Mean is better for testing of statistical significance through ANOVA.

Median is better for testing of statistical significance through Non Parametric Test.

Naturally, ANOVA assesses the arithmetic mean (arithmetic meanings) and the variability of the values of the modalities of the characters. This parameter test is based on the assumption of symmetry, that is, the normal distribution of the values of the variables. To evaluate the median most commonly used non-parametric tests: median test, an expanded median test .....

Mean. Median is usually used for small samples.

My view is the same as that of Kosta Sotiroski. However, I like to add that t test is used for testing single mean and two means, based on small sample/samples. In this cases, z test can be used if the sample (or samples) is (or are) large. ANOVA is used for testing more than two means.

The non-parametric tests for testing single median or two medians, based on small sample/samples, are run test, sign test arc sign test etc. In this case also, z test can be used if the sample (or samples) is (are) large.

@ Mirna Leko-Šimić, Mean and Median can be tested by small sample (or samples) as well as by large sample (samples). If the sample (or samples) is (are) large, z test is to be applied.

Dr. Dhritikesh can you please tell me the difference between Z test and ANOVA. I do not know.

What is the difference between T-test, F-Test and anova tests in statistics?

https://www.researchgate.net/post/What_is_the_difference_between_T-test_F-Test_and_anova_tests_in_statistics

ANOVA or F test is used to measure difference between variances but this not respect location of the mean.

Z test is used to difference between mean when researcher know the sigma ( SD of the population ) , old wrong concept in 1970 said if you make all tests on all sample then it means you can apply it to all population. A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known in order for an accurate z-test to be performed.

But the concept depends on probabilities not on samples.

Z test is used in design as design of 6 sigma (DFSS) , design of experiment , others.

@ Ashish Chauhan, Z denotes the standard normal variate. Z test is nothing but normality test. It is based on the area property of the standard normal distribution.

From the theory of normality approximation, it is known that if a data set is large (i.e. data size is more than 30) then the probability distribution of the data set can be approximated by normal probability distribution.

Again the distributions of chi-square statistic, t statistic etc. approach normal distribution as the respective degrees of freedom ( equivalently the respective data sizes) become large.

Hence, z test can be an alternative of the other tests if the data sizes are large.

On the other hand, ANOVA is not a test statistic but a statistical tool for testing the significance of differences among several means.

@ Khaled Almaz ,

t test is a statistical test, based on a test statistic known as t statistic, which is used to test a single mean or two means (regarding assumed values or regarding the difference) based on small random sample when the population standard deviation is unknown.

F test is a statistical test, based on a test statistic known as F statistic, which is used to test the difference between two standard deviations of two different populations based on small random samples from the two populations.

On the other hand, ANOVA is not a test statistic but a statistical tool for testing the significance of differences among several means.

@ Khaled Almaz ,

It is correct that F test is used to measure/test the difference between two population variances but not to measure/test the difference between two population means.

However, ANOVA is not used to measure/test the difference between two population variances. It is used to test the significance of differences among several (more than two) population means.

Thank you dear professor about the difference between F test and ANOVA.

ANOVA as a parametric test examines differences in the average values of two or more independent samples. (In Excel -Data Analysis you have options: ANOVA one factor, two or more modalities and two factors with multiple modalities where you have samples with or without replication). For the median examination, a median test or an expanded median test as a non-parametric test (in SPSS) is used.

@ Kosta Sotiroski ,

I am of the same view that for the median examination, a median test or an expanded median test as a non-parametric test (in SPSS) is used.