A Proposed Distribution-Free Test For Symmetry of Grouped Data | ||||
| Computational Journal of Mathematical and Statistical Sciences | ||||
| Volume 3, Issue 2, November 2024, Page 417-431 PDF (346.04 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/cjmss.2024.288527.1052 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Mahmoud Eltehiwy  1; Abu Bakr Abdul-Motaal2
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| 1statistics department, the Politics and Economics faculty, Beni -Suef university, Egypt | ||||
| 2Faculty of Commerce, Department of Statistics, South Valley University, Egypt. | ||||
| Abstract | ||||
| This paper introduces a new, straightforward test for analyzing the symmetry of data represented in frequency distributions. Unlike other methods, this test doesn't require any assumptions about the underlying statistical distribution of the data. The only prerequisite is that the data has equal-sized categories (bins) and none of these categories have a frequency of zero. This makes the test both statistically robust and computationally efficient. In simpler terms, the test offers a user-friendly way to assess whether a data set leans towards one side or the other (positive or negative skew) without relying on specific statistical models. The test relies on a statistic denoted by G, which was introduced by \cite{Eltehiwy}. We introduce and study the properties of G statistic and obtain its mean and variance. We explore the Asymptotic distribution of the G Statistic. Finally, a worked example and a practical example is presented to illustrate how the test is implemented. | ||||
| Keywords | ||||
| Asymptotic normal distribution; distribution-free test; skewness; symmetry | ||||
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