Non parametric problems

[oldoak]

Hello.
I have got myself into some real problems (mainly from not gaining my data in the best way!) in my degree dissertation.

I have been looking at a waterborne tree disease and some of the environmental factors. I have rated the health of the trees ranging from 0- dead to 4 perfectly healthy.

One factor I was looking at is water speed. I recored the speed of the water at each tree. The feel is that there is a weak correlation on water speed to the health of the trees, but the random selection of 5 sites where I have recoreded did not give a huge varience in water speed. i recoreded water speed from 0- still, to 6 very fast. most reedings were from 2 to 4.

All sets of data appear to be non parametric, Non transformable, and here is were my problems begin. using non-parametric tests that tend to use medians. now obviously choosing medians from just 0 to 6 creates rather unrealistic results.

My tree health data can be used as values from 0-3.81 in values as 0.01 so the tree health rating is ok for these non-parametric tests.

My feel is that because I didn't take exact values for water speed, rahter ranking it, is that the non parametric tests are not going to give an accurate result.

Has anyone any advice?

Many thanks

Dave Bailey

[SE_Lazic]

You have 5 levels of health (0-4) and 7 levels of water speed (0-6) which can be displayed in a 5x7 contingency table, with the number in each cell indicating the number of trees. You might want to consider correspondence analysis (http://en.wikipedia.org/wiki/Correspondence_analysis).

p.s. Note that tests are either parametric or nonparametric, not data.

[Junes]

I'm confused though, because you say that "My tree health data can be used as values from 0-3.81 in values as 0.01", which seems to suggest that the health data is continuous.

[oldoak]

Thanks for all the posts, some good things to think about there.

I am rather good at forgetting my stats 'talk', i do appologise.

the tree health data is continuous, but i have ranked it into the 5 differnt ratings, so i can go back to use the continuous data.

cheers

dave

[SE_Lazic]

In that case a standard ANOVA would work, with health as the dependent variable. It would be useful to treat water speed as an ordered categorical variable, and the the linear contrast might be of more interest (and have more power) than the overall ANOVA F-statistic.

[oldoak]

it is funny, because i initially used ANOVAS and t-tests on a variety of data after mistakedly finding the data to be normally distributed. The ANOVA and t-test gave p values in the range of what I 'felt' the data should be saying.

However, should not ANOVA be used on data that is only nornmally distributed?

Thanks for your help

Dave

[SE_Lazic]

The raw data need not be normal, so long as the residuals are normal. The results of ANOVA are not influenced a huge amount by non-normal distributions, but if you have a large deviation from normality, it might be worth transforming the data, e.g. by taking the logarithm of the raw values. The type of transformation will depend on how the data are "not normal". A log-transform is good if you have a positive skew in your data for example (see http://en.wikipedia.org/wiki/Data_tr...8statistics%29).

[Dason]

The raw data need not be normal, so long as the residuals are normal. The results of ANOVA are not influenced a huge amount by non-normal distributions, but if you have a large deviation from normality, it might be worth transforming the data, e.g. by taking the logarithm of the raw values. The type of transformation will depend on how the data are "not normal". A log-transform is good if you have a positive skew in your data for example (see http://en.wikipedia.org/wiki/Data_tr...8statistics%29).

Or use a generalized linear model to actually model the data.

[SE_Lazic]

Or use a generalized linear model to actually model the data.

Yes, good point. A GLM would be my preferred method... just trying to pitch it at a familiar level.

[Dason]

Yes, good point. A GLM would be my preferred method... just trying to pitch it at a familiar level.

Oh definitely. A transformation would probably be much more familiar to them. I'm just not a huge fan of transformation unless there is good reason for them.