- In Descriptive statistics, functions of the sample data that are intrinsically interesting in describing some feature of the data. Classic descriptive statistics includes mean, min, max, standard deviation, median, skew, kurtosis.It gives information that describes the data in some manner.
- In Inferential statistics, a function of the sample data that assists you to draw an inference regarding a hypothesis about a population parameter. Classic inferential statistics includes z, t, χ2, F-ratio, etc. It makes inferences about populations using data drawn from the population instead of using the entire population to gather the data
If there is no knowledge about the population or paramters, but still it is required to test the hypothesis of the population. Then it is called non-parametric test. Eg: mann-Whitney, rank sum test, Kruskal-Wallis test
The difference between parametric model and non-parametric model is that the former has a fixed number of parameters, while the latter grows the number of parameters with the amount of training data.
In other words, we want to know if we have relationships, associations, or differences within our data and whether statistical significance exists. Inferential statistics help us make these determinations and allow us to generalize the results to a larger population. We provide background about parametric and nonparametric statistics and then show basic inferential statistics that examine associations among variables and tests of differences between groups.
In the world of statistics, distinctions are made in the types of analyses that can be used by the evaluator based on distribution assumptions and the levels of measurement data. For example, parametric statistics are based on the assumption of normal distribution and randomized sampling that results in interval or ratio data. The statistical tests usually determine significance of difference or relationships. These parametric statistical tests commonly include t-tests, Pearson product-moment correlations, and analyses of variance.
Nonparametric statistics are known as distribution-free tests because they are not based on the assumptions of the normal probability curve. Nonparametric statistics do not specify conditions about parameters of the population but assume randomization and are usually applied to nominal and ordinal data. Several nonparametric tests do exist for interval data, however, when the sample size is small and the assumption of normal distribution would be violated.
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