Abstract

It can be seen from the above that the appropriate sample size for an experiment depends upon three quantities. (I) The size of the treatment difference which is regarded as of practical importance. (2) The rates of the various types of error which can be tolerated in the light of their costs. (3) The variability of the experimental material. Something needs to be said about variability. With a quantal response there is often not a great deal that can be done to reduce variability to any substantial extent, always provided that the normal standards of good experimentation (which include proper randomization) are adhered to. With a continuous response there are more possibilities. Arranging the experimental material in homogeneous pairs or larger blocks (such as those constituted by litter-mate animals, or by contiguous positions in the laboratory) can often lead to very substantial reductions in variability, enabling notable savings to be made in experimental material at negligible cost. It should be repeated that the statistical arguments given above only lead to a fairly rough assessment of the appropriate size for a proposed experiment. This does not detract from their usefulness. The drawbacks of undertaking an experiment which is unnecessarily large are fairly obvious. Those of embarking on one which is foreseeably too small to detect the required treatment effect are less obvious but may well be more serious, particularly if they are linked to the common fallacy of equating 'not significant' with 'nonexistent'.

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