Parametric vs Non-Parametric Tests: A Comparison Guide - Petroleum County Prevention


January 2023

If you don’t meet the sample size guidelines for the parametric tests and you are not confident that you have normally distributed data, you should use a nonparametric test. When you have a really small sample, you might not even be able to ascertain the distribution of your data because the distribution tests will lack sufficient power to provide meaningful results. Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. Non-parametric tests are “distribution-free” and, as such, can be used for non-Normal variables. 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.

Nonparametric algorithms are not based on a mathematical model; instead, they learn from the data itself. This makes them more flexible than parametric algorithms but also more computationally expensive. Nonparametric algorithms are most appropriate for problems where the input data is not well-defined or is too complex to be modelled using a parametric algorithm. It describes parametric vs nonparametric how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. For a statistical test to be valid, your sample size needs to be large enough to approximate the true distribution of the population being studied. Statistical tests assume a null hypothesis of no relationship or no difference between groups.

  1. Parametric algorithms are most appropriate for problems where the input data is well-defined and predictable.
  2. If you have a choice between a parametric and a non-parametric test that answer the same research question, compare the results and see if they are consistent or different.
  3. Parametric methods are statistical techniques that rely on specific assumptions about the underlying distribution of the population being studied.
  4. You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment, or through observations made using probability sampling methods.
  5. Non-parametric methods do not make any assumptions about the underlying distribution of the data.

To explore your data, you can use histograms, boxplots, or tests of normality and homogeneity of variance. If you have a choice between a parametric and a non-parametric test that answer the same research question, compare the results and see if they are consistent or different. Finally, if you have a choice between a parametric and a non-parametric test that answer different research questions, use the one that matches your research question better.

Nonparametric statistical tests: friend or foe?

Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis. The fundamentals of data science include computer science, statistics and math. It’s very easy to get caught up in the latest and greatest, most powerful algorithms —  convolutional neural nets, reinforcement learning, etc.

The types of variables you have usually determine what type of statistical test you can use. If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data. For example, the center of a skewed distribution, like income, can be better measured by the median where 50% are above the median and 50% are below. If you add a few billionaires to a sample, the mathematical mean increases greatly even though the income for the typical person doesn’t change. The next question is “what types of data are being measured?” The test used should be determined by the data.

How the Nonparametric Method Works

Thus, you are more likely to detect a significant effect when one truly exists. On the other hand, when we use SEM (structural equation modeling) to identify the model, it would be a nonparametric model – until we have solved the SEM. I think clustering algorithms would be nonparametric, unless we are looking for clusters of certain shape. Because due to the different number of effective parameters, as Aksakal pointed out, the accepted answer implies that Ridge and Lasso are non-parametric, but it doesn’t seem to be true. Effective parameters (effective degrees of freedom) are characteristics of a learning algorithm, but not a model itself. Originally I thought “parametric vs non-parametric” means if we have distribution assumptions on the model (similar to parametric or non-parametric hypothesis testing).

Conversely, nonparametric tests have strict assumptions that you can’t disregard. 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. 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.

Calculus for Machine Learning

But both of the resources claim “parametric vs non-parametric” can be determined by if number of parameters in the model is depending on number of rows in the data matrix. 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. Rather than assume that the earnings follow a normal distribution, she uses the histogram to estimate the distribution nonparametrically. The 5th percentile of this histogram then provides the analyst with a nonparametric estimate of VaR. 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.

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. 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. Consider for example, the heights in inches of 1000 randomly sampled men, which generally follows a normal distribution with mean 69.3 inches and standard deviation of 2.756 inches.

For a second example, consider a different researcher who wants to know whether average hours of sleep are linked to how frequently one falls ill. Because many people get sick rarely, if at all, and occasional others get sick far more often than most others, the distribution of illness frequency is clearly non-normal, being right-skewed and outlier-prone. Eventually, the classification of a method to be parametric completely depends on the presumptions that are made about a population. These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated. The decision often depends on whether the mean or median more accurately represents the center of your data’s distribution.

Can you solve 4 words at once?

Where f(X) is the unknown function to be estimated, β are the coefficients to be learned, p is the number of independent variables and X are the corresponding inputs. When you don’t need to make such an assumption about the underlying distribution of a variable, to conduct a hypothesis test, you are using a nonparametric test. Neural network — Neural networks are a type of machine learning algorithm that are used to model complex patterns in data. Neural networks are inspired by the workings of the human brain, and they can be used to solve a wide variety of problems, including regression and classification tasks. The test statistic tells you how different two or more groups are from the overall population mean, or how different a linear slope is from the slope predicted by a null hypothesis. 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.

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In an OLS regression, the number of parameters will always be the length of $\beta$, plus one for the variance. I am confused with the definition of non-parametric model after reading this link Parametric vs Nonparametric Models and Answer comments of my another question. This website is using a security service to protect itself from online attacks. There are several actions that could trigger this block including submitting a certain word or phrase, a SQL command or malformed data. These examples are programmatically compiled from various online sources to illustrate current usage of the word ‘parameter.’ Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors.

Statistical analysis plays a crucial role in understanding and interpreting data across various disciplines. Two prominent approaches in statistical analysis are Parametric and Non-Parametric Methods. While both aim to draw inferences from data, they differ in their assumptions and underlying principles. This article delves into the differences between these two methods, highlighting their respective strengths and weaknesses, and providing guidance on choosing the appropriate method for different scenarios.

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Parametric tests deal with what you can say about a variable when you know (or assume that you know) its distribution belongs to a “known parametrized family of probability distributions”. 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.

Nonparametric statistics, therefore, fall into a category of statistics sometimes referred to as distribution-free. Often nonparametric methods will be used when the population data has an unknown distribution, or when the sample size is small. The main advantage of non-parametric tests is that they are more robust and flexible than parametric tests, meaning that they can handle data that are skewed, have outliers, or have different scales or units. However, the main disadvantage of non-parametric tests is that they are less powerful and precise than parametric tests, meaning that they have a lower chance of detecting a true effect or difference if it exists.

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