The data collected is on time to appearance of different developmental stages, of fish eggs in concentrations of toxicant. Five concentrations of toxicant and eight egg developmental stages were monitored (total of 40 cases). The data was ranked with the following results: the distribution of 15 variables were normally distributed (Shapiro-Wilk test) both before and after ranking using SPSS version 25 (37.5%). Twenty-one variables became normally distributed (52.5%), while two cases were not affected. I read somewhere that data normalized by ranking can be analyzed using parametric methods. Does this apply here? Thanks.
In other words, is ranking an acceptable method of normalization of non-normal data?
Hi, Chukwuma Ofor ,
- Basically, whatever transformations you apply to your variables is allowed if it results in data that meet the assumptions of the model you want to use.
- But it may not be the most desirable approach.
- I suspect that you have some misconceptions about the assumptions of anova. I assume you are conducting a two-way anova. In this case, the model is a general linear model, and the assumption is that the errors are normally distributed. We can check this by looking at the residuals from the analysis.
- It's not very helpful to use a hypothesis test to test the assumptions of a model. It's better to look at plots of the residuals, or to understand the nature of the population that was sampled.
Ranking and using parametric methods is a well known way of handling data with odd distributions. See: https://www.jstor.org/stable/2683975?origin=crossref
However, it may not be the best approach. In particular you lose the quantitative link between your outcome and the original data - which can be important if you are trying to predict outcomes, get interval estimates or look at interactions. There can be ways round this, but not necessarily easily. On the other hand rank approaches can be OK if all you need is a hypothesis test (though I tend to find that unsatisfactory).
As you have time data you might think of using a common transformation such as log or if you have trickier data a generalized linear model or specific models for time data. The log transformation is nice in this context because it changes the model from an additive one to a multiplicity one in which change is effectively a proportionate one. For time data its kind of implausible that effects add or subtract constant amounts of time regardless of the observed time. Modeling proportionate changes is often more sensible - so a predictor might increase time by 10% rather than by x seconds (or whatever).
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