I think that after explaining them about confidence intervals and test of hypotesis (and about power of a test) you can show them how to compute the sample size in the most simple sampling design. Then you can show them that other designs may be better or worst than this simple one in terms of sampling error with a fix sample size and explain about the Kish effect. If you know the Kish effect of any design you can use it to adjust the sample size from the more simple to the other more complex.

There are some formulas and methods how to estimate the sample number or sample size. Maybe methods cited below can help. I think the most practical way is to calculate it and use examples (real situation).

Henderson 2003:

"Never undertake an ecological study without considering how many samples will be required to meet your objective. When estimating mean abundance, the sample number cannot be accurately determined, but a working approximation can be obtained using an estimate or reasonable guess of the mean and variance of the population.These estimates may be derived from preliminary sampling or from published studies.Within a homogeneous habitat, in which the organisms under study are normally distributed, the number of samples (n) required is approximated by:

n=(t^2.s^2)/ (D.x)^2

where x = the mean number of organisms per sample, s^2 = sample variance, D

= the proportional precision of the mean (i.e. to obtain an estimate within

±5% of the true value of the mean, then D = 0.05), and t = the “Student’s t”

obtained from standard statistical tables, but it is approximately 2 for n > 10

at the 5% level."

or

"Another type of sampling program concerns the measurement of the frequency of occurrence of a particular organism or event, for example the frequency of occurrence of galls on a leaf. If it was found in a preliminary survey that 25% of the leaves of oak trees bear galls, the probability is 0.25.

The number of samples (N ) is given by:

N=(t^2.p(p-1))/D^2

where p = the probability of occurrence (i.e. 0.25 in the above example), and

D = the proportional precision of the mean (i.e. to obtain an estimate within

±5% of the true value of the mean, then D = 0.05)."

or

Quinn and Keough 2002

"The need for replication is closely allied to the need for an adequate sample size in an observational study. Whereas replication deals with the need for replicate units within treatment levels, in an observational study without treatments per se there is an equivalent need for multiple samples to obtain a reasonable representation of the “population”. It almost goes without saying that our ability to estimate population parameters precisely is directly related to the number of observations we have. Recall that we already discussed sample size in the context of statistical power in the chapter on stochastic simulation. The examples presented there demonstrated that statistical power, our ability to correctly reject the null hypothesis, is directly related to the sample size. More generally, it can be shown that the precision in our estimates of population parameters is directly related to sample size as well. This is because the precision in parameter estimates is usually given by the standard error of the estimate and standard errors decrease with increasing sample size. Recall that the standard error of the mean is equal to the standard deviation divided by the square root of the sample size. Aside from the issue of statistical power (in the general sense), sample size is critical to the issue of sufficiency. Sufficiency has to do with whether an ecological relationship is sampled enough to reliably characterize it, and it is perhaps more an ecological consideration than a statistical one. For example, in the spadefoot toad example, let’s say our sample of 100 plots included only 1 plot with 100% shrub cover. The relationship between shrub cover and reproductive success at the extreme end of

the shrub cover gradient is not sufficiently sampled to be able to infer anything ecologically reliable about the relationship at that point on the gradient. Increasing sample size is one way to improve the likelihood that each ecological condition is sufficiently represented in the sample. The other way is to use a stratified or systematic sampling design to ensure equal and sufficient sampling of the full range of the explanatory variable."

Thank you Peter

Hom. this is what I do

I help my students program the 4 basic sampling formulae in excel, protect the formulae, except the input cells, and save them. This only takes about 30 minutes.

Then I teach them how to use the random sampling (selection) in the Excel Analysis Toolpak. This takes about 10 minutes.

Definitely, the basic concepts and "cautions" mentioned by my peers in this forum are necessary.

Thank you Eddie

You are welcome Hom

Eddie : Can you share the excel file with illustrative example.

Home my email address is [email protected]. Email me on this account so I can email you the excel files. Ed

You may use this as reference

https://www.researchgate.net/publication/260082130_R_D_Management_in_State_Universities_and_Colleges_in_the_Philippines_Sampling_in_Business_and_Management_Research?ev=prf_pub

Data R& D Management in State Universities and Colleges in the Ph...

Or you may use these quick solutions

https://www.researchgate.net/publication/260082130_R_D_Management_in_State_Universities_and_Colleges_in_the_Philippines_Sampling_in_Business_and_Management_Research#share

Data R& D Management in State Universities and Colleges in the Ph...

Thank you so much Eddie, I will go through the link you have shared.

These are the programs

https://www.researchgate.net/publication/262564897_Easy-to-use_Sampling_Formulae?ev=prf_pub

Data Easy-to-use Sampling Formulae

https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

Swell. This phone lost everything but a reference I just put on it. 

Trying again: 

Basically the pursuit of sample size depends on your application. And we have to consider the impact of data quality, not just quantity. I have seen additional data actually increase, rather than decrease standard error, say, of a total being estimated. In fact, this is the reason that a sample can sometimes be more accurate than a census, especially if data are collected frequently. 

In the case of sampling from a finite population, a good old book would be 

Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.

On pages 77 and 78, Cochran discusses estimating sample size needs for a simple random sample. Note there that the s/y that he considers nearly constant in order to make this estimate of sample size need would inflate if low quality data were collected just to increase the sample size. Nonsampling error, such as measurement error, is an important consideration. 

I added my reference as a similar approach in the case of prediction from a linear model through the origin. 

Applications in say, natural and social sciences may differ, but the idea of a larger sample is to increase accuracy. But formulas you find will assume good data, which may actually be the bigger problem. 

Thanks - Jim 

Hom -  Your question was how to help your students calculate sample size, and there are formulas in texts, and tools such as the excel use that Eddie pointed out. But I think it best that you also teach the concept to go with these formulas: larger samples of high quality data give more accurate results.  -   As for hypothesis tests, they are generally misused.  The fact that a p-value is a function of sample size means that people often change their conclusions by just changing the sample size. With enough (good) data you can reject anything. Standard errors, and perhaps appropriate confidence intervals (appropriate distribution or Chebyshev), are far more practical. - Jim 

Thank you so much James R Knaub.