Just after a bit of advice (sensible only please :wink:) on some stats quoted in a report I’m proof reading/editing.

For background purposes – it’s an Excel table with results of chemical analyses. They’ve given an average of 5 analyses of each specimen, and have shown the standard deviation for each ‘element column’.

I’ve noticed that some of the trace elements have Std Devs almost as high as the average i.e. 0.32% average with 0.29% SD.

My feeling is that the average values with the high SD’s should be disregarded in case they mislead – What do people think?

TIA

It’s telling you that 5 samples in this context is not enough to be statistically significant.

My feeling is that the average values with the high SD’s should be disregarded in case they mislead – What do people think?

The average (mean?) value would appear to be meaningless, but the SDs + the mean will indicate a range.

They’ve given an average of 5 analyses of each specimen, and have shown the standard deviation for each ‘element column’

What does this mean?

That a specimen is analysed 5 times on average.

Or,

That across 5 seperate specimen analysis they’ve given an average and SD for each?

Regardless… you can’t disregard some stats because you think they’re misleading… surely that would definitely be misleading?

You can’t necessarily disregard – 0.3% with SD of 0.3 mean’s it’s pretty unlikely to really be 2%. Sure, you aren’t able to really say that the value is not 0 – the value still holds some meaning.

Ah, it’s coming back to me now 🙂

See what you’re saying with the range, and the not enough to be stat significant. The latter would suit the nature of the analysis done and target audience of the report – so if it’s OK to go with that, I will.

(the reliability of the analytical technique and equipment used for the analyses means that anything detected in amounts <0.3 weight % are, IME, suspect – but wanted some stat back up as well if that makes sense).

Although 5 samples is a minute sample set to be working with, could you use Dixon’s Q Test to identify outliers?

EDIT: Ignore me. I’m talking pish.

Out of interest, what is the analytical technique?
(Thin Layer Chramatography?!)

0.3% seems quite high for a limit of quantitation.

That a specimen is analysed 5 times on average.

Or,

That across 5 seperate specimen analysis they’ve given an average and SD for each?

5 areas of the each specimen have been analysed, then the average (mean) and SD of the results of the 5 have been given. I know that, in addition to the potential ‘iffyness’ of the results that are at, or below, 0.3 weight %, the results have been normalised, so there’s potential for some drift from what was actually detected. (err…I think these results could certainly be described as qualitative 😕 )

It means that the amount of these trace elements is not statistically significant, i.e. you can’t be certain that the amount in the next sample you take will be non-zero.

Oh, for those interested, the technique used was SEM-EDX – but, just to add to the iffyness, not all specimens were analysed on the same SEM!

iffyness

Superb terminology.

You have to be a bit careful using quantitative EDX analysis, especially at low concentrations. The values you have quoted sound suspiciously like the values that most EDX analysis programs will output of you ask it to do a quantitative analysis on a spectrum.

To determine the the concentration the EDX program must de-convolute the spectrum and then determine the concentration. If you have a number of elements in you sample there can be a significant amount of peak overlap in the spectrum. When you have an element with low concentration the software can struggle to determine the concentration and it tells you this by giving a large standard deviation. If the std dev is in the order of the concentration it suggests that the element may or may not be there (i.e. has the operator identified the element correctly – do you know what should be in your sample?).

If it is critical to know the concentrations of these trace elements it would be advisable to cross check using another technique which is more sensitive to trace concentrations (such as ICP-MS or maybe XRF).

BTW, the samples being analysed on different SEMs shouldn’t matter as long as care has been taken to ensure beam currents, counting times etc are comparable.

The Southern Yeti – Member

Regardless… you can’t disregard some stats because you think they’re misleading… surely that would definitely be misleading?

isnt that what bell curves are all about??! 😆

Easy way of giving some context to mean and standard deviation: for a set of samples, ~70% of values will be within mean +/- 1 S.D., 95% will be in mean +/- 2xS.D.

Cheers for the replies everyone. R979, that’s very informative & useful ta. I agree that another technique would be useful, frustratingly, there’s no budget left for any further analysis tho (just for a change 🙄 )

I know what elements are expected in the specimens, but some of the ‘trace’ type ones were a little bit more unusual. I think I might mention that their presence was detected, but further analysis would be required to allow reliable interpretation.

The reason I was a bit cautious regarding the use of different SEM’s is that I’m not 100% confident that the count times were the same for all specimens – have seen mention of 60s and 100s count times (I wasn’t the SEM driver).

Anyway, ta again for all the replies.

It means the precision of the results is poor at the concentration you are trying to quantify.

How significant that lack of precision is, is dependant on the use to which you intend to put the data.

Presence/absence it’s probably OK. Anything with a quantitative aspect I think you might need another method.

[Edit] Your analysts need a slightly more prescriptive SOP next time!

Matt

Well, at 60-100 seconds I would not have a lot of confidence in those results. In my opinion, they are very short collection times to be using for quantification. You would barely be able to detect those elements above the background.

If your samples are insulating they may also have been thin coating of gold or carbon (other coatings are available), which would show up in the EDX spectrum.

It could be sample preparation, blah, blah, I could go on.

Total minefield.

Easy way of giving some context to mean and standard deviation: for a set of samples, ~70% of values will be within mean +/- 1 S.D., 95% will be in mean +/- 2xS.D.

I don’t think that’s right. It’s Standard Error and not Standard Deviation you use in that equation.

And the original post seems to be about Limits of Detection and Limits of Quanitification (can’t beleive I’m writing about these twice in one week!).

A standad deviation the same as the mean is indicating you’re probably somewhere around the LOQ.

But, if I’m reading the post correctly, you’ve taken ONE sample and analysed it five different ways? To be honest – I’d have no idea how to interpret that unless you had a calibrated/validated assay result to use as your population mean against which to assess the sample means.

I hate statistics.

Total minefield.

Very apt description of the whole project. One of these jobs where the original contractor subbed out various bits of work, then went bust, then some bits were picked up by two other contractors…..it goes on, but I’m sure you get the picture. Trying to do a ‘proper job’ with about 30% budget of the orignal costings – I can appreciate why one of my former colleagues dodged the bullet on this project!

Urggh…where’s the Paracetomol.

I would agree with r979.

I assume you don’t have any relevant quantitative limit of detection data for these elements in similar matrices?

If I had to report the data I would report it as “less than val%” where val is the mean result+1.645sd this will give you the one sided 95%ile confidence level. Ie for the example you gave 0.32 + 1.645*0.29 %, so report as < 0.8%

Personally I would add a note that the method was not optimized for detection of these elements at this level too.

Drswank, I don’t think you understood correctly. I read that as he analysed one sample (say a 5mm by 5mm piece of metal) by looking at 5 discrete regions, say each 100 Micron by 100 Micron the error MAY not be in the analysis but in the homogeneity of the sample.

Oh and the previous poster was right with 2sd for 95%ile c.I. not system error as you suggested (assuming of course a normal distribution of results). 1.96 is the actual value not 2, but this assume 2 sided confidence interval which is meaningless in this case.

I read that as he analysed one sample (say a 5mm by 5mm piece of metal) by looking at 5 discrete regions, say each 100 Micron by 100 Micron the error MAY not be in the analysis but in the homogeneity of the sample.

Yep, that’s about right – each specimen has a polished surface approx 10mm x 10mm and there were scans of 5 areas 600 micron x 400 micron on each specimen.
To make things a bit more ‘interesting’, from what I’ve seen of the photomicros, the specimens are not particularly homogenous. Think I might be mentioning ‘potential for further research’ on this one.

Anyways, I’d better stop surfing and get back to grinding the report out 😡