If an outlier appears in small study data, the risk o f making an incorrect decision is substantially increased particularly when rho is moderate. Spearman, might provide a better estimate since the outlier will become an extreme rank rather than extreme value.

You _could_ use Spearman's correlation. It sounds like you're reading something in to the idea of the monotonic relationship that Spearman assesses.

In general, you will not be well served by using a statistical test or a z statistic to assess normality of data. With a large sample size, you are likely to find a large z value, even if the data don't diverge much from the normal distribution. This is probably what your Hair reference is getting at. If a large z value doesn't tell you anything, why bother looking at it all?

Also note that non-normality doesn't imply that there are outliers.

It _is_ a good idea to assess the data for outliers or for points that have high influence or high leverage. With bivariate data, plotting the data and looking for these observations will be useful. Depending on your software, you also might be able to analyze the data with a linear regression, and have the software identify high-leverage points.

If an outlier appears in small study data, the risk o f making an incorrect decision is substantially increased particularly when rho is moderate. Spearman, might provide a better estimate since the outlier will become an extreme rank rather than extreme value.

Toni Hall , estimate (and report) the correlation parameter with and without the influential observation(s), this way you will see the effect of the influential observation(s) on the estimated correlation. I see also no problem in using non-parametric correlation coefficients as Spearman or Kendall (providing that you have a moderate to large sample), but I would still report the results with and without the outliers.

You may find the attached of some interest Best, D. Booth

Dear Toni Hall ,

I fully agree with the information provided already by Salvatore S. Mangiafico , Rolando Gonzales , Rolando Gonzales and David Eugene Booth , but have a few pointers to make.

The Pearson’s correlation coefficient is very sensitive to outliers. In conditions where outliers are presents, both the Pearson’s correlation coefficient (rho) and the fit of the model that may be formulated can get affected quite substantially. In addition, measures of central tendency can also become far away from rho and can become further far away from rho as the size become smaller. However, I think it is worth mentioning that since some departures from normality are common (Hill & Dixon, 1982; and Micceri, 1989) in real world applications, some researchers argue that the coefficient is robust and powerful even under extreme violations of the normality assumption due to outliers (Fowler, 1987), while others argue that the effectiveness of the rho is reduced in the presence of data anomalies (McCallister, 1991; & Halperin, 1986). In my view and from practice, I think the detection and treatment of outliers should be based on assessment of whether or not the elimination of outliers from the dataset would make substantial changes in the degree of strength of correlation coefficient (low, moderate and high), potentially subject to the size and frequency of outliers.

Bearing in mind that outliers may arise from of three common ways (a). inherent data variability, (b). measurement error, (c). execution error (Anscombe 1960; Barnett, 1978; Beckman & Cook 1983; and Grubbs, 1969), it is crucial to note that interpretations of magnitudes or strengths (low, moderate and high) of correlations can vary across studies – eg. validity studies, cognitive measurement studies, timeseries econometric studies, etc.