Monday, April 9, 2012

Menjalankan Ujikaji dengan Kaedah Analisis Varian (ANOVA)

Dalam melaksanakan projek ICC/KIK, kumpulan seharusnya boleh menentukan samada sesuatu punca masalah itu adalah punca sebenar atau tidak berdasarkan kepada ujikaji (eksperimen) yang dijalankan. Kaedah statistik yang sesuai dilaksanakan adalah dengan menggunakan ujikaji Analisis Varian. Sebagai contoh, salah satu punca masalah adalah dibawah faktor manusia: iaitu pengalaman pekerja menyumbang kepada berlaku peningkatan terhadap sesuatu masalah. Oleh itu, ujikaji Anova boleh dijalankan menerusi pengumpulan data terhadap pengalaman bekerja (X) dan peningkatan masalah (Y). Berikut adalah contoh ujikaji daripada ANOVA yang dijalankan. Ujian dianalisis dengan menggunakan software SPSS.

Let’s consider our research question from the Education studies example.  Do the standardized math test scores differ between students that passed the exam and students that failed the final exam? This question indicates that our independent variable is the exam result (fail vs.  pass) and our dependent variable is the score from the math test.  We must now check the assumptions.
First we examine the multivariate normality of the dependent variable.  We can check graphically either with a histogram (Analyze/Descriptive Statistics/Frequencies) and then in the menu Charts…)  

The ANOVA can be found in SPSS in Analyze/Compare Means/One Way ANOVA. The result consists of several tables.  The first table is the Levene Test or the Test of Homogeneity of Variances (Homoscedasticity).  The null hypothesis of the Levene Test is: the variances are equal.  The test in our example is significant with p = 0.000 < 0.05 thus we can reject the null hypothesis and cannot (!) assume that the variances are equal between the groups with variations.  Technically this means that the t-test with unequal variances is the right test to answer our research question.  However, we proceed with the ANOVA.

The next table presents the results of the ANOVA.  Mathematically, the ANOVA splits the total variance into explained variance (between groups) and unexplained variance (within groups), the variance is defined as Var(x) = sum of squares(x) / degrees of freedom(x).  The F-value, which is the critical test value that we need for the ANOVA is defined as F = Varb / Varw .

The ANOVA’s F-test of significance results in p < 0.001.  It tests the null hypothesis that the mean scores are equal; which is the same as saying that the independent variable has no influence on the dependent variable.  We can reject the null hypothesis and state that we can assume the mean scores to be different.
The last part of the output is the ANOVA’s Means Plot.  The means plot shows the marginal means for each group.  If several factors are included in the analysis the slope of the line between the marginal means indicates which variable has a stronger influence on the dependent variable.

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