ISSUE: Minimum sample size

MINIMUM SAMPLE SIZE TO CONDUCT STUDY: In general, if the population size is known, the Yamane method is used to determine sample size. However, the method is not efficient, i.e. it tends to requires larger than necessary sample size and it cannot handle unknown population size scenario. See below for citation.

Assume that the total population (N) is non-finite, if we need the minimum sample size to study the ants in this case the following formula may be used:

nmin = (Z2σ2) / E2             ... where E = σ / sqrt(nobs)

... where Z = 1.65 for 95% confidence interval; σ = 22.92 using the t-equation to solve for the estimated mean (μ = 23.39) and the Z-equation to solve for σ, thus:

t = (X^ - μ) / (S / sqrt(n))

... where X^ =27.40; S = 23.06; and t = 1.64 using 0.95 CI for infinity degree of freedom. Solve for μ. The solution is μ = 23.39.

Z = (X^ - μ) / (σ / sqrt(n))

Substitute the value of μ into the Z-equation and solve for σ. The solution is σ = 22.92. Now put the values into equation (1) and solve for nmin. The solution is nmin = 242.18. This is the minimum sample needed to conduct a study of this population. The confidence interval used was 95%. If you need higher confidence interval, change the relevant value for t and Z according to the confidence interval level.

REFERENCES:

[1] Yamane, Taro (1967). Statistics: Introduction to Analysis. New York: Harper and Row. p. 886.

[2] Montgomery, C., Runger, G. C. and Hubele, N.F. (2001). Engineering Statistics, 2nd ed. John-Wiley, ISBN 0-471-38879-3. p. 172.

I dont know...may be this could sounds crazy but you could make a curve of accumulative anthills destroyed by each transect... and when you get the stable slope of your curve there is the minimal number of transects to be done... using Clench curve.... I said...may be it could sounds crazy!!! but you can try.... once you reach the the asymptote of the curve it means that even if you introduce more and more transects you will continuous obtaining similar values of anthills.... I dont know...just a crazy idea...

http://jhortal.com/pubs/2003-Jimenez-Valverde&Hortal_Rev_Ib_Aracnol.pdf

ISSUE: Minimum sample size

MINIMUM SAMPLE SIZE TO CONDUCT STUDY: In general, if the population size is known, the Yamane method is used to determine sample size. However, the method is not efficient, i.e. it tends to requires larger than necessary sample size and it cannot handle unknown population size scenario. See below for citation.

Assume that the total population (N) is non-finite, if we need the minimum sample size to study the ants in this case the following formula may be used:

nmin = (Z2σ2) / E2             ... where E = σ / sqrt(nobs)

... where Z = 1.65 for 95% confidence interval; σ = 22.92 using the t-equation to solve for the estimated mean (μ = 23.39) and the Z-equation to solve for σ, thus:

t = (X^ - μ) / (S / sqrt(n))

... where X^ =27.40; S = 23.06; and t = 1.64 using 0.95 CI for infinity degree of freedom. Solve for μ. The solution is μ = 23.39.

Z = (X^ - μ) / (σ / sqrt(n))

Substitute the value of μ into the Z-equation and solve for σ. The solution is σ = 22.92. Now put the values into equation (1) and solve for nmin. The solution is nmin = 242.18. This is the minimum sample needed to conduct a study of this population. The confidence interval used was 95%. If you need higher confidence interval, change the relevant value for t and Z according to the confidence interval level.

REFERENCES:

[1] Yamane, Taro (1967). Statistics: Introduction to Analysis. New York: Harper and Row. p. 886.

[2] Montgomery, C., Runger, G. C. and Hubele, N.F. (2001). Engineering Statistics, 2nd ed. John-Wiley, ISBN 0-471-38879-3. p. 172.

Thank you all for the valuable comments! All were upvoted!

Attila

The proposals made by the other colleagues are very suitable. Besides the statistical calculation of sample size is important to consider the objectives and context of the study. If you are going to make comparisons between different situations, then it is very important to control variability factors (which in the case of the study you mention, can affect the vulnerability of anthills or the behavior of bears). Sampling should be able to include this variability in all compared situations. You can reduce the number of samples if you reduce this variability (eg considering areas that are equal for the factors affecting such variability as soil structure, etc.), if not possible, we must increase the number of transects so as to include all possible options.

@Angel.....a very valid point indeed. By considering all options and select the most appropriate, we will avoid inferential errors.

What's the question?

Hi Attila:

One question? What do you exactly want to monitor:

Bear presence/absence?

Intensity of habitat use?

Bear abundace?

Please note that in each case you need different methods and assumptions.

With your current design what you seem to be monitoring is number of anthill predated, which is related to bear activity but also to other issues like: anthill abundance, availability of other food sources, etc...

If you can explain better what is the ultimate purpose of the monitoring will really help in obtaining good advice

To do power analysis to estimate your sample size, you have to write your hypothesis, and based on that you decide what statistical test you will use. It should be one of the inferential statistics. so you need to determine the following: alpha {standard to be .05}, power [standard to be .80], effect size {small, moderate, or large, each test has its own value, you can find these values in the net}. Then download free programs to calculate the sample size such as G. power.

Doing power analysis to estimate your sample size, the researcher have to write the hypothesis first, and based on that you decide what statistical test you will use. It should be one of the inferential statistics. so you need to determine the following: alpha {standard to be .05}, power [standard to be .80], effect size {small, moderate, or large, each test has its own value, you can find these values in the net}. Then download free programs to calculate the sample size such as G. power.

You can use the attachment PDF below. But would you mind sending me the full text book of [1] Yamane, Taro (1967). Statistics: Introduction to Analysis. New York: Harper and Row.