I do not thing that you can compare SOC of each layer and the sum of SOC. It is enough that %C is significantly different even though bulk density is not. Where did you find the equation for SOC, can you give the citation?

Hi Simone,

I'm not sure whether I fully understand your experiment. The t-test has been designed to test for difference in the means of two Gaussian-distributed samples with more than 30 measurements each. Are you sure that your two samples are Gaussian-distributed? And do you have enough measurements?

You say that you took samples from four different layers. Maybe there is a non-Gaussian process involved creating a trend in the means between the layers (as an example) and therefore your samples are not Gaussian-distributed? You need to examine the sample for this non-Gaussian process first before running a t-test for the difference in the means.

There are other tests without the requirement of normality, e.g. the Mann-Whitney test for measures of central tendency and the Ansari-Bradley test for differences in dispersion.

Kind regards, Martin

The problem is not the test that he is going to use but the fact that SOC comes from an equation where the two variables have different number of replications. Even if he had the same number of replications for bulk density and %C, he can not construct replications for SOC because the %C and bulk density were not and cannot be measured in the same sample. Thus he is obliged to use the mean value of %C and BD to estimate SOC and not the values of the replications. This problem do not allow him to construct SOC replications and consequently statistical tests can not be performed. %C and SOC are the same thing but in different units, so I recomend to use directly the statistical tests for %C for each layer and stop.

Continuing with the suggestion of non-parametric tests, Mood's median and the Kruskal wallis test may be alternatives to t tests

Dear Vahid,

I think that your reply is a bit confusing. I do not say that it is incorrect but confusing. It uses William Gosset's original terminology, which is more than a hundred years ago. Yes, it's all about errors of means of samples. But trying to explain Simone how to use the t-test it is all about comparing means and standard deviations, which are the two parameters of the Gaussian distribution and which are used, together the sizes of the two samples (Gosset calls them "groups") to calculate the test statistic of the t-test. The underlying distribution of the two samples definitely needs to be Gaussian (if you wish, it's the error of the means you wish to compare) and the distribution of the test statistic is the t-distribution by Gosset.

Kind regards, Martin

Dear Vahid,

Thanks for your response, and sorry, Simone, if we are filling up your thread :-) The article was the original article by William Gosset on the t statistic. Gosset was an employee of the Irish Guinness Brewery and was not allowed to publish research results. For that reason he published his t distribution under the pseudonym Student (Student 1908).

Kind regards, Martin

In this case, it is better to apply the Newman-Keuls multiple comparison test in which you could consider a factorial arrangement by taking ecosystems as one effect and layer type as another effect. In this way, you will be able to obtain the significant difference for the two effects.

In this case, it is better to apply the Newman-Keuls multiple comparison test to compare the interaction effect between ecosystem and layers effects. It is impossible when it used the T test.

Hi all,

thank you very much for all your input. It's clear that this analysis is not trivial. I'm going through some of the tips I had and let you know if I need more help. It's being interesting all the discussion, so no problem for "filling up my thread"!

@Vahid, you asked me more details:

there are 4 layers per 2 sites, and i want to compare the soil organi carbon content between them.

(1) no, I meant that the %C of every layer of one site was compared with the %C of the same layer of the other one (same=same depth).

(2) I meant that the %C in the two more superficial layers was different between the sites: so the layer 1 of site 1 had a statistically different %C content from layer 1 of site 2, and that layer 2 of site 1 had a statistically different %C content from layer 2 of site 2. While layers 3 and 4 were not statistically different between sites.

The SOC was calculated with the formula reported above. In this formula I used the averages from each layer, so that i have one value per layer. Then I summed up the SOC of every layer to have the total SOC: that is what i meant with "what about the sum?". I can propagate the standard deviations from %C and BD to calculate the uncertainty.

Thank you all

Simone Sabbatini

@Vahid thank you it's much more clear now. I'll try paired t-test and Wilcoxon test.

And thank you all!

Simone

Hi there,

first off, I think would be interesting to know if the variable has a parametric o non-parametric behavior. In case of being non-parametric, I recommend use another test to asses the differences. On the other hand, if the variable presents a parametric behavior another option would be carry out an ANOVA test. Surely, this test will give you more information than T-test. Good luck!

I suggest you use ANOVA with Tukey Post-Hoc for this scenario which gives you the comparison among all groups together.

Dear all,

sorry for bothering you again but i would like to check some results with you.

I tried the paired t-test as suggested by @Vahid. I copy-paste the results:

*******

"Paired T for src - agr

N Mean StDev SE Mean

src 4 6.17 2.92 1.46

agr 4 7.68 2.44 1.22

Difference 4 -1.505 0.699 0.349

95% CI for mean difference: (-2.617; -0.394)

T-Test of mean difference = 0 (vs not = 0): T-Value = -4.31 P-Value = 0.023"

*******

src is one site, agr is the second one. It looks like there is a difference, as we have a low p-value and the 0 is not included in the CI.

I also tried the Mann-Withney test (in the software I used, Minitab, the Wilcoxon was usable only for a single sample, and the MW was indicated as "the Mann-Whitney test, or the two-sample Wilcoxon rank sum test) :

*******

"Mann-Whitney Test and CI: src; agr

N Median

src 4 6.181

agr 4 7.499

Point estimate for ETA1-ETA2 is -1.693

97.0 Percent CI for ETA1-ETA2 is (-7.569;4.182)

W = 15.0

Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.4705"

*******

In that case the difference is not found. So, who's right? Is it possible that I have an error of I type in the paired t-test? Or do i have an error of II type (if we can call it so for a non parametric test) in the MW test?

Thank you again!

Simone

Thank you all!

Simone