Hello everyone,
I have a data analysis problem to solve. I measured 4 different concentrations with 3 different methods. For each measurement I have its error. I refer to the attached image as example. I have to say if the results between the methods are the same. Looking to the data is obvious that method A differs from B and C, while B and C are the same, even if the uncertainty with C is bigger. But I need a statistical proof. I thought to t-test or ANOVA but, in my knowledge, they work on measurement of the same quantity, not if the quantity under investigation changes.
I am looking for a simple mathematical tool, that maybe I could perform in excel, which statistically tells me what I see looking at the dataset.
Thank to everyone for your time.
Dear Walter,
If you need to compare three methods (A, B, and C) at each solution (1, 2, 3, and 4) separately, you can use one-way ANOVA. Make sure to include Tukey's post hoc comparison. Then you can compare methods pairwise.
Ex-
Compare A, B, and C at solution 1
Compare A, B, and C at solution 2 and so on...
Using the results (p values) you can say whether there is a difference between each couple of methods or not.
Otherwise, you can use two-way ANOVA to compare them all at the same time.
However, you should have at least three or more data at each point to carry out these statistical tests.
Cheers
First of all, thanks for the replies.
Let's imagine that I want to compare only the results of solution 1. However, with ANOVA I cannot use the results with their uncertainty, but I should use the data set that led to that results. Unfortunately these data are not mean and standard deviation of several measurements but single results and propagation of the error of that data.
Hello Walter. I suspect that you and I speak somewhat different dialects of Statisticalese. What do you mean when you say propagation of error? Show us an example of how you computed it if you can.
I thought you were reporting the mean and standard error (SE) for each cell. But if that were so, you would have to have more than one measurement per cell. Thanks for clarifying.
I report a simple example to be clearer:
If I have a 50 + - 0.1 mL volumetric flask and take a sample with a 5 + - 0.05 mL pipette I can find the relative error =sqrt((0.1/50)^2+(0.05/5)^2)=0.01. If the concentration value is 10 the uncertainty will be 0.1.
Regarding my problem I thought of doing this: instead of performing the excel function of the t-test directly, I used the equation t=|x1-x2|/(sqrt((s1^2/n1) + (s2^2/n2))). Where x is the result, s the uncertainty and n=1; I then used excel's T.DIST function to derive the distribution and compared the result with the reference value set at p=0.05.
Following this reasoning I obtained the following results for each solutions
A vs B p0.05 null hypothesis accepted
B vs C p>0.05 null hypothesis accepted
attached I plotted the gaussian distribution of solution 1 (A blue, B red, C green), the results seems appropriate.
What do you think?
Hi Walter. If I follow, n1=n2=1. For an ordinary unpaired t-test, df = n1 + n2 - 2. How are you able to compute a p-value when df = 0? I get missing values when I try that with both Excel and Stata.
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