# Parametric and Nonparametric Methods in Statistics

These hypothetical testing related to differences are classified as parametric and nonparametric tests.The parametric test is one which has information about the population parameter. B The Kruskal-Wallis test is used for comparing ordinal or non-Normal variables for more than two groups, and is a generalisation of the Mann-Whitney U test. C Analysis of variance is a general technique, and one version (one way analysis of variance) is used to compare Normally distributed variables for more than two groups, and is the parametric equivalent of the Kruskal-Wallistest.

Additionally, we will explore their main differences as well as their main advantages and disadvantages. Methods are classified by what we know about the population we are studying. Parametric methods are typically the first methods studied in an introductory statistics course. The basic idea is that there is a set of fixed parameters that determine a probability model. We will find out what the difference is between parametric methods and nonparametric methods. The way that we will do this is to compare different instances of these types of methods.

- Some examples of non-parametric tests include Mann-Whitney, Kruskal-Wallis, etc.
- Logistic regression — Logistic regression is used to predict the value of a target variable based on a set of input variables.
- It is a true non-parametric counterpart of the T-test and gives the most accurate estimates of significance especially when sample sizes are small and the population is not normally distributed.

Frequently used parametric methods include t tests and analysis of variance for comparing groups, and least squares regression and correlation for studying the relation between variables. All of the common parametric methods (“t methods”) assume that in some way the data follow a normal distribution and also that the spread of the data (variance) is uniform either between groups or across the range being studied. For example, the two sample t test assumes that the two samples of observations come from populations that have normal distributions with the same standard deviation. The importance of the assumptions for t methods diminishes as sample size increases. Alternative methods, such as the sign test, Mann-Whitney test, and rank correlation, do not require the data to follow a particular distribution. They work by using the rank order of observations rather than the measurements themselves.

An example of this type of data is age, income, height, and weight in which the values are continuous and the intervals between values have meaning. In contrast, well-known statistical methods such as ANOVA, Pearson’s correlation, t-test, and others do make assumptions about the data parametric vs nonparametric being analyzed. One of the most common parametric assumptions is that population data have a “normal distribution.” Hypothesis testing is one of the most important concepts in Statistics which is heavily used by Statisticians, Machine Learning Engineers, and Data Scientists.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship. One division that quickly comes to mind is the differentiation between descriptive and inferential statistics. There are other ways that we can separate out the discipline of statistics. One of these ways is to classify statistical methods as either parametric or nonparametric. Logistic regression — Logistic regression is used to predict the value of a target variable based on a set of input variables. It is often used for predictive modeling tasks, such as predicting the likelihood that a customer will purchase a product.

## Q. What is the difference between non-parametric method and distribution free method?

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## Calculus for Machine Learning

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test, which have fewer requirements but also make weaker inferences. Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis. The key differences between nonparametric and parametric tests are listed below based on certain parameters or properties. Consider a financial analyst who wishes to estimate the value-at-risk (VaR) of an investment. The analyst gathers earnings data from hundreds of similar investments over a similar time horizon.

## Data Structures and Algorithms

In hypothesis testing, statistical tests are used to check whether the null hypothesis is rejected or not rejected. These Statistical tests assume a null hypothesis of no relationship or no difference between groups. So, In this article, we will be discussing the statistical test for hypothesis testing including both parametric and non-parametric tests. Non-parametric methods do not make any assumptions about the underlying distribution of the data. Instead, they rely on the data itself to determine the relationship between variables. These methods are more flexible than parametric methods but can be less powerful.

## Choosing the Right Statistical Test Types & Examples

These tests are common, and therefore the process of performing research is simple. The term “nonparametric” is not meant to imply that such models completely lack parameters, but rather that the number and nature of the parameters are flexible and not fixed in advance. A histogram is an example of a nonparametric estimate of a probability distribution.

A parametric method would involve the calculation of a margin of error with a formula, and the estimation of the population mean with a sample mean. A nonparametric method to calculate a confidence mean would involve the use of bootstrapping. In a parametric model, the number of parameters is fixed with respect to the sample size. In a nonparametric model, the (effective) number of parameters can grow with the sample size. Parametric is a statistical test which assumes parameters and the distributions about the population are known.

It is used to determine whether the means are different when the population variance is known and the sample size is large (i.e, greater than 30). In other words, we need to learn a function that maps the input (i.e. the set of independent variables X) to the output (i.e. the target variable Y) as shown below. In one of my previous articles, I discussed the difference between prediction and inference in the context of Statistical Learning. Despite their main difference with respect to the end goal, in both approaches we need to estimate an unknown function f. The p-value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

Although this difference in efficiency is typically not that much of an issue, there are instances where we do need to consider which method is more efficient. I think if the model is defined as a set of equations (can be a system of concurrent equations or a single one), and we learn its parameters, then is parametric. That includes differential equations, and even Navier-Stokes’ equation.

Parametric tests, on the other hand, are based on the assumptions of the normal distribution and can be more powerful if the assumptions are met. Both types of tests have their own advantages and disadvantages, and it is important to understand the differences between them in order to choose the appropriate test for your data. Hope you know the difference between parametric and non-parametric tests now!

E There are a number of more advanced techniques, such as Poisson regression, for dealing with these situations. However, they require certain assumptions and it is often easier to either dichotomise the outcome variable or treat it as continuous. It is helpful to decide the input variables and the outcome variables. For example, in a clinical trial the input variable is the type of treatment – a nominal variable – and the outcome may be some clinical measure perhaps Normally distributed. However, if the input variable is continuous, say a clinical score, and the outcome is nominal, say cured or not cured, logistic regression is the required analysis.

The null hypothesis of both of these tests is that the sample was sampled from a normal (or Gaussian) distribution. Therefore, if the p-value is significant, then the assumption of normality has been violated and the alternate hypothesis that the data must be non-normal is accepted as true. I’ve been lucky enough to have had both undergraduate and graduate courses dedicated solely to statistics, in addition to growing up with a statistician for a mother. So this article will share some basic statistical tests and when/where to use them.

Some examples of non-parametric tests include Mann-Whitney, Kruskal-Wallis, etc. Parametric and non-parametric methods offer distinct advantages and limitations. Understanding these differences is crucial for selecting the most suitable method for a specific analysis.