Choosing the Right Statistical Test Types & Examples

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. Many of these nonparametric methods are easy to apply and to understand. The t-statistic test holds on the underlying hypothesis, which includes the normal distribution of a variable. For finding the sample from the population, population variance is identified. It is hypothesized that the variables of concern in the population are estimated on an interval scale. Although nonparametric statistics have the advantage of having to meet few assumptions, they are less powerful than parametric statistics.

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. Linear regression — Linear 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 sales volume of a product based on historical sales data. Familiar clinical examples include blood pressure, ejection fraction, forced expiratory volume in 1 second (FEV1), serum cholesterol, and anthropometric measurements.

  1. The way that we will do this is to compare different instances of these types of methods.
  2. It is also a kind of hypothesis test, which is not based on the underlying hypothesis.
  3. However, the inferences they make aren’t as strong as with parametric tests.
  4. 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.

Nonparametric tests are also less sensitive to outliers, which can have a significant impact on the results of parametric tests. Nonparametric tests and parametric tests are two types of statistical tests that are used to analyze data and make inferences about a population based on a sample. Nonparametric tests are used when the data do not follow a normal distribution or when the assumptions of parametric tests are not met.

The next question is «what types of data are being measured?» The test used should be determined by the data. The choice of test for matched or paired data is described in Table 1 and for independent data in Table 2. A neural net with fixed architecture and no weight decay would be a parametric model. 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 $k$. It uses F-test to statistically test the equality of means and the relative variance between them.

What Is the Nonparametric Method?

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Statistics: Parametric and non-parametric tests

In the case of the non-parametric test, the test is based on the differences in the median. If the independent variables are non-metric, the non-parametric test is usually performed. One of the main drawbacks is that they are generally less powerful than parametric tests, which means that they may not be able to detect small but significant differences between groups. Nonparametric tests also tend to have less precise estimates of the population parameters and may not provide as much information about the relationships between variables as parametric tests. Parametric methods are statistical techniques that rely on specific assumptions about the underlying distribution of the population being studied.

Comparison tests

If you have any concerns regarding content you should seek to independently verify this. 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. 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.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests. Rank methods can generate strong views, with some people preferring them for all analyses and others believing that they have no place in statistics. We believe that rank methods are sometimes useful, but parametric methods are generally preferable as they provide estimates and confidence intervals and generalise to more complex analyses. Non-parametric methods are statistical techniques that do not rely on specific assumptions about the underlying distribution of the population being studied. These methods are often referred to as “distribution-free” methods because they make no assumptions about the shape of the distribution.

When the p-value falls below the chosen alpha value, then we say the result of the test is statistically significant. T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults). Connect and share knowledge within a single location that is structured and easy to search. This website is using a security service to protect itself from online attacks.

I think that the word «effective» in the accepted answer should be deleted. 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.


This means that they may not show a relationship between two variables when in fact one exists. To make a choice between parametric and the nonparametric test is not easy for a researcher conducting statistical analysis. The t-statistic rests on the underlying assumption that there is the normal distribution of variable and the mean in known or assumed to be known. It is assumed that the variables of interest, in the population are measured on an interval scale. Why do we need both parametric and nonparametric methods for this type of problem? Many times parametric methods are more efficient than the corresponding nonparametric methods.

If you want to know more about statistics, methodology, or research bias, make sure to check out some of our other articles with explanations and examples. However, a non-parametric test (sometimes referred to as a distribution free test) does not assume anything about the underlying distribution (for example, that the data comes from a normal (parametric distribution). In Statistics, a parametric test is a kind of hypothesis test which gives generalizations for generating records regarding the mean of the primary/original population. The t-test is carried out based on the students’ t-statistic, which is often used in that value. Where n1 is the sample size for sample 1, and R1 is the sum of ranks in Sample 1. It is also known as the “Goodness of fit test” which determines whether a particular distribution fits the observed data or not.

Peter Westfall is a distinguished professor of information systems and quantitative sciences at Texas Tech University. He specializes in using statistics in investing, technical analysis, and trading. A. The 4 non-parametric tests are wilcoxon signed-rank test, mann-Whitney U test, kruskal-Wallis test and spearman correlation coefficient. This test is used for comparing two or more independent samples of equal or different sample sizes. Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

PCA would be parametric, because the equations are well defined, but CCA can be nonparametric, because we are looking for correlations across all variables, and if these are Spearman’s correlations, we have a nonparametric model. I think clustering algorithms would be nonparametric, unless we are looking for clusters of certain shape. Originally I thought «parametric vs non-parametric» means if we have distribution assumptions on the model (similar to parametric or non-parametric hypothesis testing). 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.

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. If there is no difference between the expected and observed frequencies, then the value of chi-square is equal to zero. An F-test is regarded as a comparison of equality of sample variances.

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 parametric vs nonparametric the sample size is small. Nonparametric tests are particularly useful when the sample size is small or the data are skewed or ordinal, as they are more forgiving of deviations from the assumptions of parametric tests.

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. Table 3 shows the non-parametric equivalent of a number of parametric tests. Statistical analysis plays a crucial role in understanding and interpreting data across various disciplines.


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