Dear Professor Muayyad Ahmad

its very good question . 

in fact the matter is related only when we are analyzing the data  manually only but in spss we are dealing with it as parametric statistics 

you may go throw parametric and nonparametric statistics shaskin book  then u will get answer of ur question

with worm regards  

Nonparametric and parametric are misleading terms, as some statistical tests that are believed to be nonparametric (such as the Wilcoxon Mann-Whitney) are parametric, and some, like Cox regression, are both parametric and nonparmetric!

All statistical tests are signal-to-noise ratios. The measure of signal-to-noise varies by test. t-statistics, for example, can be positive or negative (depending on the sign of the effect) but F statistics are not (F is t-squared, so it's always positive). 

The interpretation of the test statistic depends on its definition, so there is no general answer to your question, I'm afraid. 

The idea with "significance" is whether or not a statistic corresponds to a p-value below a given level.  The word "significance" is often misleading because the effect size may not be substantial. Setting one level for all cases, usually 0.05, is a bad idea, because the p-value is a function of sample size.  An isolated p-value is rather meaningless. A power/type II error analysis or other sensitivity analysis is needed. If you can use a confidence interval, even if you have to use Tschebychev's inequality, you are generally much better situated to make informed, practical decisions. 

Parametric tests generally have more "power," because they generally make fuller use of the available information. But they also make assumptions. A distribution-free test generally, say a rank, or more infamously, a sign test in general, will not use available information fully, but also does not make distributional assumptions. They thus have lower 'power.'  

Note that the consideration of power should not just be for a consideration when picking a test. It is important to know for a given outcome to go with a given 'achieved' p-value.   

Thanks for all scholars who tried to answer the question. However, no one have answered the question yet.!!

Precisely what tests/test statistics are you referencing?  As my first sentence said: the idea with a p-value is whether or not you are below a threshold (which should be determined using power).  The statistics you reference being above or below a level must both correspond to "below" for p, or you could be looking at an error in a textbook. 

I don't understand your propositions?

Critical values for a test of hypothesis depend upon a test statistic, which is specific to the type of test, and the significance level, α, which defines the sensitivity of the test. A value of α = 0.05 implies that the null hypothesis is rejected 5 % of the time when it is in fact true. The choice of α in practice usually has values of 0.1, 0.05, and 0.01. Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie; for example, a region where the critical value is exceeded with probability α if the null hypothesis is true. The null hypothesis (no difference in means, no association, no correlation, no rank correlation, no good regression) is rejected if the test statistic lies within this region which are referred to as rejection region(s). Note: some of these I have listed are parametric test hypotheses, others are non-parametric. The procedures for acceptance or failure to accept a null hypothesis are the same for parametric and non-parametric tests. Critical values can be found in published tables for different distributions.

An alternative quantitative measure for reporting the result of a test of hypothesis is the p-value (usually acquired from statistics package outputs or calculators. The p-value is the probability of the test statistic being at least as extreme as the one observed given that the null hypothesis is true. A small p-value is an indication that the null hypothesis is false. This is The same principle as choosing a significance level, α, for test. For example, we decide either to reject the null hypothesis if the test statistic exceeds the critical value (for α = 0.05) or analagously to fail to accept the null hypothesis if the p-value is smaller than 0.05. It is important to understand the relationship between the two concepts (of α  and p-values) as many statistical software packages report p-values. Again the principle of acceptance or failure to accept a null hypothesis is the same for parametric and non-parametric tests.

Whether it is parametric or Non-parametric it the critical region depends on 1) the alternative hypothesis

2) comparing test statistics value with critical value or p-value with a  fixed level of significance ( usually  alpha)  by the experimenter.

there is nothing like in parametric test it should be larger than critical value  and NP it should be below critical value. 

 In the textbook "Munro's Statistical methods for health care research" 6th edition, p. 142, it says: “To say that the depression level in participants who receive therapy plus exercise is different than that of participants who receive therapy only, using the Wilcoxon matched-pairs test, the computed value of the statistic must be smaller than the critical value”

Please, just clarify why the word "SMALLER" here, and not larger as in inferential statistics.

I think the answer for the Question: the books that say: for non-parametrics tests, the calculated statistcs to be less than the critical value in order to be considered significant is MISTAKEN.

I think the Munro reference just wrote things differently - like a double negative. You say he said “To say that the depression level in participants who receive therapy plus exercise is different..." But I think that the null hypothesis was something like that they were the same, not different. So, he reversed the direction of what side of which a so-called "critical value" you would be testing would be "significant." Right?

At any rate, hypothesis testing can still be misleading, as I noted.

The first link below is to a letter that explains this, and the second can be followed to another nonparametric test that might be of interest to you for comparison.

Article Practical Interpretation of Hypothesis Tests - letter to the...

Conference Paper On the Lehmann power analysis for the Wilcoxon rank sum test

Dear Professor Muayyad Ahmad

the article   of James R Knaub  is giving answer to ur question 

the is has been attached