Inferential statistics operates on probability (p, level of significance, degree of confidence, margin of error, estimates of variance, etc.). It requires probability samples.

For those using SPSS and other packages, p appears as the final decision criterion.

For those familiar with the traditional process of testing significance, critical values of t, F, r, Z, etc. (that are determined based on alpha and degrees of freedom) are compared with t, F, r or Z statistic.

Purposive samples are a non-probability sample. Inferential statistics cannot be appropriately applied unto them.

Many times I have shared this information in RG. But in almost the same number of sharing I was down voted. I hope this time, I will not be.

But many other members came out in support of this hard fact. However, to my estimate, we are still outnumbered.

No. Eddie gave a very good answer.

As one who did not even know what purposive sampling was, I went to check it out. Here's a very good explanation that I presume is correct:

http://dissertation.laerd.com/purposive-sampling.php

And, according to this, Eddie's explanation is accurate. Apparently, a purposive sample is used for qualitative purposes. Inferential statistics are quantitative and, most importantly, probabilistic. That is, they recognize there is a great degree of uncertainty in the sample and try to decide if the results we are seeing for that sample are "normal" (as compared to what we presume to be the full population) or not. So, no, inferential statistics are not appropriate for purposive samples.

I would say given that your sample is not random, you cannot just do general inferential statistics.

however, if your purposeful sampling resulted in a very large and theoretically very representative sample of your target population ( not the general population, as you used purposeful sampling, you are looking at a smaller  sub group of the population with some unique characteristics.). If you change your sampling frame so it connects your sample and the targeted population, his making it possible in inquire about the generalisability of your friending from the sample to the population, then you may be able to use some variation of the inferential statistics using a different distribution given the non random nature of your sample.  

So the question you should be asking in your case, is thaT "is the finding found your purposeful sample different from random affects. " If so, you can argue that the effects in your non random sample exists.

Hi, ..

So in this case we are satisfied with the descriptive analysis only, or we can resume some correlation & ANOVA analysis also ?!!

Chems - descriptive analysis produces descriptive statistical results where inference is excluded when using parametric statistical methods where the normal distribution of the errors is assumed as a prerequisite. 'Satisfaction' should also be guarded and guided by the objectives of the study i.e. do descriptive statistical results answer your research questions? With correlation, correlation analysis based on bivariate normal distribution (parametric statistics) for the Pearson's coefficient stops with the correlation coefficient - no inference is applicable. With use of the non-parametric method, the SPEARMAN's correlation coefficient is the statistic that is calculated, and inference is applicable. The same applies to ANOVA and other statistical tests where you can use either non-parametric or parametric approaches to data analysis.

Inferential statistics, unlike descriptive statistics, is a study to apply the conclusions that have been obtained from one experimental study to more general populations. This means inferential statistics tries to answer questions about populations and samples that have never been tested in the given experiment.

Inferential statistics infer from the sample to the population, they determine the probability of characteristics of a population based on the characteristics of your sample, they also help assess the strength of the relationship between your independent variables, and your dependent (effect) variables. With inferential statistics, you can take the data from any samples and make generalizations about a population. 

There are two main areas in case of inferential statistics, estimating parameters. This means taking a statistic from your sample data and using it to say something about a population parameter and hypothesis tests, this is where you can use sample data to answer research questions. 

Regards

It's still a question: I have 16 fish ponds in an area. Some ponds are known by fishermen to yield fish species A, B and C (1) while others yield A, C and D only (2). I want to know the nature of association and its strength between species A and D.

Question: Do I need to include samples in category 1 where species D is absent?

Abirami  - 

For inference, purposive sampling requires regressor (auxiliary/independent variable/'predictor') data associated with every member of the population, and the population broken into subpopulations where one regression model applies to each. 

   ... 

Model-based inference is thus possible, and it has even been argued as being preferable to randomization, as inference from randomization is an artifact of data selection, rather than the data structure.  (I would say that stratification is done based on data structure, regardless.)  A randomized design does reduce the chance of a sample that may not be considered to 'represent' a population well, though an unfortunate selection can lead to a bad estimate for mean or total, and also for standard error and bias.  An important example would be if you have a population with a very few, very large members, then a simple random sample may or may not select one of them, which would make a huge difference to inference, including estimated standard error.  You could do much better with a stratified random sample, but you need auxiliary information to know how to form the strata.  With good regressor data on the whole population, you could do better with a model-based (regression) methodology, or perhaps better still by combining this with a randomized design (i.e., model-assisted design-based methods). 

Note that the "representativeness" argument for randomization is up to chance, but for a model, one can use "balanced sampling," where you select a sample such that the corresponding regressor data mean is its population mean.  That could argue more strongly for "representativeness."

Consider this Waksberg Award article: 

Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology,

(December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X.

http://www.statcan.gc.ca/pub/12-001-x/2013002/article/11883-eng.htm

The one model shown there in Section 4 is for a classical ratio estimator.   (See equation (4.3).)

The classical ratio estimator understates true heteroscedasticity usually found in highly skewed establishment surveys (i.e., a very few large, some medium, and many small establishments).  However, because small establishments are difficult to sample frequently, say in a weekly or monthly sample for official statistics, but there is often good, less frequently collected census data for regressor data, the smallest may have disproportionately large measurement error in a frequently collected sample.  One must consider "total survey error."  Thus a cutoff sample using a classical ratio estimator may not only be the least expensive option, but also the most accurate (imputing generally for the smallest cases), as testing and much experience has shown: 

 https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development

 https://www.researchgate.net/publication/303496276_When_and_How_to_Use_Cutoff_Sampling_with_Prediction

.......................

You might be interested in work done by Mike Brick, such as

"2014 WSS PRESIDENT’S INVITED SEMINAR,"

http://washstat.org/seminars/2014/20140326_brick.html

There Mike Brick addressed this committee report:

https://www.researchgate.net/publication/273561892_Summary_Report_of_the_AAPOR_Task_Force_on_Non-probability_Sampling

"The Future of Survey Sampling," J. Michael Brick, Public Opinion Quarterly 75(5):872-888 · December 2011,

https://www.researchgate.net/publication/261967521_The_Future_of_Survey_Sampling

"Beyond traditional survey taking: adapting to a changing world,

Explorations in Non-Probability Sampling Using the Web," J. Michael Brick, Proceedings of Statistics Canada Symposium 2014

http://www.statcan.gc.ca/sites/default/files/media/14252-eng.pdf

......

If you have no information, simple random sampling is best, but you usually have some information to at least stratify.  Even a purposive sample can be improved by stratification, but without regression, there is no formal inference. 

Best wishes - Jim

PS -  You might also be interested in this:

 https://www.researchgate.net/post/What_is_the_best_sampling_method_in_Survey_design