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. You may have heard that you should use nonparametric tests when your data don’t meet the assumptions of the parametric test, especially the assumption about normally distributed data.
Parametric statistics
In this chapter, the authors describe what is the parametric and non-parametric tests in statistical data analysis and the best scenarios for the use of each test. It provides a guide for the readers on how to choose which of the test is most suitable for their specific research, including a description of the differences, advantages, and disadvantages of using the two types of tests. Before using the different statistical methods in R (see Chap. 6), the users need to understand the differences and conditions under which the various tests or methods are applied.
Parametric vs. Non-Parametric Tests: A Comprehensive Guide for Data Scientists
We will start off by discussing cases were parametric tests perform well then we will move on to discussing cases where nonparametric tests really shine. Different nonparametric tests work in different ways so it is difficult to make one broad statement about how all nonparametric tests work. That being said, there are a few key themes that appear over and over again as you look at different types of parametric tests. In total, 19,114 participants enrolled in the ASPREE study, 2,411 of whom were from the United States. After excluding 120 participants due to missing data, 1,141 were assigned to the Training & Validation set, and 1,150 were assigned to the Testing set for a total of 2,291 participants analyzed after accounting for missing data.
Reasons to Use Parametric Tests
- Then, participants were stratified into subgroups by risk quintile, with group 1 containing the fifth with lowest predicted risk, and group 5 containing the fifth with highest predicted risk.
- 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.
- We trained classification trees on 30 bootstraps of the augmented training and validation set (one on each bootstrap) to predict the primary composite outcome and provide confidence intervals.
- However, it is designed to distinguish recrudescence of reinfections and hence requires paired samples (i.e., two or more sample points for at least some patients).
While the bias is lowest from data generated from a conditional Poisson distribution (Figure 4), the bias remains similar if the data is generated from a conditional negative binomial distribution (Figures 5 and 6). However, the bias increases with increasing over-dispersion for unbalanced frequency distributions. Heuristic methods to estimate the distribution of MOI are typically biased; methods based on a solid statistical framework are preferable (Schneider, 2021).
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parametric vs nonparametric for a number of reasons. The main reason is that we are not constrained as much as when we use a parametric method. We do not need to make as many assumptions about the population that we are working with as what we have to make with a parametric method.
We trained classification trees on 30 bootstraps of the augmented training and validation set (one on each bootstrap) to predict the primary composite outcome and provide confidence intervals. In other words, a typical decision tree model for this method has 6 terminal nodes representing 6 groups in the data. We then selected the decision tree with median test accuracy as our representative model to partition the set aside test data into 6 leaves with different distributions of outcome, creating subgroups for assessing HTE.
However, there are several meaningful strategies to restrict oneself to a finite-dimensional parameter space. This, however, requires the additional assumption that infectious bites are rare and independent. A similar assumption is that MOI follows a positive negative binomial distribution and is hence characterized by two parameters (cf. Hill and Babiker, 1995; Schneider et al., 2022). The negative binomial distribution allows modeling https://www.1investing.in/ over-dispersion in the number of infectious bites. However, since the observations will tend to look under-dispersed (because only absence/presence rather than MOI is observed), one needs to estimate the amount of over-dispersion from an additional data source. A proposed alternative to conventional subgroup analysis is to create subgroups based on research participants’ baseline predicted risk of experiencing an event [3].
EX, JV, YW, AP, JF, DSR, RCS, and RT all participated in the design of the project and the critical writing and editing of the manuscript. JTN, RW, CXG, and JJM all participated in the critical writing and editing of the manuscript. The authors recognize the significant contributions made by the research participants, staff, and investigators for the ASPirin in Reducing Events in the Elderly clinical trial.
The reason is that nonparametric statistics discard some information that is available in the data, unlike parametric statistics. As a refresher, a parametric one-way ANOVA is a test you would run if you have three or more samples of data and you wanted to test whether the mean value in each sample of data is the same. The nonparametric version of the test more generally tests whether the distributions of the data in the different samples are the same. Next we will talk about the nonparametric equivalent to a standard two sample t-test.
