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Difference between Parametric and Non Parametric Statistics – Key Differences | Statistical Analysis

Difference between Parametric and Non Parametric Statistics

Parametric Statistics

Parametric statistics is a branch of statistics which assumes that the data have come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well known elementary statistical methods are parametric. 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.

Generally speaking, parametric methods make more assumptions than non-parametric methods. If those extra assumptions are correct, parametric methods can produce more accurate and precise estimates. They are said to have more statistical power. However, if assumptions are incorrect, parametric methods can be very misleading. For that reason they are often not considered robust. On the other hand, parametric formulae are often simpler to write down and faster to compute. In some cases, but not all, their simplicity makes up for their non-robustness, especially if care is taken to examine diagnostic statistics.

Non-parametric Statistics

Non-parametric statistics are statistics not based on parameterized families of probability distributions. They include both descriptive and inferential statistics. The typical parameters are the mean, variance, etc. Unlike parametric statistics, nonparametric statistics make no assumptions about the probability distributions of the variables being assessed. 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. Note that the non parametric model is not none-parametric: parameters are determined by the training data, not the model.

Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of measurement, non-parametric methods result in “ordinal” data.

There are two types of test data and consequently different types of analysis. As the table below shows, parametric data has an underlying normal distribution which allows for more conclusions to be drawn as the shape can be mathematically described. Anything else is non-parametric.

The key Difference between Parametric and Non Parametric Statistics are as Follows: 

Basis

Parametric Statistics Non Parametric Statistics

Assumed Distribution

Normal Any

Assumed Variance

Homogeneous Any

Typical Data

Ratio or Interval Ordinal or Nominal

Data Set Relationships

Independent Any

Usual Central Measure

Mean Median

Benefits

Can draw more conclusions Simplicity; Less affected by outliers

Tests

Choosing

Correlation Test

Pearson Spearman

Independent Measures, 2 Groups

Independent Measures t-test Mann-Whitney test

Independent Measures, >2 Groups

One-way, Independent- measures ANOVA Kruskal-Wallis test

Repeated Measures, 2 Conditions

Matched-pair t-test Wilcoxon test

Repeated Measures, >2 Conditions

One-way Repeated measures ANOVA Friedman’s test
Smirti

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