Yitzhaki (1996) showed that the OLS estimator of the slope coefficient in a simple regression is a weighted average of the slopes delineated by adjacent observations. The weights depend only on the distribution of the independent variable. In this paper I demonstrate that equal weights can only be obtained if and only if the independent variable is normally distributed. This characteristic is used to develop a new test for normality which is distribution free and not sensitive to outliers. The

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... est is compared with standard normality tests, in particular, the popular Jarque-Bera test. It is shown that the new test is a better power for testing normality against all classes of alternative distributions. Finally, the test is applied to check normality in time series data from major international financial markets.