Detection of Non-Normality in Data Sets and Comparison between Different Normality Tests

Abstract

The paper provides five tests of data normality at different sample sizes. The tests are the Shapiro-Wilk (SW) test, Anderson-Darling (AD) test, Kolmogorov-Smirnov (KS) test, Ryan-Joiner (RJ) test, and Jarque-Bera (JB) test. These tests were used to test for normality for two secondary data sets with sample size (155) for large and (40) for small; and then test the simulated scenario with standard normal “N(0,1)” data sets; where the large samples of sizes (150, 140, 130, 130, 110 and 100) and small samples of sizes (40. 35, 30, 25, 20, 15 and 10) are considered at two levels of significance (5% and 10%). However, the aim of this paper is to detect and compare the performance of the different normality tests considered. The normality test results shows Kolmogorov-Smirnov (KS) test is a most powerful test than other tests since it detect the simulated large sample data sets do not follow a normal distribution at 5%, while for small sample sizes at 5% level of significance; the results showed the Jarque-Bera (JB) test is a most powerful test than other tests since it detects that the simulated small sample data do not follow a normal distribution at 5%. This paper recommended JB test for normality test when the sample size is small and KS test when the sample size is large at 5% level of significance.

The effects of digital innovations and sustainable supply chain management on business competitive performance post-COVID-19

“…Besides, the data are appropriate and fulfill the statistical conjectures (Hair et al, 2017). Besides, the data normality in this research was analyzed using the Kolmogorov Smirnov which was insignificant and thus reveals the data normality (Biu et al, 2020). Thus, relationships among dependent and independent factors were computed employing coefficient of Pearson.…”

“…, 2017). Besides, the data normality in this research was analyzed using the Kolmogorov Smirnov which was insignificant and thus reveals the data normality (Biu et al. , 2020).…”

Eksplorasi Variabel Pembangunan Berkelanjutan untuk Indeks Desa Membangun Pulau Jawa.

“…Normalisasi data dengan membuang data outlier tidak dilakukan dalam metode probabilistik ini, karena dikhawatirkan akan mengurangi sampel yang digunakan, sehingga hasil yang didapatkan tidak menggambarkan desa-desa di Pulau Jawa. Pengujian distribusi data ini menggunakan jumlah sampel sejumlah 84 untuk masing-masing tahun penelitian, dengan 31 variabel awal (yang kemudian diberi nama X1, X2 dan seterusnya sesuai urutan), dengan tingkat signifikansi 5%, sehingga data yang dianggap normal harus memiliki nilai signifikansi Kolmogorov-Smirnov lebih besar dari 0,05 (Biu, Nwakuya, & Wonu, 2020). Tahapan terakhir dalam analisis faktor adalah pengujian terhadap kestabilan dan konsistensi faktor yang terbentuk.…”

“…Data yang tidak normal kemudian dilakukan transformasi data. Hasil dari transformasi data terdapat delapan variabel berdistribusi normal ditandai dengan nilai signifikansi Kolmogorov-Smirnov di atas 0,05 (Biu, Nwakuya, & Wonu, 2020;Blain, 2014) Guna mengeksplorasi kemungkinan yang muncul, maka peneliti melakukan sejumlah analisis faktor dengan menggunakan beberapa gabungan variabel yang berdistribusi normal. Hasil uji tersebut ditunjukkan dalam tabel 3.…”

Design of a Test for Detecting the Presence of Impulsive Noise

“…Furthermore, the K-S test is used in a multiple-input multiple-output (MIMO) system for blind identification of spatial multiplexing and Alamouti space-time block code based on the correlation property of adjacent samples in [19]. In a previous study [22], the performance of normality tests for non-normal data with the various tests are compared. Their simulation results indicate that the K-S test is the most powerful test when the sample size is large (>100).…”