The sample size formula will only be as accurate as the preliminary data used in the calculation. In general, You may already have sufficient replication if you have good enough information to yield a highly accurate estimate of sample size. Basing sample size estimation on a preliminary study with 4 replicates is little better than using a random number generator.

I would look at the recent literature to find manuscripts that will use methodologies similar to yours in journals where you might consider publishing. Use a sample size that is at least slightly better than average. Statistically, this is a terrible approach. However, it results in a sample size that potential reviewers will have difficulties rejecting. If the manuscript is rejected because of small sample size, you can then argue with the editor that similar studies have been published with this sample size (and would the editor please reconsider the decision).

Things to consider in planning sample size:

1) Level of variability in populations being studied.

2) The degree of difference between populations that you want to identify as significant.

3) The cost of making a mistake (falsely claiming a significant difference when there are none, or falsely claiming no difference when there is a difference).

4) Non-response rate. In survey data this is the number of surveys with one or more questions that go unanswered. It would include people that simply refuse to take the survey. In animal behavior it would be the number of subjects that do not express all behaviors. In transect sampling it could be the number of animals that start in the sampled area but escape detection.

5) Ethical issues. Animal cruelty, ethical treatment of animals, humans as research subjects, and similar concerns. These will always override any justification based on a sample size calculator.

6) Cost in time and money. Here you have to balance what you can afford versus published sample size. If most of the published papers use a sample size of 30, but you can only afford a sample size of 10, then you may have trouble publishing. If the sample size calculator suggests a sample size of 400 and most published papers have a sample size of 5, then your sample size of 10 will have no trouble in this regard.

    If there is some feature about your study that makes it extraordinarily expensive, and reviewers can see this, then you may have no problem with even a small sample size. So I want to study a rare pelagic shark. Only seven specimens have been captured in the last 200 years. I happen to be able to capture 3. In general a sample size of 3 is not good. In this case, a sample size of 3 is amazing.

7) Risk. Maybe I want to study the effect of war on farmer attitudes. One sample site is in an active war zone where there are fewer farmers and there is considerable risk of getting killed. Reviewers should be willing to overlook a small sample size in this case, especially if the sample size is ample in the low conflict areas.

8) Utility, or maybe futility. Proponents of small sample sizes often argue that large sample sizes detect effects that are so small that they are trivial.Conceptually, this is a valid concern. However, it would take a great deal of data to quantify what level of difference constitutes a trivial effect. It would also require a more in-depth analysis of data than is typically found in the published literature.

I typically suggest taking more samples than you think you will need. That provides a buffer in case things do not go as expected. It may provide opportunities to better understand the original question and direct future research. I have yet to find a published manuscript where the methods state that half the data were randomly discarded to prevent detection of statistically significant yet unimportant differences. Too much data is survivable, to little data isn't.

Dear Amadou

The minimum sample size depends on your population, is it finite population or infinite population.

In the case of finite population, you can use the attached table to estimate the suitable sample size.

But in case of infinite population: 

The sample size for any study depends on the standard deviation of the variable ( from previous studies ) and the margin of error you decided . My advice to use G*Power .

G*Power software is effective tool to calculate sample size for many ranges of experiments. Also, you can determine effect size and power of the test, G*Power is free to download and easy to use after reading the manual, the download link:

http://download.cnet.com/G-Power/3000-2054_4-10647044.html

The link to download G*Power manual:

http://www.gpower.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf

Good Luck

Amadou, what is the outcome variable?  What type of statistical analysis is planned?  It's difficult to suggest anything without knowing these things.  HTH.

The very easy way of calculation of sample size -read who manual for sample size calculation