# parametric and non parametric test

Parametric tests and non-parametric tests are two types of statistical hypothesis tests used to make inferences about a population based on a sample. The choice of which test to use depends on the type of data and assumptions made about the population.

Parametric tests assume that the data being analyzed follows a specific distribution, usually the normal distribution. These tests make specific assumptions about the population parameters, such as mean and standard deviation, and use these parameters to make inferences about the population. Examples of parametric tests include t-tests, ANOVA, and regression analysis.

Non-parametric tests, on the other hand, do not make any assumptions about the population distribution or parameters. These tests are often used when the data is not normally distributed or when sample sizes are small. Non-parametric tests rely on the rank order of the data rather than the actual values of the data. Examples of non-parametric tests include the Wilcoxon rank-sum test, Kruskal-Wallis test, and Mann-Whitney U test.

In general, parametric tests are more powerful than non-parametric tests when the assumptions about the population are met. However, if these assumptions are violated, non-parametric tests may be more appropriate.

## Which are parametric tests?

Parametric tests are statistical tests that assume that the data being analyzed follows a specific distribution, usually the normal distribution. These tests make specific assumptions about the population parameters, such as mean and standard deviation, and use these parameters to make inferences about the population.

Examples of parametric tests include:

1. T-tests: used to compare the means of two groups.
2. ANOVA (Analysis of Variance): used to compare the means of three or more groups.
3. Regression analysis: used to examine the relationship between a dependent variable and one or more independent variables.
4. Pearson correlation: used to measure the strength and direction of the linear relationship between two continuous variables.
5. Parametric survival analysis: used to analyze survival data and estimate the survival function of a population.

It is important to note that parametric tests are based on assumptions about the population, and if these assumptions are not met, the results of the tests may not be accurate. In such cases, non-parametric tests may be more appropriate.

## What is the difference between parametric and nonparametric tests?

The main difference between parametric and nonparametric tests is the assumptions they make about the population from which the data is sampled.

Parametric tests assume that the data follows a specific distribution, usually the normal distribution, and make assumptions about the population parameters, such as mean and variance. These tests require that the data meet certain criteria, such as being normally distributed and having equal variances, in order to produce valid results. Examples of parametric tests include t-tests, ANOVA, and regression analysis.

Nonparametric tests, on the other hand, do not make any assumptions about the population distribution or parameters. Instead, they use the ranks of the data rather than the actual values to make statistical inferences. Nonparametric tests are often used when the data does not meet the assumptions of parametric tests, such as when the data is not normally distributed or when the sample size is small. Examples of nonparametric tests include the Wilcoxon rank-sum test, Kruskal-Wallis test, and Mann-Whitney U test.

Overall, the choice of whether to use a parametric or nonparametric test depends on the type of data and assumptions made about the population. Parametric tests are more powerful when the assumptions are met, but nonparametric tests are more robust when the assumptions are violated.

## What are parametric test examples?

Parametric tests are statistical tests that assume that the data being analyzed follows a specific distribution, usually the normal distribution. These tests make specific assumptions about the population parameters, such as mean and standard deviation, and use these parameters to make inferences about the population. Here are some examples of parametric tests:

1. t-Tests: used to compare the means of two groups.
2. ANOVA (Analysis of Variance): used to compare the means of three or more groups.
3. Regression analysis: used to examine the relationship between a dependent variable and one or more independent variables.
4. Pearson correlation: used to measure the strength and direction of the linear relationship between two continuous variables.
5. One-way ANOVA: used to compare means across three or more independent groups.
6. Paired t-test: used to compare the means of two related groups.
7. Analysis of Covariance (ANCOVA): used to compare means across two or more independent groups, controlling for the effects of one or more covariates.
8. Multivariate Analysis of Variance (MANOVA): used to compare means across two or more independent groups on two or more dependent variables.

It is important to note that parametric tests have certain assumptions that must be met in order to produce valid results. If the data does not meet these assumptions, nonparametric tests may be more appropriate.

## What is parametric test and t-test?

A parametric test is a statistical test that assumes that the data being analyzed follows a specific distribution, usually the normal distribution. These tests make specific assumptions about the population parameters, such as mean and standard deviation, and use these parameters to make inferences about the population.

The t-test is a common parametric test used to determine whether there is a significant difference between the means of two groups. The test assumes that the data is normally distributed and has equal variances. There are two types of t-tests: the independent samples t-test and the paired samples t-test.

The independent samples t-test is used to compare the means of two independent groups. For example, it can be used to compare the mean test scores of two different groups of students. The test compares the difference between the means of the two groups to the variability within the groups. If the difference is larger than expected due to chance, the result is considered statistically significant.

The paired samples t-test is used to compare the means of two related groups. For example, it can be used to compare the mean test scores of the same group of students before and after a teaching intervention. The test compares the differences between the paired values to the variability within the pairs. Again, if the difference is larger than expected due to chance, the result is considered statistically significant.

