Data analysis for Geochemists9/25/12 Lecture outline: 1)designing an analytical strategy 2)error analysis in isotope geochemistry 3)clean rooms & chemical.

Data analysis for Geochemists 9/25/12

Lecture outline:1) designing an analytical strategy

2) error analysis in isotopegeochemistry

3) clean rooms &chemical separation

Contents of the sample canister from NASA’s Genesis mission,in a “cleanroom”.

Designing an analytical strategy for isotopic analysis

1. How much material do you have available for analysis?- often set by external factors (no sample is unlimited)

2. What is the expected concentration of the isotopes of interest?

3. What is the error on the isotope ratio expected from counting statistics?

4. What are the other sources of error?- blanks (know the sources of contamination and their isotopic signatures)

5. Is the expected/desired isotopic signal larger than the sum of all expected errors?yes? proceedno? back to square one – can you use more sample? limit blanks? etc

6. What instrument will deliver you the required precision?

7. What particular sources of error are associated with this analysis technique?- poor yield from sample injection to detection (lowers N)- mass fractionation, abundance sensitivity, etc

8. Is the expected/desired isotopic signal larger than the sum of all expected errors?

A review of terms

accuracy: how close the measurement is to a true value

precision: how well we can measure something analytically

Good science: quote values that are accurate within the precision

Systematic error: cannot be assessed by repeated measurements (ex?)

Random error: can be assessed by repeated measurements (ex?)

Internal error: measure ratio repeatedly, assess scatter (aka precision)

External error: compare measurements of standards with internal errors to truth (aka accuracy)

Reducing systematic errors: 1) minimize systematic errors, add them to random errors2) make sure systematic errors are small compared to random errors (<10%)3) measure unknowns relative to a standard so systematic errors cancel out* Different applications require different approaches (2 & 3 most popular in mass spec work)

Systematic error

Examples: detector gain (only counts a fraction of signal, usually close to 1)uncorrected blank or “memory”wrong mass discrimination law assumedspike calibration not accurate

How do you hunt forsystematic errors?

Random error

Counting Statistics: problem of counting subset of a large set (sometimes the subset will reflect the

large set, sometimes over-estimate, sometimes under-estimate) theoretical limit: 68% chance of being within of measured values

so need 10,000 realizations to get 1% error (at 68% confidence, or 1)

1/ n

Internal error: derives from imperfect measurement (collector noise, electronic noise, etc)

measure ratio repeatedly and use scatter to assess uncertainty

External error: the ability to reproduce standards over many runs (why might this change long-term?)measure standard repeatedly, over a very long timecite as 2 s.d. and mention how many standards based on

Ex.: “External reproducibility was assessed with repeated measurements of the NBS-19 carbonate standard, and is reported as ±0.05‰ (2 s.d., N=550).”

238U/235U ratios over typical multi-collector ICPMS run

1.40E+02

1.40E+02

1.40E+02

1.40E+02

1.40E+02

1.40E+02

0 50 100 150 200

Scan number

238U

/235

U

Example – U isotope ratios in single run

What is the 238U/235Uratio in nature?

What sources of error are implicit

in this plot?

Statistic1) mean = 140.0833

2) standard deviation (1) = 0.038 * variance = ()2

3) standard error (1) = 0.0027

4) relative standard error (1) = 1.93 x 10-5

ix

N

21( )

1 ix xN

. .s eN

. .. . .

s er s e

238U/235U ratio

Fre

quen

cy

ME

AN

-1

+1

-2

+2

0.9999994

0.9999366

0.9973002

0.9544997

0.6826895    

CIrange

The Gaussian, or “normal” distribution

21 1

exp22

G

xP

Probability density equation:

238U/235U ratio

Fre

quen

cy

ME

AN

-1

+1

-2

+2

Would the distributionfor many standard runs

be greater or smaller thanfor individual runs?

Fun with Gaussian statistics

How could you test whethera process is Gaussian?

Would the shape of thisdistribution change withmore measurements?

What’s limiting the precisionof this measurement?

How many measurements should fall outside the 2

boundaries?

A note on error propagation

Addition and subtraction: square root of sum of squared absolute errors

Example: subtracting a blankblank = 230 ± 20 pg 230Thmeasurement = 3532 ± 50 pg 230Th

blank-corrected 230Th = 3302 ± 70 pg 230Th

multiplication and division: square root of sum of squared relative errors

Example: correcting value for mass discrimination by normalizing to standard valuemass discrimination = std ratio(meas) / std ratio(true) = 1.003322 ± 0.01%unknown ratio = 1932 ± 10 or 1932 ± 0.52%m.d.-corrected ratio = 1926 ± 0.53%

Usually you are dealing with multiple sources of errorerrors from….mass spectrometry 2 s.d. externalweighing 2 s.d. of repeat measurements on balancespike calibration 2 s.d. of repeat spike calibration attemptsblank correction 2 s.d. of blank variability

IF errors are unrelated (orthogonal) – no error correlation (examples?)then combine errors quadratically

A reminder about significant figures

Number of significant figures: 1. leftmost nonzero digit is the most significant digit2. if there is no decimal point, rightmost nonzero digit is the least significant digit3. if there is a decimal point, the rightmost digit is the least significant digit (0 included)4. all digits between the least and most significant digits are counted as significant digitsExample:How many significant figures in the following numbers?

