[bankai]

hello long time lurker, first time poster! 

I want to know if my values are ''statistically different''. i did detection limits on 5 different days on an ICP and my results for Fe are (in ppb)
day 1: 5.2 ppb
day 2: 7.6 ppb
day 3: 3.1 ppb
day 4: 2.7 ppb
day 5: 6.4 ppb

I tried to look on wiki and did google search but couldn't find a proper formula. I'm not interested in ''statistically significance'' though (i don't think it applies here).

thanks for your *delete me*

[cliverlong]

I am not familiar with your experiment:

detection limits on 5 different days on an ICP and my results for Fe are (in ppb)

But I feel without more information on how you performed this experiment and how you took the measurements, it is virtually impossible to make any judgement about the validity of your measurements.

Yes, one can calculate some simple statistics such as mean and variance from your data but what use are those without context and some way to judge whether these are expected values from the experiment you performed?

Also you ask if the values are ''statistically different'' but say you are not interested in ''statistically significance''. I have not come across the first expression and am curious why you think the second is irrelevant. Have you studied statistical significance or confidence intervals/ limits?

Clive

[Borek]

My stat is so rusty pieces are falling off, but for me statistically different would mean "differences between values are statistically siginificant".

[JGK]

It depends on what you mean by "statistically different", I can't find any references to this terminology in my stats texts other than calulating statistical difference between the means of of two methods, not refering to data from a single method like you have.

You can test for outliers in your data using Dixons Q test (you don't have any by the way).

Student's T test will give you a 95% confidence interval of the mean. (I calculated this as 5 ± 2.61, i.e. based on this, 95 % of the data should fall within the range 7.61 - 2.39, it's 100% for your data) .

[bankai]

thanks! yeah that's what i was looking for!
i'm surprised that statistically different didn't mean anything, it was a question from the chemistry teacher ! well maybe she's not well versed in statistics after all.
i was under the impression that statistically significant was more applied to sociology or psychology or political survey where you wanna know if your sample of population is representative of a bigger population, so that's why i thought it wasn't relevant here. oh well.

[JGK]

There are a large number of volumes on statistics for chemistry out there, The one I prefer is:

Statistics and Chemometrics for Analytical Chemistry,  James N. Miller & Jane C. Miller

Prof. Miller (JN) was the Statistics course lecturer on my MSc course, the book is well explained and contains worked examples of many of the tests described.

[jrd89]

I would be very careful with what conclusions you try to draw from your data, considering you only have 5 pieces of data.  Another thing to note is that you're acting under the assumption of normality for this and, having had some experience with measurement system analysis, I can tell you that I've run into quite a few interesting distributions which even after 100+ readings failed a normality test (both using KS and AD tests). 

I went ahead and did a confidence interval for your data, as pointless as it is, to double check JGK and I found the same thing he did.

t-value for 95% confidence using a conservative (n-1) degrees of freedom is 2.7765 rounded to 2.78
where avg. is the average value you found and std. dev. is the standard deviation of the sample (using bessel's formula due to small sample size)

avg +- std.dev*t-value/sqrt(n)
average = 25/5 = 5
standard deviation = sqrt((5.2-5)^2 + (7.6-5)^2 + (3.1-5)^2 + (2.7-5)^2 + (6.4-5)^2)/sqrt(n-1) = sqrt(.04 + 6.76 + 3.61 + 5.29 + 1.96)/sqrt(n) = sqrt(17.66)/sqrt(4) = 2.10
sqrt(5) = 2.24
{5-2.61, 5+2.61} = {2.39, 7.61}



To JGK --
I haven't seen a Dixon Q test before so I looked it up.  It seems to be a very weak tool in determining outliers, and here's why I think so:
Say you have 10 data points

1, 2, 94, 95, 96, 97, 98, 99, 100, 101

Using this test, you would not tag 1 or 2 as an outlier, as the magnitude of the distance between the two of them is 1 and the range is 100.  Granted not all situations will be like this, but I feel it's worth mentioning nonetheless.

As far as your interpretation on the confidence interval for the mean, I believe you might be mistaken as to what it actually means.  You wrote that 95% of the data should fall within the range, and this is not quite correct.  It means that we are 95% confident that the true mean value of whatever it is this guy is measuring lies between 2.39 and 7.61.  If you wanted to determine the range that 95% of the data would fall into, it would merely be avg-+t*statistic*st.dev. The values you get for that are something like {-.84, 10.84}.