Hi there,
I do not have a solid understanding of the statistics - I am seeking advice regarding the correct data analysis. I am helping my colleague to analyze the oxidative stability of oil. Please help us!
This is what our data looks like
We checked oxidation products in oil samples in triplicate (n=3) at 6 different time points (0, 2, 4, 6, 8, and 10 weeks) under 2 different relative humidities (11 vs 44%).
I am confused as to which statistical test(s) would be the suitable one.
I really look forward to hearing from you awesome scientists:-)
Dear Pankaj Arora ,
Enough of the flattery! It sounds like a two way ANOVA. The complications are your small sample size and your time dependent sampling which may well violate the random sampling assumption. Let's see what others think...
Hello Pankaj,
Do I understand correctly that you have a total of 6 samples (three exposed to lower humidity; three exposed to higher humidity) measured on each of 6 occasions?
If so, then this sounds like a 1-between (humidity: 2 levels), 1-within (occasion: 6 levels) anova design (which could be called a two-way design as suggested by Peter Samuels ). Older texts might refer to this as a "mixed" anova design; others as a repeated measures design (the occasions factor). This is a pretty straightforward analysis, but as Peter mentions, the small N may make tests of the humidity effect (or humidity x occasion interaction) not very powerful unless the magnitude of the difference is pretty large.
Good luck with your work.
Pankaj Arora , complementing David Morse 's answer, you may want to consider a Bayesian ANOVA design, as Bayesian methods work well in small samples:
Chapter Bayesian Analysis of Variance (Anova)
David Morse Peter Samuels Rolando Gonzales sorry I forgot to mention one important info. The oils were encapsulated within wall materials in three different ratios, 1:1, 1:3, and 1:9.
So, we checked the oxidation products of oil samples, which were encapsulated within wall materials in three different ratios (1:1, 1:3. 1:9) at 6 different time points (0, 2, 4, 6, 8, and 10 weeks) under 2 different relative humidities (11 vs 44%).
so, would it be 3-way ANOVA with factors
1) Wall material ratio
2) Relative humidities
3) Time
Also, what software would you recommend for conducting this analysis (GraphPad doesn't allow 3 way ANOVA with this data as it says we have more than 4 columns while entering the data)
Dear Pankaj Arora ,
There are many different types of statistical analysis. Choosing the correct analytical approach for your situation can be a daunting process. In this section you’ll get an overview of the statistical procedures that are potentially available and under what circumstances they are used.
https://www.dataanalytics.org.uk/data-analytics-knowledge-base-tips-tricks-r-excel/statistics-guide/which-statistics-test/
Regards,
Shafagat
I have a problem with the advices to use ANOVA. In the usual way to understand this, it means to investigate independent groups, and that the statistical model is based on the assumption of a normal distributed response (with the same variance in all groups).
Regarding the response you just wrote " We checked oxidation products...". This provides no information about what you are actually emasuring, what the response variable is, and what reasonable assumptions about its distribution would be.
Further, as you measured at subsequent time-points, the different "groups" are not independent (the response at adjacent time points should is more similar than at time points that are further apart). This calls for a regression analysis (instead of ANOVA). Actually, all predictors are quantitative (-> multiple regression), but "time" is the only predictor with a reasonably large number of different values, whereas the other predictors should better be treated as qualitative variables. Such models (including quantitative + qualitative predictors) are sometimes called ANCOVA models, but this term may also be misleading. It's just a statistical model with quantitative + qualitative predictors.
It's also not very clear if the samples were taken at different time points from the same specimen/solutions. If so, this should be considered by using a repeated-measures or hierarchical/multilevel/mixed effects model.
Finally, there are several interactions between the variables possible. It is not clear if all these possible interactions are reasonable. This should be clarified.
So there is relevant information missing to give any specific advice. After all, I think the only hint one could give is that it should be some kind of a general, or possibly generalized, linear or possibly non-linear model, possibly including a random intercept term (not to mention a possible random time term).
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