HOW MANY PLOTS? If you have 80 plants per plot, how many plot? take that number of plot multiplied by 80 plants per plot, the answer is your population. That is to say "finite population," i.e. N = population size known. In that case, the formula to calculate sample size is:

(1)   nY = N / (1 + N(e2)

... where subscript Y = Yamane; and e = precision error level, i.e. 5% or 1% error that you would allow. with known total plots, sample size could be calculated.

REPRESENTATIVE OF THE 80 PLOTS: Here according to the statement, you are treating 80 plots as a total population (sub-population or sub-group). In that case, according to the equation above, if error is 1%, the minimum sample size is 79.94 or 80.

POPULATION UNKNOWN: Assume that the population (N) is not known---this is non-finite case---you have 80 "samples" from one plot; "what is the minimum sample that is representative of the population 'out there'?" obtain the descriptive and inferential statistics of the 80 test sample plants and find you minimum sample size:

(2)   nmin = Z2σ2 / SE2

... where SE = standard error: SE = σ / SQRT(ntest). recall that ntest = 80. Can you use test sample less than 80? You could use ntest = 30.

ONLINE CALCULATOR: http://www.raosoft.com/samplesize.html

http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm

http://www.isixsigma.com/tools-templates/sampling-data/how-determine-sample-size-determining-sample-size/

http://www.raosoft.com/samplesize.html

The Finite Population Correction (FPC) factor for the standard error of the Mean, or proportion, is given by:

FPC=sqrt((N-n)/(N-1))

where N=population size and n=sample size.

So you can set your desired confidence level and then solve for n.

A detailed explanation with demonstration is here: https://onlinecourses.science.psu.edu/stat414/node/264

And you can use this handy calculator to play with options: http://www.surveysystem.com/sscalc.htm

Sampling never provides a true value but an estimate

Your question should have an obvious simple answer: 80! So I assume you are not really expecting to obtain a true value. I expect you mean to know how many samples are needed to generalize the observation to the entire set.. Well this depends of the analysis you are doing and the power you wish to achieve. In other words, it depends to which point you accept chance to potentially play a role when answering your hypothesis.

So without the estimates related to your hypothesis, it is impossible to answer your question.

The sample size is useful to infer on a parametric function of the interest variable defined for the population units. For this reason, if possible it is better to take a sample of the 80 units, and to describe objectively this sample or this finite population of size 80. Of such way you will not have errors of sampling.

But, if you prefer to take other sample which does not coincide with the finite population, the sample size will depend of the used sampling design. It is not equal simple random sampling with replacement, simple random sampling without replacement, sampling with unequal probabilities, etc. Each appropriate sampling design has got its formula for calculating the sample size. In general, each formula of the sample size depends or can depend of the variance of the finite population, of the amplitude of the confidence interval for estimating the parametric function, and of the minimum confidence level we assume.

Dear  Lukong Hilary Kerla,

The answers provided by Paul Louangrath  and Hume Francis Winzar are excelent.

I would like to add: it depends on the definition of your population:

Is the population these 80 plants per plot (lets call it: the total production); meaning you want to say something about these plots and only these plots?

In this case the answers provided above are valid.

Or is the population all the plants that may grow in the futre, in other words: do you want to generalise to other (future) plots/plants?

in that case; your sample is 80 plants per plot (because that is how you sampled).

If however you see the 80 plants as context for each other (and not as a sample), than you might consider power analysis (which of course depends on the statistical analysis you want to perform).

Anyhow, it does not make much difference in practice...

greetings,

Pierre

Dear RG colleague,

Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.

For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.

Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).

Regards,

see raosoft formula... easy to apply; just don't get muddled into the theory