Handling Data and Figures of Merit. Data comes in different formats time Histograms Lists But…. Can contain the same information about quality. What is meant by quality?. (figures of merit) Precision, separation (selectivity), limits of detection, Linear range. My weight .
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Data comes in different formats
Can contain the same information about quality
What is meant by quality?
(figures of merit)
Precision, separation (selectivity), limits of detection,
Plot as a function of time data was acquired:
background is white (less ink);
Font size is larger than Excel default (use 14 or 16)
Do not use curved lines to connect data points
– that assumes you know more about the relationship of the data than you really do
A grade curve which lists number of students who got between 95 and 100 pts
95-100 would be a bin
Make a frequency chart (histogram) of the data
Create a “model” of my weight and determine average
Weight and how consistent my weight is
s = 1.4 lbs
s = standard deviation
= measure of the consistency, or similarity, of weights
Peak height, A
Peak location (mean or average), m
Peak width, W, at baseline
Peak width at half height, W1/2
Standard deviation, s, estimates the variation in an infinite population, s
At inflection point =
Triangulated peak: Base width is 2s < W < 4s
Pp = peak to peak – or – largest separation of measurements
Area +/- 2s = 95.4%
Area +/- 3s = 99.74 %
Peak to peak is sometimes
Easier to “see” on the data vs time plot
s~ pp/6 = (144.9-139.5)/6~0.9
Scale up the first derivative and second derivative to see better
Peak is at the inflection
Of first derivative – should
Be symmetrical for normal
Population; goes to zero at
Peak is at the inflection
Determines the std. dev.
A. F. (≠Alanah Fitch) = asymmetric factor
Is there a difference between my “baseline” weight and school weight?
Can you “detect” a difference? Can you “quantitate” a difference?
The data into different measurement populations
Model of the data as two normal populations
Of the school weight
Of baseline weight
We have two models to describe the population of measurements
Of my weight.
In one we assume that all measurements fall into a single population.
In the second we assume that the measurements
Have sampled two different populations.
Which is the better model?
How to we quantify “better”?
The measured data
Fits the model
The red bars represent the difference
Between the two population model and
The purple lines represent
The difference between
The single population
Model and the data
Has less summed
Did I gain weight?
Both positive and negative differences.
This process (summing of the squares of the differences)
Is essentially what occurs in an ANOVA
Analysis of variance
In the bad old days you had to work out all the sums of squares.
In the good new days you can ask Excel program to do it for you.
if false = hypothesis false, can not be explained
by a single population at the
5% certainty level
For an assumption of
A single population
Is larger than for
The assumption of
Resolution of two peaks
Mean or average
In this example
Peaks are baseline resolved when R > 1
In this example
Peaks are just baseline
resolved when R = 1
In this example
Peaks are not baseline resolved
when R < 1
What is the R for this data?
X limit of detection
Of the observations
Of the blank will lie below the mean of the
First detectable signal (LOD)
Limit of quantification requires absolute
Certainty that no blank is part of the measurement
Signal = xsample - xblank
Noise = N = standard deviation, s
Estimate the S/N of this data
Red and white potatoes begins?
What is the signal (length of white)?
What is the background (length of red)?
What is the S/N ?
Peak height grows with # of measurements.
+ - 1 s always has same proportion of total number of measurements
However, the actual value of s decreases as population grows
A calibration curve is based on a selected measurement as linear
In response to the concentration of the analyte.
Or… a prediction of measurement due to some change
Can we predict my weight change if I had spent a longer time on
The calibration curve contains information about the sampling
Of the population
From “format” data
Using the analysis
Get an error
That determine you’re the “noise” associated with the background
Sometimes you forget, so to fall back and punt, estimate
The standard deviation of the “blank” from the linear regression
But remember, in doing this you are acknowledging
A failure to plan ahead in your analysis
Extrapolation of the associated error
Can be obtained from the Linear
Signal LOD ≠ Conc LOD
We want Conc. LOD
The concentration LOD depends on BOTH
Stdev of blank and sensitivity
Difference in slope is one measure selectivity
In a perfect method the sensing device would have zero
Slope for the interfering species
R = resolution
LOD = both signal and concentration
Sensitivity (calibration curve slope)
Selectivity (essentially difference in slopes)
Can be expressed in terms of signal, but better
Expression is in terms of concentration
Why is the limit of detection important?
Why has the limit of detection changed so much in the
Last 20 years?
To have better numerical value for the
Ability to distinguish between two different
Bell curve <1
Which population is more variable?
How can you tell?
Increasing the sample size decreases the std dev and increases separation
Of the populations, notice that the means also change, will do so until
We have a reasonable sample of the population