{"id":23023,"date":"2025-12-14T21:46:21","date_gmt":"2025-12-14T21:46:21","guid":{"rendered":"https:\/\/scientificassociation.org\/?post_type=journal-paper&#038;p=23023"},"modified":"2025-12-14T21:46:21","modified_gmt":"2025-12-14T21:46:21","slug":"a-proposed-distribution-free-test-for-symmetry-of-grouped-data","status":"publish","type":"journal-paper","link":"https:\/\/scientificassociation.org\/ar\/journal-paper\/a-proposed-distribution-free-test-for-symmetry-of-grouped-data\/","title":{"rendered":"A Proposed Distribution-Free Test For Symmetry of Grouped Data"},"content":{"rendered":"<div class=\"padding_abstract justify ltr\">This paper introduces a new, straightforward test for analyzing the symmetry of data represented in frequency distributions. Unlike other methods, this test doesn&#8217;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.<\/div>\n","protected":false},"featured_media":23022,"template":"","meta":{"_acf_changed":false},"journal-name":[218],"paper-tag":[224,226],"class_list":["post-23023","journal-paper","type-journal-paper","status-publish","has-post-thumbnail","hentry","journal-name-cjmss","paper-tag-no-2","paper-tag-vol-3"],"acf":[],"_links":{"self":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/journal-paper\/23023","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/journal-paper"}],"about":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/types\/journal-paper"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/media\/23022"}],"wp:attachment":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/media?parent=23023"}],"wp:term":[{"taxonomy":"journal-name","embeddable":true,"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/journal-name?post=23023"},{"taxonomy":"paper-tag","embeddable":true,"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/paper-tag?post=23023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}