I have problems getting my data to be normally distributed. I hope someone more experienced can help.
I have the following data:
Type Grade Conc Type Grade Conc A 0 424.294872 B 0 1082.300570 A 4 2035.972222 B 0 0.000000 A 0 423.842964 B 0 43.750000 A 0 0.000000 B 5 532.500000 A 0 0.000000 B 0 2133.152913 A 2 593.103448 B 3 694.747475 A 0 2164.427663 B 0 0.000000 A 4 709.972527 B 0 4.347826 A 0 69.696970 C 0 321.271930 A 0 521.052632 C 2 2132.975078 A 0 394.137931 C 0 562.832080 A 0 2108.531746 C 0 0.000000 A 1 459.126560 C 0 0.000000 A 0 42.857143 C 2 340.939824 A 5 4.347826 C 4 2386.016949 B 4 574.067599 C 5 1104.029605 B 0 3760.888889 C 1 11.041667 B 2 660.801839 C 2 29.069767 B 0 0.000000 C 3 835.454545 B 0 0.000000 C 4 2690.442890 B 1 640.073145 C 5 685.518018 B 0 3204.793028 C 1 7.575758
I want to determine if y is significantly dependent on x (I want the p-value and R^2) and if the type has an influence on it.
However, I asked several professors and a colleague of mine which would be the best way to do this. Each of them gave me a completely different answer, leading to very different results. Now I'm not sure which to use.
First one suggested simply sqrt:
fit <- lm(Grade~sqrt(Conc)*Type, data = data) par(mfrow=c(2,2),mar=c(5,4,1.5,0.2)) plot (fit) anova(fit)
Next one told me I could divide 1 by "Conc" like this:
fit <- lm(Grade~(I(1/Conc+0.0001))*Type, data = data) par(mfrow=c(2,2),mar=c(5,4,1.5,0.2)) plot (fit) anova(fit)
This one I've never seen done before, and I'm not sure if it really transforms the data to normal distribution.
Another insists that the only right way is using
fit <- glm(Grade~Conc*Type, family = poisson, data = data) anova(fit, test="Chisq") summary (fit, test="Chisq")
However, a colleague is sure that Poisson would be wrong and instead quasiPoisson should be used (with
anova(fit, test="F") )
As my knowledge of statistics is very limited, I have no idea which one is right. All of them give completely different results. So I'm just utterly confused
I also thought about using non-parametric test for my analysis, in order to avoid having to transform the data. However, none of my professors could help me with that and they insisted that transforming is the better way to do it (which I don't agree with, but since I never used non-parametric tests I have no idea how).
Edit: Thank you @Nick Cox for your very elaborate answer! I realize now how little my understanding of statistics actually is. Especially your question "What is it that you think should be normally distributed and why?" threw me off. I thought that the concentration (conc) needed to be normally distributed. As for why, simply because I was taught so in our (very basic) statistics course. However, thinking about it I don't even know if that makes sense in this case... Also I see how the missing information is an issue: I'm very sorry I didn't realize that from the start. I will look over my data again, think about it more carefully this time and I will try to edit my question to be less general.