I have 40 values with 40 standard deviations that I calculated using the approximation sf=SQRT((df/dx)^2*sx^2+(df/dy)^2*sy^2+(df/dz)^2*sz^2+...).
Now I need the calculate the average and st.dev. of the 40 values. So if the values are A, B, C, etc., I did:
AVERAGE=(A+B+C+...)/40
STDEV=SQRT((1/40)^2*sA+(1/40)^2*sB+(1/40)^2*sC+...)
Usually, when I calculate the propagation of uncertainty in this way, the st. dev. calculated is higher than ones used in the calculation. However, here the calculated st. deviation is lower. That is why I can tell I am not doing good.
could you please give me some notions?
I hope my question is clear.
Please see the attached file.
Thank you
You can easily calculate standard deviation in excel following this step
Formula,-------- More function-------- Statistical=======and AVDEV
or you can use Minitab software to calculate average deviation
Getachew Weldemichael thank you for the response. I have google it and I found that: "Excel AVEDEV function calculates the average of absolute deviations from the mean in a given set of data."
the problem is that I am not handling absolute deviations but standard deviations, so I still do not think it will be useful
Dear Alejandro Moure Abelenda I my opinion you just must to calculate the SD for the whole of your data. Remember that SD is a measaure of dispersion of data respect to average. Calculating the SD for all data you'll obtain the average standard deviation.
Ricardo Julian Licea-Moreno Thank you. I cannot calculate the standard deviation for the whole data set. It is difficult to explain. I have 40 values each with its own error (standard deviation)
I think it's a statistical mistake trying to average standard deviations. Maybe I am wrong, but when you try to average that It looks like trying to cheat results or something (I'm not telling what it is, I'm telling you that it looks weird). I really don't know the aim of it.
J.D. Franco-Navarro sure. Probably the problem was on the design of the experiment. I was in that situation and I needed to sort it out. I will improve the calculation of the propagation of uncertainty in future experiments.
Alejandro Moure Abelenda just try to increase the number of observations, the most the stronger will be the statistical analysis. I also recommend you to use the STANDARD ERROR, is a little bit cheaty but It's well accepted in papers.
SE = DESVEST (RANGE OF DATA)/(square root(COUNT(RANGE OF DATA)))
The count tool will count the size of the population of data in the Range of data you have for each treatment. Normally the number is smaller than the Standard Deviation.
J.D. Franco-Navarro I think one of my supervisors has already told me about the standard error. On the other hand, my fellow @Cristopher Da Silva A. preaches the use the confidence interval in the graphs.