Hello,
Assuming a scenario such as: if one collected water samples from 9 different sites in a time series of four months (within two different seasons were each season had two months as a representative) from a river, a stream and a lake (each water body having received 3 random sites as a representative).
With each visit to the site, only one time the water was collected, so no replica! The tests were intended to find heavy metals concentration like cadmium and bismuth. Unfortunately due to cost sometimes two sites or all three of the representative of the water body turned into a composite/mixture representative for this water body.
So, can any inferential statistics be performed on these?
Please, if more information is needed, I will provide it here. If a link exists for such small details that would be great.
I think you could use multivariate statistics without any problems. But you need to be aware of different land uses or possible sewage contamination between sites, especially when the results between sites are statistically different.
Statistical analysis of the number of water sources with elements
You can do a statistical analysis of the two seasons for two months, which means a good job, and the comparison will be the elements of the months and seasons of the sampling sources.It geographically locates water sources
yes indeed, you can use 2-way ANOVA( you have two factors: site and season and the responses so you can use each responses/ dependent variables independently .i.e., 2-way ANOVA for each dependent variable) or Multivariate ANOVA analysis method.
Remember that many water parameters are log-normally distributed, especially those which are solids-related, COD, BOD, TSS, TN and metals.
Along with the multivariate test (PCA, HCA, Correlation) you should perform descriptive statistics, non-parametric tests on the samples.
Standardizing the samples.
Moreover, you can try with some broader aspect and can find their correlation with your objective.
Multivariate tests are indeed used in such cases. Cluster analysis, PCA...But I came across other things as well such as using t-test only if I were to compare two seasons (I could potentially do so since each season has two months so they would already count as two replicas for its corresponding season).
Do correlation of the seasons with simple regression analysis and compare all the analysis parameters and fit them into nonlinear relationships and predictive models
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