In general, they require the variables to have a Normal distribution. Parametric methods and statistics rely on a set of assumptions about the underlying distribution to give valid results. Techniques for a non-Normal distribution Parametric or non-parametric statistics? However, if the sample size is sufficiently large, the Central Limit Theorem allows use of the standard analyses and tools. Non-parametric techniques are available to use in such situations, but these are inevitably less powerful and less flexible. For example, there could be a long tail of responses to one side or the other (skewed data). This is always the case when the underlying distribution of the data is Normal, but in practice, the data may not be Normally distributed. Many techniques rely on the sampling distribution of the test statistic being a Normal distribution (see below). (See How to collect data for notes on types of data) What assumptions can – and can’t – you make? The type of data you have is also fundamental – the techniques and tools appropriate to interval and ratio variables are not suitable for categorical or ordinal measures. The analysis must relate to the research questions, and this may dictate the techniques you should use. Start to think about the techniques you will use for your analysis before you collect any data.
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