To understand the way in which statistical values are arrived at, it is preferable to work through the calculations ourselves since this practice will check our grasp of the steps involved. These calculations are relatively easily and quickly carried out by hand when the data consist of a small set of low whole numbers and when the statistics are comparatively straightforward like those presented in the previous chapter. However, with larger sets of numbers, the manual calculation of even these simple statistics is time-consuming and may result in elementary mistakes being made. These two drawbacks become more serious when we need to employ more complicated statistics and/or when we want to examine the data in different ways, as is often the case. The advent of computers has led to the development of various computer programs for calculating statistics. These programs are not difficult to operate and carry out the required computations very quickly. With the ready accessibility of these packages, calculating statistics by computer is generally more efficient than doing so by hand, once the principles underlying the statistical tests have been grasped.