It is important to note that t-tests have certain assumptions that must be met in order to produce valid results. If the data does not meet these assumptions, nonparametric tests may be more appropriate.

## Is Chi Square a parametric test?

The chi-square test is a non-parametric test that is used to determine if there is a significant association between two categorical variables. It does not assume any particular distribution for the data, unlike parametric tests that assume the data follows a specific distribution, usually the normal distribution.

The chi-square test compares the observed frequencies of the data to the expected frequencies under the null hypothesis of no association between the variables. If the observed frequencies are significantly different from the expected frequencies, the test rejects the null hypothesis and concludes that there is a significant association between the variables.

There are different types of chi-square tests, such as the chi-square goodness of fit test and the chi-square test of independence, each used for different purposes.

In summary, the chi-square test is a non-parametric test, and it does not require the data to follow a specific distribution.

## Is ANOVA a parametric test?

Yes, ANOVA (Analysis of Variance) is a parametric test that assumes that the data being analyzed follows a normal distribution. It is used to compare the means of three or more groups to determine if there is a statistically significant difference between them.

ANOVA assumes that the populations from which the samples are drawn have equal variances, and that the observations within each group are independent and identically distributed. The test compares the variance between the groups to the variance within the groups. If the variance between the groups is significantly larger than the variance within the groups, the test concludes that there is a significant difference between the means of the groups.

There are different types of ANOVA tests, such as one-way ANOVA, two-way ANOVA, and repeated measures ANOVA, each used for different purposes. It is important to note that ANOVA has certain assumptions that must be met in order to produce valid results. If the data does not meet these assumptions, nonparametric tests, such as the Kruskal-Wallis test, may be more appropriate.

## What are the 4 parametric tests?

There are many different types of parametric tests, but here are four common ones:

1. t-Test: used to determine if there is a significant difference between the means of two groups.
2. Analysis of Variance (ANOVA): used to determine if there is a significant difference between the means of three or more groups.
3. Pearson correlation: used to measure the strength and direction of the linear relationship between two continuous variables.
4. Regression analysis: used to examine the relationship between a dependent variable and one or more independent variables.

It is important to note that these tests make certain assumptions about the data, such as the normality of the distribution and homogeneity of variance, and if these assumptions are not met, non-parametric tests may be more appropriate. Additionally, there are other parametric tests that may be used for specific situations or types of data.

## What are the 4 non-parametric tests?

Here are four common non-parametric tests:

1. Mann-Whitney U test: used to determine if there is a significant difference between the medians of two independent groups.
2. Wilcoxon signed-rank test: used to determine if there is a significant difference between the medians of two related groups.
3. Kruskal-Wallis test: used to determine if there is a significant difference between the medians of three or more independent groups.
4. Spearman correlation: used to measure the strength and direction of the monotonic relationship between two continuous or ordinal variables.

Non-parametric tests are used when the data do not meet the assumptions of normality or equal variance that are required for parametric tests. Non-parametric tests can also be used when the data are ordinal or ranked, rather than continuous. However, non-parametric tests may have less power than parametric tests, meaning they may have a harder time detecting significant differences or relationships in the data.

## Why is chi-square non-parametric?

The chi-square test is considered a non-parametric test because it does not make any assumptions about the underlying distribution of the data being analyzed. In other words, it does not assume that the data comes from a specific probability distribution, such as the normal distribution.

Instead, the chi-square test is used to test for associations or differences between categorical variables, which are discrete and not continuous, making it a non-parametric method. The test examines the observed frequencies in a contingency table and compares them to the expected frequencies, assuming that there is no association between the variables under investigation.

The test statistic is calculated by summing the squared differences between observed and expected frequencies, and dividing by the expected frequencies. This test statistic follows a chi-square distribution, which is a theoretical distribution that describes the sampling distribution of the test statistic. However, this distribution is derived using assumptions about the sample size and independence of observations, rather than assumptions about the underlying data distribution. Therefore, the chi-square test is a non-parametric test.

## Is one sample z test parametric?

Yes, the one-sample z-test is a parametric test that is used to test a hypothesis about the population mean of a normally distributed variable when the population standard deviation is known. It assumes that the data being analyzed comes from a normal distribution.

In a one-sample z-test, the sample mean is compared to a known population mean, and the test statistic is calculated as the difference between the sample mean and the population mean, divided by the standard error of the mean. The resulting test statistic follows a standard normal distribution, which is a theoretical distribution that describes the sampling distribution of the test statistic.

However, it is important to note that the one-sample z-test has certain assumptions that must be met in order to produce valid results, such as the normality of the distribution and known population standard deviation. If these assumptions are not met, non-parametric tests or alternative parametric tests may be more appropriate.