statistical tools for data analysis and interpretation

Standard error is inversely related to sample size, so the larger your sample, the smaller the standard error, and the greater chance you will have of identifying statistically significant results in your analysis.

The smaller the sample size, the less you can get out of your data. How much can you expect to get out of your data? In practice, this can be applied to test statistics calculated from more than 30 observations. Central limit theoremĪs the sample size increases, the shape of the sampling distribution of the test statistic tends to become Normal, even if the distribution of the variable which is being tested is not Normal. when the sample size is small (below 30 observations). Non-parametric techniques must be used for categorical and ordinal data, but for interval & ratio data they are generally less powerful and less flexible, and should only be used where the standard, parametric, test is not appropriate – e.g. 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.

Statistical tools for data analysis and interpretation