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Descriptive statistics are those that characterise samples without attempting to draw conclusions. The purpose of them is to help investigators to form an understanding of what the data might be capable of telling them. Descriptive statistics include graphs as well as measures of location, scale, correlation, and so on.
Parametric statistics are those that are based on probabilistic models (ie, mathematical models involving probability) that involve parameters. For instance, an investigator might assume that her results have come from a population that is normally distributed with a certain mean and standard deviation; this would be a parametric model. She could estimate this pair of parameters, the mean and standard deviation, using parametric statistics, or test hypotheses about them, again using parametric statistics. In either case the parametric statistics she uses would be based on the parametric mathematical model she has chosen for her data.
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The simplest answer is that parametric statistics are based on numerical data from which descriptive statistics can be calculated, while non-parametric statistics are based on categorical data. Takes two example questions: 1) Do men live longer than women, and 2), are men or women more likely to be statisticians. In the first example, you can calculate the average life span of both men and women and then compare the two averages. This is a parametric test. But in the second, you cannot calculate an average between "man" and "woman" or between "statistician" or "non-statistician." As there is no numerical data to work with, this would be a non-parametric test. The difference is vitally important. Because inferential statistics require numerical data, it is possible to estimate how accurate a parametric test on a sample is compared to the relevant population. However, it is not possible to make this estimation with non-parametric statistics. So while non-parametric tests are still used in many studies, they are often regarded as less conclusive than parametric statistics. However, the ability to generalize sample results to a population is based on more than just inferential statistics. With careful adherence to accepted random sampling, sample size, and data collection conventions, non-parametric results can still be generalizable. It is just that the accuracy of that generalization can not be statistically verified.
nominal and ordinal
Discuss the importance of descriptive statistics
descriptive statistics