Need help with statistics to evaluate a proposed design model

R

RadekSkylark

Guest
#1
Hallo guys.

I'm a structural engineer and I'm doing a study for my bachelors or maybe masters degree (haven't decided yet for which of them I'll use it).

I have taken a load model for a structure, which is influenced by many variables and used it to determine results which I compare to the correct values obtained from theory. The thing I want to do with this sort of study is to verify whether the load models I checked are generally valid and can be used for calculations in everyday design problems with predetermined safety margin - I need the results from the load model to be within 5% of the theoretical values 95% of the time, so that in the majority (95%) of situations the results are in the predefined error limits (5%), but in the other situations error can be bigger.

As I understand I need to calculate some statistical data and should arrive at conclusions based on the data. I'm talking about things like standard deviation, mean, etc. The problem is that I don't have a background in statistics, I have tried to read a bit for a day on the mean, median, mode, range, percentiles, standard deviation, coefficient of variation, standard error of the mean, standard error of the standard deviation and standard error of the coefficient of variance, as well as skew and excess kurtosis. So far I arranged the data in 54 sample groups based on meaning in the design. Each group contains ~80 to ~400 measurements. The measurements actually are proportions "r" of the value obtained from theory "Et" to the one obtained from load model "Em", thus "r=Et/Em", so that if the load model prediction has been correct the r=1, if the load model predicted a higher value than theoretical one r<1, and vice versa. I have calculated the above mentioned statistical data for all of the sample groups. So I want to verify every of the sample groups to the precision mentioned above. And at the end, I would like to merge few (3) sample groups together in a larger sample group (then there will be total of 18 larger sample groups) and to check if that as well is within the previously mentioned safety/precision limits.

The problem is that I'm really confused and I'm not really sure of what I'm doing from the statistics standpoint. From what I've understood in a day of reading on statistics, the majority of statistical data (mentioned above) I calculated show that the mean is always pretty close to the median and mode (all around 0,99 to 1,01), so I interpret it that the tendency of the model is to be accurate and that the most likely result from the load model will be almost exact. I have calculated percentiles at 2,5% and 97,5% to see where the core 95% of results have landed, thus, what is the margin of error for the core group of 95% of the results - mostly these values have been in the 3% to 5% error range. Although from what I understand, strictly speaking this is a conservative evaluation, because if I'm after anything between 0,95 and 1,05, than I really should be looking for the core of 95% of measurements that have approximately the same margin of error on the respective percentile values, for example, it could be that the percentile at 5% is 0,95 and the maximum measurement is 1,05 which both within the 5% error range, thus showing that 95% of the measurements are in this range, instead of checking percentile at 2,5% which could be, for example 0,93, and one at the 97,5%, which could be 1,03, thus implying that 95% of the data are within 7% error range, when actually it is not the case, as I'm only concerned that 95% of the results should be withing the 5% margin of error. Standard deviations in general are around 0,005, in few extreme cases for sample groups with simplified models which I already thought won't suffice around 0,05. Coefficients (in percent %) of variance in general is thus below 1%, and only in few cases is 3-5%, and in one extreme case 7%. Standard error of the mean in general is either 0,000 or 0,002, thus relatively to the mean itself only of around 0,2% maximum. Standard error of the standard deviation in general is 0,000, in few cases 0,001 and in only few extreme cases 0,002 or 0,003, of course speaking in relative terms to the standard deviation itself it is in general 3,5% to 7,5%. As for the standard error of the coef. of variance in general it is between 0,00% to 0,15% and only in few extreme cases 0,20% to 0,40%, but speaking relatively to the coef. of variance it self it becomes is generally in the same range as the error for standard deviation, thus in general within 3,5% to 7,5%. Skew varies quite dramatically and in general lies between absolute of 0,5 to absolute of 3,0 and in extreme cases to absolute of 5,0 (I don't care if there are mostly values below or above 1,000, thus if my model predicts higher or lover results than the theoretical). Excess kurtosis in general is positive with values ranging from ~1,0 to ~5,0, but in the most relevant sample groups it is usually way higher in the range of 10,0 to 20,0, with extreme cases of 30,0 to 55,0. From excess kurtosis I have concluded that the majority of results are within the acceptable precision limit, although when it is breached the results can be quite outside it, thus the error can be significant. From standard errors of the mean, standard deviation and coef. of variance I've concluded that the sample results approximate population quite well.

First of all I seem to be sure of my conclusions regarding the results and statistical data of the samples, although anyone who does not have really strong knowledge will think that his conclusions are correct, as one doesn't know better - so the first question is - are my conclusions correct?

The seconds and probably the most important question is - what I need to do/calculate from mathematical statistics standpoint to show that the proposed load model will provide results within 5% margin of error 95% of the time?

The last question: is the number of measurements sufficient? And how could I actually calculate the required amount of measurements for this test to obtain good range of data and thus give good basic for statistical judgement?

P.S. I don't have a really strong foundation in mathematics if this make any difference (I did have a good background, but it was few years ago in the beginning of my studies, but now I've forgotten almost everything).

P.S.S. Sorry if my terminology and anything else is off - English is not my native language.

Thanks, and I really hope you'll be able to guide me, as I"m really thrilled to make confirm that Indeed the proposed load model is usable in practical everyday design.