Kuliah Minggu ke-9 GGGB6323: Normality

Pensyarah: Dr. Jamil Ahmad, Fakulti Pendidikan UKM

  • Saiz sampel yang besar, secara langsung taburan data akan NORMAL!
  • Contoh permasalahan. Satu kajian terhadap prestasi pelajar MRSM di seluruh negara. Secara asasnya, prestasi pelajar MRSM adalah tinggi, dan perkara ini menjadikan data tidak bertabur secara normal. Namun, oleh kerana saiz sampel yang besar, persoalan kenormalan data boleh diketepikan kerana bagi sampel yang besar, data akan menjadi normal (Central Limit Theorem, CLT).
  • CLT menyatakan bahawa, “mean of sampling distribution of the mean is equal to the population mean. That tells you that repeated sampling will, over the long run, produce the correct mean.” [mean of sampling mean = mean population].
  • Dalam kes populasi pelajar MRSM seluruh negara yang tidak normal, tetapi, merujuk CLT, sampel tetap akan menjadi normal! Walauapapun bentuk taburan populasi, CLT menawarkan solusi yang menarik kepada pengkaji di mana taburan sampel pasti akan normal.
  • Dalam CLT, persampelan yang dilakukan secara teliti dan betul (jujur, mencukupi) dan mewakili populasi, mean bagi sampel dan populasi akan menjadi sama.
  • Std error (ralat piawai) dapat memberi petunjuk sama ada data yang diperolehi itu betul atau sebaliknya. Saiz sampel yang besar akan menyebabkan std error menjadi kecil! Namun, bermasalah bagi sampel yang kecil. Apapun, perkara ini dapat disokong dengan teori-teori tertentu (Don’t worry!).
  • Berikut kenyataan Pallant (2011) dalam perkara berkaitan:

Descriptives also provides some information concerning the distribution of scores on continuous variables (skewness and kurtosis). This information may be needed if these variables are to be used in parametric statistical techniques (e.g. t-tests, analysis of variance). The Skewness value provides an indication of the symmetry of the distribution. Kurtosis, on the other hand, provides information about the ‘peakedness’ of the distribution. If the distribution is perfectly normal, you would obtain a skewness and kurtosis value of 0 (rather an uncommon occurrence in the social sciences). Positive skewness values indicate positive skew (scores clustered to the left at the low values). Negative skewness values indicate a clustering of scores at the high end (right-hand side of a graph). Positive kurtosis values indicate that the distribution is rather peaked (clustered in the centre), with long thin tails. Kurtosis values below 0 indicate a distribution that is relatively fl at (too many cases in the extremes). With reasonably large samples, skewness will not ‘make a substantive difference in the analysis’ (Tabachnick & Fidell 2007, p. 80). Kurtosis can result in an underestimate of the variance, but this risk is also reduced with a large sample (200+ cases: see Tabachnick & Fidell 2007, p. 80). While there are tests that you can use to evaluate skewness and kurtosis values, these are too sensitive with large samples. Tabachnick and Fidell (2007, p. 81) recommend inspecting the shape of the distribution (e.g. using a histogram).” ~Pallant 2011~

 

“Skewness and kurtosis value giving information about the distribution of scores for the two groups. In the table labelled Tests of Normality, you are given the results of the Kolmogorov-Smirnov (and Shapiro-Wilk) statistic. This assesses the normality of the distribution of scores. A non-significant result (Sig. value of more than .05) indicates normality. In case, the Sig. value is .000, suggesting violation of the assumption of normality. This is quite common in larger samples.” ~Pallant 2011~

 

Rujukan Lanjut: Pallant, J. 2011. SPSS Survival Manual 4th Edition.

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