Given the cost, both financial and even more importantly in terms of human effort, in building High Energy Physics accelerators and detectors and running them, it is important to use good statistical techniques in analysing data. Some of the statistical issues that arise in searches for New Physics are discussed briefly. They include topics such as: Should we insist on the 5 sigma criterion for discovery claims? The probability of A, given B, is not the same as the probability of B, given A. The meaning of p-values. What is Wilks Theorem and when does it not apply? How should we deal with the `Look Elsewhere Effect? Dealing with systematics such as background parametrisation. Coverage: What is it and does my method have the correct coverage? The use of p0 versus p1 plots.
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