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24 Jun 2010 distribution described by a few parameters (Normal distribution with mean µ and variance ?2). ? Nonparametric methods: do not make parametric assumptions. (most often based on ranks as opposed to raw values). ? We discuss non-parametric alternatives to the one and two sample t-tests. 3 / 30
Assumption of normality. Parametric tests assume that the data follows a particular distribution e.g for t-tests,. ANOVA and regression, the data needs to be normally distributed. Parametric tests are more powerful than non-parametric tests, when the assumptions about the distribution of the data are true. This means that they
7 Jun 2011 Assumptions. The statistic follows a t-distribution if the differences are normally distributed ? t-test = parametric method. Observations are made independent: selection of a patient does not influence chance of any other patient for inclusion. (Two sample t test): populations must have same variances.
Statistical reference is concerned two types of problem: Estimation of population parameters. Tests of hypotheses. When the data under analysis are met those assumptions for parametric tests, we should choose parametric tests because they are more powerful than non-parametric tests.
1. Nonparametric tests make less stringent demands ofthe data. a. For a parametric test to be valid, certain underlying assumptions must be met. i. example: For a paired t test, assume that: data are drawn ITomnormal distribution; every observation is independent of each other, and the SDs of the two populations are equal.
Determining the ex- act power for such a test would require defining both the type and the extent of the deviation from normality. In general, statistical tests used to detect deviations from normality or the violation of other parametric assumptions have low power. power as their parametric equiv- alents.
Nonparametric statistics (also called “distribution free statistics") are those that can describe some attribute of a population, test hypotheses about that attribute, its relationship with some other attribute, or differences on that attribute across populations , across time or across related constructs, that require no assumptions
Error Type, Power, Assumptions. Parametric vs. Nonparametric tests. Type-I & -II Error. Power Revisited. Meeting the Normality Assumption. - Outliers, Winsorizing, Trimming. - Data Transformation. 2. Parametric Tests. Parametric tests assume that the variable in question has a known underlying mathematical distribution
As discussed in Chapter 5, the t-test and the variance-ratio test make certain assumptions about the underlying population distribu- tions of the data on which they are used; for example that they are normal. Such tests are often called 'parametric' as these assump- tions are about population parameters. (Parameters are
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