Testing for normality of distribution

In general the chi-squared test should be used only if the total number of observations is 50 or more and the individual expected frequencies are not less than 5. This is not a rigid rule a reference is given at the end of this chapter which discusses this point further. Other applications of the chi-squared test are also described in this reference. 

As has been emphasized in this chapter, many statistical tests assume that the data used are drawn from a normal population. One method of testing this assumption, using the chi-squared test, was mentioned in the previous section. Unfortunately, this method can only be used if there are 50 or more data points. It is common in experimental work to have only a small set of data. A simple visual way of seeing whether a set of data is consistent with the assumption of normality is to plot a cumulative frequency curve on special graph paper known as normal probability paper. This method is most easily explained by means of an example. 

Use normal probability paper to investigate whether the data below could have been drawn from a normal population  

Tabie 3.5 Data for normal probability paper example 

The Kolmogorov-Smirnov method is another method, which may, among other applications, be used to test for normality. The principle of the method involves comparing the sample cumulative distribution function with the 

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In terms of the statistical methods of the partial life cycle whole-effluent tests, survival, growth, and reproduction data from the 7 day cladoceran or fish exposure are often analyzed using hypothesis testing to determine acceptable concentrations. In order to determine the appropriateness of using parametric statistical methods, the data are first tested for normality of distribution and homogeneity of variance, for which the US EPA recommends the use of Shapiro-Wilk s test and Bartlett s test, respectively. Kolmogorov test for normality and Levine s test for homogeneity can be also used for these purposes. Dunnett s anova test is typically used for a... 

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