Testing Assumptions of Normality and Equal Variances

Testing Assumptions of Normality and Equal Variances -...

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1 Testing Assumptions: Normality and Equal Variances So far we have been dealing with parametric hypothesis tests, mainly the different versions of the t -test. As such, our statistics have been based on comparing means in order to calculate some measure of significance based on a stated null hypothesis and confidence level. But is it always correct to compare means? No, of course not; parametric statistics, by definition, assume that the data we want to test are normally distributed, hence the use of the mean as the measure of central tendency. Sample data sets are often skewed to the right for various reasons, and if we cannot normalize the data we should not compare means (more on normalizing data sets later). In other words, in order to be consistent we need to formally test our assumptions of normality. Luckily this is very easy in MINITAB. For example, say we have a sample of fifty ( n = 50) excavated units and we are interested in the artifact density per unit. Before we think about comparing the data set to another sample (for example) we need to see if the data is normal. To do this we run our descriptive statistics as usual and produce some graphics: Descriptive Statistics Variable N Mean Median Tr Mean StDev SE Mean C1 50 6.702 5.679 6.099 5.825 0.824 Variable Min Max Q1 Q3 C1 0.039 25.681 2.374 9.886 30 20 10 0 10 5 0 C1 Frequency Histogram of C1, with Normal Curve In this case we see that the data set is skewed to the right, and looks more like an exponential distribution than a normal distribution. To test formally for normality we use either an
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This note was uploaded on 04/07/2012 for the course IBE 340 taught by Professor Valerieozaki during the Spring '09 term at Sophia University.

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Testing Assumptions of Normality and Equal Variances -...

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