group. Therefore the number of ways in which two letters can be chosen from a group of four letters A, B, C, D is equal to 6 i.e. AB, AC, AD, BC, BD, CD. This is written as in expression 1.12. The equation of a straight line is given by Equation 1.16, where X is the independent variable, y the dependent variable, m the slope of C2 = 6 (1.12) the line and C its intercept on the y axis. The factorial expansion is frequently used in combination calcu- y = m x + c (1.16) lations where factorial n is written as in expression 1.13. C is negative if the line intercepts the y axis on its negative part n!=nx(n-1)x(n-2) x3x2x1 (1.13) and m is negative if the line slopes the other way to that shown in Figure 1.6. Using this the number of combinations of r times from a group of The best straight line to fit a set of points is found by the method n is given by Equation 1.14. of least squares as in Equations 1.17 and 1.18, where n is the number of points. The line passes through the mean values of X and y, i.e. n "C, = ( n n! - ! (1.14) x and y. 1/6 Statistical analysis (1.17) The value of R will vary from +1 when the two ranks are identical to -1 when they are exactly reversed. 1.8 Probability (1.18) If an event A occurs n times out of a total of m cases then the probability of occurrence is stated to be as in Equation 1.23. P(A)= (1.23) 1.7.2 Correlation Probability varies between 0 and 1. If P(A) is the probability of occurrence then 1 - P(A) is the probability that event A will not Correlation is a technique for establishing the strength of the rela- occur and it can be written as P(A). tionship between variables. In Figure 1.6 the individual figures are If A and B are two events then the probability that either may scattered on either side of a straight line and although one can occur is given by Equation 1.24. approximate them by a straight line it may be required to establish if there is correlation between the reading on the X and y axis. P brB)=P(A)+P(B)-P(A = and B) (1.24) Several correlation coefficients exist. The 