Hello everyone!
I have a question from our mammologist group: they counted the number of anthills destroyed by bears on 89 transects (800 m each). They had a huge SD: 23.06, and the mean of destroyed anthills per transects was 27.4.
How should we calculate the minimal number of transect needed to monitor the bear activity reliably?
Thanks,
Attila
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.
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.
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.
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.
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