23.54 26.30 28.85 32.00 34.27 ily indicate an improvement in quality. 25.99 28.87 31.53 34.81 37.16 1.11.2 Chi-square test 28.41 31.41 34.17 37.57 40.00 40.26 43.77 46.98 50.89 53.67 This is written If O is an observed result and E is the expected 51.81 55.76 59.34 63.69 66.77 result then Equation 1.53 is obtained. (1.53) as in Table 1.4. Does this indicate that most of the accidents occur during the late night and early morning periods? Applying the The X 2 distribution is given by tables such as Table 1.3, from tests the expected value, if there was no difference between the time which the probability can be determined. The number of degrees of periods, would be the mean of the number of accidents, i.e. 5. freedom is the number of classes whose frequency can be assigned Therefore from Equation 1.53, expression 1.56 is obtained. Bibliography 1/11 (1.57) Table 1.4 The Chi-square distribution Tables are then used, similar to Table 1.3, which give the prob- Time (24 hour clock) Number of accidents ability level for (n - 2) degrees of freedom. The Student t for the rank correlation coefficient is given by Equation 1.58, and the same Student t tables are used to check the significance of R. 12-18 18-24 (1.58) Bibliography (1.56) Besterfield, D.H. (1979) Quality control, Prentice Hall. Caplen, R.H. (1982) A Practical approach to quality control, Busi- ness Books. There are three degrees of freedom, therefore from Table 1.3 the probability of occurrence of the result shown in Table 1.4 is seen to Chalk, G.O. and Stick, A.W. (1975) Statistics for the engineer, Butterworths. be greater than 10%. The conclusion would be that although there is a trend, as yet there are not enough data to show if this trend is Cohen, S.S. (1988) Practical statistics, Edward Arnold. significant or not. For example, if the number of accidents were David, H.A. (1981) Order statistics, Wiley. Dudewicz, E.J. and Mishra, S.N. (1988) Modern mathematical each three times as large, i.e. 27, 9, 6, 18 respectively, then X would statistics, Wiley. be c