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In this set of steps, readers will calculate either a parametric or a nonparametric statistical analysis, depending on whether the data for the dependent variable reflect a normal distribution. A parametric statistical procedure requires that its data be reflective of a normal curve whereas no such assumption is made in the use of a nonparametric procedure. Of the two types of statistical analyses, the parametric procedure is the more powerful one in ascertaining whether or not a statistically significant difference, in this case, exists. As such, parametric procedures are preferred over nonparametric procedures. When data are not normally distributed, however, parametric analyses may provide misleading and inaccurate results. According, nonparametric analyses should be used in cases where data are not reflective of a normal curve. In this set of steps, readers are provided with information on how to make the determination of normally or nonnormally distributed data. For detailed information regarding the assumptions underlying parametric and nonparametric procedures, readers are referred to the Hyperstats Online Statistics Textbook at http://davidmlane.com/hyperstat/ or to the Electronic Statistics Textbook (2011) at http://www.statsoft.com/textbook/
For this nonparametric independent samples t -test to be appropriately used, at least half of the standardized skewness coefficients and the standardized kurtosis coefficients must be outside the normal range (+/-3, Onwuegbuzie&Daniel, 2002). Research questions for which nonparametric independent samples t -tests are appropriate involve asking for differences in a dependent variable by group membership (i.e., only two groups are present for t -tests). The research question, “What is the difference between boys and girls in their science performance among middle school students?” could be answered through use of a nonparametric independent samples t -test.
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