1234123,400123.4100110.100.0001010100.0

NOTE: When performing calculations with data, the number of significant figures in the answermust be equal to the smallest number of significant figures in the input data

Rules for reporting data:Do not report data as more precise than the error (internal or external).Example: mass spec printout reads -5.322‰, external error = ±0.05‰, report as -5.32‰

Linear regression, R-value, and slope uncertainty

Fitting your data to a linear model y=ax+b

Questions to ask yourself:1)which is my dependent (x) and independent (y) variable?

- if error in both variables, then use total least squares (minimize residuals in both x and y) versus ordinary least squares (y only)

3) What is the uncertainty in my slope?-can use LINEST in Excel -if the slope is used in a calculation, the uncertainty in slope must be propagated through

2) How do I interpret my R value?-R2 represents the amount of variance that are you explaining with the relationship, in %Ex: if R=0.6, then you are explaining 36% of the variance in your variables

http://www.gifted.uconn.edu/siegle/research/correlation/corrchrt.htm

Assessing the significance of an R-value

Is the relationship between x and y significant?Note: you can have a very high R-value that is meaningless!

Can use several approaches, most common isthe Student’s T-test, where you are testingwhether your R value is significantly differentfrom ‘0’, given your degrees of freedom.

Table at right uses a Pearson’s Product-MomentCorrelation Coefficient.

Ex: For 7 sample pairs of x and y,I have 5 degrees of freedom.

I need an R-value of ≥0.754 for a 95% significance.≥0.874 for a 99% significance.

Every geochemical measurement must be corrected for a blank.In general, the blank correction should be at least an order of magnitude less than

the analytical error of the measurement.

Your relative blank contribution depends on:- the concentration of the element of interest and the amount of sample available- the amount of contaminants that will be incorporated into the sample

(depends on analytical technique)

Three scenarios

Determining your need for clean

14C/12C in carbonates-introduction of modern CO2 gas during conversion of sample CaCO3

to CO2 is fatal-blanks are extremely important-conversion performed in evacuated vacuum line-blanks carefully monitored

18O/16O in carbonates-oxygen is 48% of CaCO3 by

weight-but we can measure R of small samples precisely (~0.005%)-atmospheric CO2, water vapor must be limited during analysis

U-Th isotopes in carbonates-U is 3ppm in carbonates Th is ultra-trace-not easy to contaminate U, but very easy to contaminate Th

(Nspl*Rspl + Ncont*Rcont)/Ntotal = Rfinal

How clean is clean?

A cleanroom is a fully-enclosed laboratory that is:1. maintained at positive pressure2. fed by filtered air3. inhabited by scientists in white labcoats, booties, gloves, and hats4. constructed entirely of white plastic (usually)

Cleanroom specifications range fromclass 10,000 to class 1.

Cleanliness costs time and money (~$500,000 to $2M).

NOTE: they only preventparticulate contaminants.

14C/12C in carbonates-introduction of modern CO2 gas during conversion of sample CaCO3

to CO2 is fatal-blanks are extremely important-conversion performed in evacuated vacuum line-blanks carefully monitored

18O/16O in carbonates-oxygen is 48% of CaCO3 by

weight-but we can measure R of small samples precisely (~0.005%)-atmospheric CO2, water vapor must be limited during analysis

U-Th isotopes in carbonates-U is 3ppm in carbonates Th is ultra-trace-not easy to contaminate U, but very easy to contaminate Th

Which analyses need to be conducted in a clean room?

Maybe.You cannot prevent CO2

from entering a cleanroom.butParticulates may containmodern CO2 (esp. if biologists using tracer 14C are nearby), so limiting sample exposureto particulates can be important.

No.You cannot prevent H2O(g)from entering a cleanroom.

Definitely.Your Th blank would renderyour analysis useless.

Chemical separation

If the isotope of interest is present in low concentrations (ppm and lower), a chemicalseparation is often required prior to analysis. benefits: -reduces mass interferences

-improves conversion of atoms to ions (ionization efficiency)

Usually achieved by column chromatography

Principle: -it’s a competition between sample ions and acid ionsfor the binding sites on the resin -ions have different binding strengths to resin beads,can be pulled off with specific acids

M+ + H-R M-R + H+

example of cation exchange reaction:

-this reaction is associated with a K-value that is specific to the acid and ion in question

Column Chromatography

Procedure:1) sample pre-concentrated, converted to solution form2) anion or cation exchange resin slurry loaded into column3) sample loaded4) progress through sequence of eluants (acids of different

strengths)5) collect fractions of interest