My dear colleagues,
Normality of data is essential assumption in Statistical Theory. But, we often face a problem of dealing with data that do not behave as normal probability distribution, this case requires to pay more attention. Because normality related usually with parametric analysis. Therefore, I look after a way in which I can transform any type of data to Normality via mathematical transformation.
You don't need to transform data. You can use non-parametric tests such as PERMANOVA. But transformation is usually done using mathematical functions such as square root or logarithm :)
Normality of data is not an essential assumption in Statistical Theory. It is the most convenient because most tests and models were developed for a normal distribution. There is nothing magic in transforming any type of data to normality. Transformed data must be interpreted in its original form. Devise a test for the data at hand that is appropriate to the question asked. Do not make the question fit your favorite statistical methods. There are many kinds of hammers and few types are best for the nail in your hand. The wrong hammer is a risk to your fingers.
The distribution of the data is not recommended to change them, remember that this change is made from mathematical assumptions such as logarithm and square root, and often apply without taking into account the data. When your data does not adjust to a normal distribution, it is correct to apply non-parametric tests. Let's think that for example: you have values of abundance of species for 10 localities and your data do not fulfill a normal distribution. What biological significance does it have to convert that data to a square root? What does it mean that you have a value of square root wealth? Biologically it is not correct, we must apply mathematics with sense because to those data you will apply another analysis later and at the end your result can give you something that does not really happen, simply influenced by mathematical assumptions
You can used non-parametric tests or go here:
https://in.sagepub.com/sites/default/files/upm-binaries/70453_Pett_Chapter_3.pdf
dear Omar,
although the Box-Cox family of transformations may help, you may not get a satisfactory transformed variable that follows the normal distribution. The tests, especially F and t are robust enough to accept some departure from the assumption of normality. You may try for lambda varying from -2 to 2. if you are not successful to approximate the normal distribution, as rightly pointed out above, go for non-parametric analysis.
best wishes
raman
I have used transformation to normal distribution.
Article The influence of environmental factors on species compositio...
I agree with Alvarez and Kouadri,
Besides logarithm and COX-BOX transformation, you can apply Regression Spesification Error Test (RESET) to mitigate statistical issues that might arise and ensure the robustness of your regression model.
Regards,
Numerically generated Gaussian white noise is often used for modelling/simulation applications. ― While investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the recursive least squares algorithm (RLS) with forgetting factor (RLS-FF) to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...