 1.6-1.7 calibration part ii

Documents

empiricalci

gun approach

counting statistics

positive values

correction

red data point

line overlap

compute coefficients