On the Effects of Non-Normality on the Distribution of the Sample Product-Moment Correlation Coefficient

Kowalski, Charles J.

doi:10.2307/2346598

Cited by 184 publications

(126 citation statements)

References 28 publications

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“…Kowalski, 1972;Habib et al, 2001;Serinaldi, 2008). In our case, the Gaussian distribution does not seem to describe very well the distribution of the random errors at short time-scales, while it is a reasonably good approximation at hourly and three-hourly scales.…”

Section: Random Componentcontrasting

confidence: 62%

Empirically based modelling of radar‐rainfall uncertainties for a C‐band radar at different time‐scales

Villarini

Krajewski

2009

Quart J Royal Meteoro Soc

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Radar-based estimates of rainfall are affected by several sources of systematic and random errors. The propagation of these uncertainties is required for improving the understanding and interpretation of the results obtained when radar-rainfall estimates are used as input or initial conditions. Despite the relevance of the problem, modelling of radar-rainfall uncertainties is still at an early stage. The authors apply an empirically based model in which the relation between true rainfall and radar-rainfall can be described as the product of a systematic distortion function (accounting for systematic biases) and random component (describing the remaining random errors). The proposed results are based on a large sample (more than six years) of data from a C-band radar (Wardon Hill) located in southwest England. The true ground rainfall is approximated by rain gauge measurements from a highly dense network deployed in the Brue catchment, located about 40 km from the radar site.The authors present results from their modelling of the radar-rainfall errors at four time-scales of hydrologic interest (5-and 15-minute, hourly and three-hourly) and 2 km spatial resolution, discussing the impact of spatial sampling errors on the proposed results.

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Section: Random Componentcontrasting

confidence: 62%

Empirically based modelling of radar‐rainfall uncertainties for a C‐band radar at different time‐scales

Villarini

Krajewski

2009

Quart J Royal Meteoro Soc

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“…Increasing the sample size does not eliminate the bias; indeed, it can actually exacerbate the problems produced by heteroskedasticity when using OLSE (Hayes, 1996;Long & Ervin, 2000). Although it is largely impossible to construct generalizable rules about the extent to which inferences from OLS regression are going to be affected by heteroskedasticity, the existing literature provides some guidance (e.g., Duncan & Layard, 1973;Edgell & Noon, 1984;Hayes, 1996;Kowalski, 1973;Long & Ervin, 2000;Rasmussen, 1989). First, relatively mild heteroskedasticity is not going to produce profound problems and is unlikely to swing the outcome of an analysis drastically one way or the other.…”

Section: What Is Heteroskedasticity and What Are Its Effects On Infermentioning

confidence: 99%

Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation

Hayes

Cai

2007

Behavior Research Methods

966

627

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“…However, the Pearson correlation coefficient is not robust to violations of the assumption of normality (e.g. Bishara & Hittner, 2012;Kowalski, 1972), and Osborne (2010) suggested that correlational analyses…”

Section: Distributions Of the Indicesmentioning

confidence: 99%

Indexing the approximate number system

2014

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Much recent research attention has focused on understanding individual differences in the Approximate Number System, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the Numerical Ratio Effect has poor testretest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or Numerical Ratio Effects.

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On the Effects of Non-Normality on the Distribution of the Sample Product-Moment Correlation Coefficient

Cited by 184 publications

References 28 publications

Empirically based modelling of radar‐rainfall uncertainties for a C‐band radar at different time‐scales

Empirically based modelling of radar‐rainfall uncertainties for a C‐band radar at different time‐scales

Using heteroskedasticity-consistent standard error estimators in OLS regression: An introduction and software implementation

Indexing the approximate number system

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