There are any numbers of programs and packages to assist with developing a minimum number of animals that must be used for the experiment. 

To provide additional assistance, the following examples are from IACUC approved protocols and might be used as a guide for developing your numbers justification.

Good narratives for numbers justification:

EXAMPLE 1:  We used the JMP statistical package to perform power analysis to arrive at the proposed group size. Using parameters of alpha = 0.05; power = 80%; effect size = 50%; and standard deviation = 30% of the mean, we arrived at a group size of 7 for a comparison of two groups.  A group size of 10 was chosen because it provides an 80% chance of observing a difference of 50% in the histologic score at a level of significance of 0.05  The formula for the sample size required at each time point is:
where Tn-2,p denotes the (1-p) percentile of the t distribution with n-2 degrees of freedom with p equal to alpha/2 or beta, and q is the proportion of biological specimens allocated to each class; n is the sample size, alpha is the significance level (the probability of declaring that the expression level of a gene is different between classes/time points when in fact there is no difference, delta=0) and  beta is the false negative rate (the probability of declaring that the expression is not different when in fact the mean difference is not zero, delta≠0). The statistical power is 1-beta, the probability of obtaining statistical significance when the true difference in mean expression level between the two classes/time-points is delta. Since gene expression for 12,000 genes will be examined, the value of  should be set small.  is the standard deviation of expression level for the gene within each class. Common! choices for microarray experiments are alpha=0.001, beta= 0.05, sigma=0.5, and delta=1 (because gene expression levels utilize base 2 logarithms of the intensities, delta=1 corresponds to a 2-fold average difference between the two classes/time-points). An iterative computational procedure is used to solve the above equation, and gives approximately 15 as the sample size for each time point. Please note that this sample size calculation is very conservative in terms of minimizing the number of independent biological replicates (animals) per time-point, since we’re planning to analyze expression ratios for each of the 12,000 genes individually. This may require future increases in sample size based on the preliminary data from this protocol.

EXAMPLE 2:   The number of animals necessary to prove significant results is difficult to predict, because we know of no published measures of neuronal firing pattern disorder in response to DBS, or even in the unstimulated 6-OHDA rat. However, in preparation for this work we have analyzed existing data taken from the MPTP-monkey under similar conditions.^1,2,3 This preliminary analysis suggests that neuronal firing pattern entropy, which is a quantified notion of disorder, can be changed by 20% in response to DBS. Assuming that 20% carries over into rats, with a paired T-test significance value of 0.05 we will need 20 recordings per brain region to reach a statistical power of 0.80. We will record from 3 of 6 nuclei (GPe, GPi, EP, VA, VLo, VPLo) in different animals, because the rat brain is too small and our electrodes too big to record from them all at once. Thus splitting the nuclei into 2 groups times 20 per group, we estimate 40 animals for this study, evenly distributed over 2 years, yields 20 animals per year.

1. Meissner W, Harnack D, Paul G, Reum T, Sohr R, Morgenstern R, Kupsch A. “Deep brain stimulation of subthalamic nucleus increases striatal dopamine metabolism and induces contralateral circling in freely moving 6-hydroxydopamine-lesioned rats.” Neurosci Lett. 328(2):105-108, 2002.
2. Shi LH, Woodward DJ, Luo F, Anstrom K, Schallert T, Chang JY. “High-frequency stimulation of the subthalamic nucleus reverses limb-use asymmetry in rats with unilateral 6-hydroxydopamine lesions.” Brain Res. 1013(1):98-106, 2004.
3. Hashimoto T, Elder CM, Okun MS, Patrick SK, Vitek JL. “Stimulation of the subthalamic nucleus changes firing pattern of pallidal neurons.” J Neurosci. 23(5):1916-1923, 2003.

EXAMPLE 3:  The statistical analysis we use to measure significance are Students t-test and repeated measures.  Sample size for each study is carefully monitored to assure no excess studies are performed. Using an alpha probability of 0.05; a power of 0.8 and an effect size of 1.2 X SD, the sample size to detect a statistical difference would be 15.  

EXAMPLE 4:  The number of animals required per experimental group is based on a statistical analysis planned to compare two groups of mice / rats directly.  A power analysis to predict that 20 animals per group will be required to detect a 25% in lesion size (beta = 0/8; alpha = 0/05).

EXAMPLE 5:    Statistical power analysis and implications for number of trials at each probe brain site: Power analysis confirms our experience that the planned experiments typically require a group size of 6 to achieve statistical significance.  Based on our pilot data means and SD, an N of 6 trials at each probe sites appears best in terms of ensuring adequate power but not being wasteful of animals and experimental cost.  For adenosine, for example, spontaneous wake vs. sleep levels in basal forebrain have a mean difference of 15 nmol/l and SD of 10, yielding, for alpha = 0.05, a power of 0.833.  This calculation generally applies to our other measures with similar (large) effect sizes.

 Rats will be operated with 1 guide cannula above different target structures for microdialysis probe insertion at a later time.  From our experience we estimate that the microdialysis probes remain functional in the brain for about 7 days after insertion, presumably due to a gradual loss of membrane permeability.  A group size of 6 in each experiment will require a minimum of 58 rats per year to complete the planned microdialysis studies (see Table below).

Total number needed: 288