Which type of data are you using? If they are compositional data (percentages, ppm, and the like) a simple log-transformation will not be enough, at least in general.

Thanks for responding. I used and arcsine transformation where the QQ plots suggested a better fit for data that was a proportion. Other types of data are not percentages of proportions, just interval level data.

Decided to change the name of the question from 'woes' to 'blues' ... and I created a little song to go along with it.

I've got problems with my p-values,

I've got the Jarque-Bera Blu-ues.

I've got problems with my p-values,

I've got the Jarque-bera Blu-ues.

My p-values are just too small,

And I don't know what to do-o.

--Just don't have a clue my son.

My advisor said to scrap it,

But I said no wa-ay.

My advisor said to scrap it,

But I said no wa-ay.

I said I'll try to transform,

My values to pla-ay.

--Playin' together well my son.

So, I'm natural login' here,

And I'm arcsinin' there,

Bu-ut the trouble is sti-ill,

Present here a-and there.

--Lord, please help me real soon.

So I posted a question,

On this forum right he-re.

So I posted a question,

On this forum right he-re.

And I'm hopin' you can help me,

And I'll buy you a be-er.

--If we ever meet that is.

I've got problems with my p-values,

I've got the Jarque-Bera Blu-ues.

I've got problems with my p-values,

I've got the Jarque-bera Blu-ues.

My p-values are just too small,

And I don't know what to do-o.

I am guessing that you are using MATLAB, is this correct? If you have not already done so I suggest doing a search on Google for "Jarque-Bera" to get a good picture of what the Jarque-Bera statistic is used for, namely as a test for normality. As with many tests for normality, normality corresponds to the null hypothesis and hence often one is interested in accepting the null hypothesis rather than rejecting it ("non-normality" includes a lot of possibilities), i.e. one would be more interested in the power of the test than the p value

You mention doing this analysis prior to "spatial analysis" and the question seems to be posed under the heading of geostatistics. In most of geostatistics the basic assumption is that the data is a non-random sample from one realization of a random function. The random function must be at least intrinsically stationary. These assumptions are rather different from those implicit in regression analysis. The derivation of the kriging equations (whether Simple, Ordinary or Universal) does not depend on any distributional assumptions, e.g. normality.

Perhaps you are attempting to deal with a non-constant mean but note that OLS is not an optimal estimator of the drift although in practice it is often used because of a lack of better choices. Several authors have written about the potential for bias in estimating the variogram when OLS is used to estimate a non-constant mean.

In summary it might be easier to give you useful advice if you would tell us more about what you are trying to do, in particular why is the Jarque-Bera statistic of interest in your problem?

I’m investigating whether children’s mental health assessment scores at intake (and admissions) relate to neurotoxicant release (i.e., specified as solvents in the data above). All of the unique children’s scores have been aggregated to the census tract level. (I was not approved to do HLM on individual client data; the state dept. was a bit sticky about analyzing individual-level data for many reasons). I’m controlling for several variables including family overcrowding, an index for economic stress, proportion of admissions that are male, child functioning, child problem severity, etc. First, I’m exploring the data with OLS in ArcMap 10.0 in order to build a parsimonious model before I run geographically weighted regression. My stats all look great, and the Koenker (BP) Statistic indicates I have non-stationarity). Unfortunately, the Jarque-Bera stat seems to indicate I have correlation amongst my residuals. My understanding is that I want this stat to be non-significant before proceeding, so my coefficients aren’t reliable.

J-B is a test for normality,not a test for correlation. If you are trying to transform to (normality and the common transforms log.sqrt etc are not working) switch eitther to box-Cox transformation, normal scores transformation, or better yet use indicator kriging as there are no distributional assumptions.

The Normal scores approach is known as the multi-gaussian model.

One simple way normal scores approach is Z=F_inverse(rank/(n+1)), where F is the cumulative normal distribution function.

Also, you don't really need independent residuals if you are trying to ultimately come up with a spatially weighted regression. Independent residuals are an indicator that there are no unexplained spatial process, and that the OLS regression is appropriate.

Thanks very mush for all of your answers. John, my understanding was that data have to be detrended before one can use NST. There don't appear to be any trends visible in the trend analysis tool of the "geostatistical wizard," so I'm assuming that I can just use NST without detrending?

Another more general question: How important is it that one of my dependent variables (e.g., child mental health admissions) be linear (see attached)? My OLS model residuals are much smaller if I don't transform the data for the child admissions rate.

You'll  have to forgive me; I didn't realize someone had asked me a question about this topic. While the author of the question may no longer be on this site, I do have a helpful answer in case others look at this question. For my research I found that census tracts with few admissions (or cases) were causing some of the variables to become unstable. When I eliminated those cases the JB statistic became significantly better. Adding spatial variables (e.g., distance from residence to treatment center) also helped, but not as much as I would have liked. I never solved the problem completely, but I got very close. 

Betsy Breyer has a great presentation on GWR that covers many of these issues: http://www.orurisa.org/Resources/Documents/CCGISUG/CCGISUG_%20Breyer_2013_ExploringLocalLariabilityInStatisticalRelationshipsWithGWR.pdf