Analysis and Presentation of Experimental Results by R. H. Leaver, T. R. Thomas (auth.)

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By R. H. Leaver, T. R. Thomas (auth.)

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Can we arrive at a more realistic estimate of their combination? 2 and multiplying out s~ = ~ {IG: oxr +I(:; oyf +2 I:: :; oxoy} Residuals of x or y are equally likely to be of either sign, and so may their products oxoy. For large values of n, therefore, there will be as many positive as there are negative products within the summation sign of the third term, 40 ANALYSIS AND PRESENTATION OF EXPERIMENTAL RESULTS hence the term itself will tend to zero. 5 is called the Superposition of E"ors Theorem, and is a basic result to which we shall be referring frequently.

The magnitude of the alteration is arbitrary; we are interested only in changes in the precision of manufacture, that is, whether the degree of variation in manufactured components has altered. In both these cases the t-test is inapplicable, as we do not have a difference of means to work with, and we must use Fisher's F-test. 3). The F-distributions, however, look rather different from the t-distributions. They are not symmetric but are skewed about their mode which is non-zero. A moment's thought will explain the phenomenon of the finite mode: unlike t, F must always be positive as it is a ratio of variances.

We would not expect to be able to conclude that all tyres having completed say 15 000 miles have some particular degree of wear. Clearly, wear results from the operation of a number of random factors such as road surface, driving technique, and so on. A situation of this kind can only be described in limited statistical terms. Alternatively, we might be faced with completely uncharted waters, where it is by no means clear if there is any genuine connection between the variables. Suppose we wish to explore the possible effect of differing amounts of oil-additive upon cylinder-bore wear.

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