Presentation on theme: "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."— Presentation transcript:
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 Plot as a function of time data was acquired:
Do not use curved lines to connect data points – that assumes you know more about the relationship of the data than you really do Comments: background is white (less ink); Font size is larger than Excel default (use 14 or 16)
Bin refers to what groups of weight to cluster. Like A grade curve which lists number of students who got between 95 and 100 pts 95-100 would be a bin
Assume my weight is a single, random, set of similar data Make a frequency chart (histogram) of the data Create a “model” of my weight and determine average Weight and how consistent my weight is
= measure of the consistency, or similarity, of weights average 143.11 s = 1.4 lbs Inflection pt s = standard deviation
Characteristics of the Model Population (Random, Normal) Peak height, A Peak location (mean or average), Peak width, W, at baseline Peak width at half height, W 1/2 Standard deviation, s, estimates the variation in an infinite population, Related concepts
Width is measured At inflection point = s W 1/2 Triangulated peak: Base width is 2s < W < 4s
+/- 1s Area +/- 2s = 95.4% Area +/- 3s = 99.74 % Pp = peak to peak – or – largest separation of measurements Peak to peak is sometimes Easier to “see” on the data vs time plot Area = 68.3%
Scale up the first derivative and second derivative to see better There are some other important characteristics of a normal (random) population 1 st derivative 2 nd derivative
Population, 0 th derivative 1 st derivative, Peak is at the inflection Determines the std. dev. 2 nd derivative Peak is at the inflection Of first derivative – should Be symmetrical for normal Population; goes to zero at Std. dev.
Asymmetry can be determined from principle component analysis 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? Comparing TWO populations of measurements
Exact same information displayed differently, but now we divide The data into different measurement populations baseline school Model of the data as two normal populations
Average Baseline weight Average school weight Standard deviation Of baseline weight Standard deviation Of the school 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”?
Compare how close The measured data Fits the model Did I gain weight? The red bars represent the difference Between the two population model and The data The purple lines represent The difference between The single population Model and the data Which model Has less summed differences?
This process (summing of the squares of the differences) Is essentially what occurs in an ANOVA Analysis of variance Normally sum the square of the difference in order to account for Both positive and negative differences. 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.
Test: is F<F critical ? If true = hypothesis true, single population if false = hypothesis false, can not be explained by a single population at the 5% certainty level
In an Analysis of Variance you test the hypothesis that the sample is Best described as a single population. 1.Create the expected frequency (Gaussian from normal error curve) 2.Measure the deviation between the histogram point and the expected frequency 3.Square to remove signs 4.SS = sum squares 5.Compare to expected SS which scales with population size 6.If larger than expected then can not explain deviations assuming a single population
The square differences For an assumption of A single population Is larger than for The assumption of Two individual populations
There are other measurements which describe the two populations Resolution of two peaks Mean or average Baseline width
xaxa xbxb In this example Peaks are baseline resolved when R > 1
xaxa xbxb In this example Peaks are just baseline resolved when R = 1
xaxa xbxb In this example Peaks are not baseline resolved when R < 1
Calibration Curve 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 Vacation?
This is just a trendline From “format” data Using the analysis Data pack Get an error Associated with The intercept
In the best of all worlds you should have a series of blanks 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 Regression data Sensitivity (slope) The concentration LOD depends on BOTH Stdev of blank and sensitivity Signal LOD !!Note!! Signal LOD ≠ Conc LOD We want Conc. LOD
Difference in slope is one measure selectivity In a perfect method the sensing device would have zero Slope for the interfering species Selectivity Pb 2+ H+H+
Summary: Figures of Merit Thus far R = resolution S/N LOD = both signal and concentration LOQ LOL Sensitivity (calibration curve slope) Selectivity (essentially difference in slopes) Can be expressed in terms of signal, but better Expression is in terms of concentration Tests: Anova Why is the limit of detection important? Why has the limit of detection changed so much in the Last 20 years?