The problem with these parametric tests is that they may be invalid if the underlying data is not actually normally distributed. Critical nonparametric tests include the Mann-Whitney U test and the Kruskal-Wallis test. The Mann-Whitney U test compares differences between two independent samples, offering an alternative to the t-test when data do not follow a normal distribution. The Kruskal-Wallis test, on the other hand, is a method for comparing more than two groups. It serves as the nonparametric counterpart to ANOVA, allowing for analysis without normality. Given that MOI in infections follows a conditional Poisson distribution, the non-parametric model introduced here performs almost as good as the conditional Poisson model (Schneider and Escalante, 2014) (the correct model in this case).
These tests are used when data distribution is unknown or when dealing with ordinal or nominal data that do not satisfy the normal distribution criteria. Given this framework, the resulting non-parametric model is more complicated than the corresponding Poisson model (cf. Schneider and Escalante, 2014), which falls into the class of exponential families (Hashemi and Schneider, 2024). This implies the usual desirable properties of maximum likelihood estimators for the Poisson model (existence and uniqueness of the MLE, efficiency, and consistency, cf. Hashemi and Schneider, 2024). Unfortunately, the non-parametric model is no longer within an exponential family and there is no proof for the same desirable theoretical properties. Namely, the MLE is the parameter choice for which the empirical prevalences coincide with the expected prevalences.
Decision tree follows an “if-then” format where conditions on variables are evaluated in sequence to determine the final prediction. We used a stratified sampling approach to ensure the sets retained a similar ratio of the composite outcome. In ASPREE, only about 10% of participants experienced the outcome by the end of the study. Machine learning techniques tend to learn more about the outcome type for which they have more examples.
These tests do not assume a specific distribution, making them adaptable to a broader range of data types and distributions. This versatility ensures that statistical analysis is accessible even when data are not perfectly aligned with the ideal conditions for parametric testing, thus maintaining the integrity and reliability of the analysis. Through nonparametric methods, researchers can confidently analyze data that would otherwise be challenging to interpret, ensuring no valuable insight is overlooked due to the limitations of the data’s distribution. The key difference between parametric and nonparametric test is that the parametric test relies on statistical distributions in data whereas nonparametric do not depend on any distribution. Non-parametric does not make any assumptions and measures the central tendency with the median value. In the first example, consider a financial analyst who wishes to estimate the value at risk (VaR) of an investment.
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. It’s very easy to get caught up in the latest and greatest, most powerful algorithms — convolutional neural nets, reinforcement learning, etc. The parametric test is the hypothesis test which provides generalisations for making statements about the mean of the parent population.
Although confidence intervals were wide, at least in part a consequence of the limited number of participants in the subgroups, the point estimate for the absolute risk reduction was greater in participants with a higher predicted risk by the decision tree model. We investigated non-parametric approaches (supervised machine learning models) as compared to a standard, semi-parametric approach for creating subgroups. To the best of our knowledge, non-parametric machine learning approaches have not been compared to the more widely utilized Cox proportional hazards model in terms of stratifying risk for discovery of potential treatment heterogeneity.
Master Kaplan-Meier Survival Analysis in R and unlock the secrets of time-to-event data analysis, empowering informed decisions. Explore our collection of articles on related statistical topics to discover more insights and elevate your data analysis skills. In an OLS regression, the number of parameters will always be the length of $\beta$, plus one for the variance. This is not disimilar to how the position and shape of graphs of quadratic functions of the following form depend only on the parameters of $a$, $h$, and $k$. The decision often depends on whether the mean or median more accurately represents the center of your data’s distribution.
Third, there is less data pre-processing required for the supervised machine learning models than the proportional hazards model. However, supervised machine learning models used in these analyses only predict occurrence of outcome while the proportional hazards model predicts time-to-event. In randomized clinical trials, treatment effects may vary, and this possibility is referred to as heterogeneity of treatment effect (HTE). One way to quantify HTE is to partition participants into subgroups based on individual’s risk of experiencing an outcome, then measuring treatment effect by subgroup.