Experimental Statistics by Mary Gibbons Natrella

Author:Mary Gibbons Natrella
Language: eng
Format: epub
Publisher: Dover Publications
Published: 2013-06-26T16:00:00+00:00

10-3.1 GRAPHICAL PROBIT SOLUTION

10-3.1.1 Procedure. To facilitate the calculations, prepare a table with nine columns, headed respectively, x, n, r, p, Y′, Y, W, nW, nWx. (See Table 10-3.)

(1) In column x, enter the levels x1, x2, …, xk used in the experiment.

(2) In columns n and r, record the values of ni and ri, corresponding to xi.

(3) In column p, compute the respective proportions responding, pi = ri/ni.

(4) Use Table A-2 to obtain zp corresponding to p. In column Y′, enter Y′ = zp + 5 corresponding to each p.

(5) Plot Y′ as ordinate against x as abscissa, on ordinary rectangular coordinate graph paper. See Figure 10-1. If probit paper* is available, it can be used, and the column Y′ is omitted from the table. The percentages responding at each x (% response = 100 pi) are plotted on probit paper, using the left vertical scale; the right vertical scale gives the corresponding zp, and hence the corresponding Y minus 5.

(6) Whichever graph paper is used, draw a straight line by eye to fit the k points. Only vertical deviations from the line are to be considered in fitting; and points for which the value of Y′ is outside the interval 2.5 to 7.5 may almost be disregarded unless ni for those points is much larger than for points inside the interval. (Points outside this interval are beyond the range of the probit paper).

(7) For each value of x plotted on the graph, read the ordinate Y of the line (on probit scale if on probit paper), and record the values in the Y column of the table.†

(8) Calculate b, the slope of the fitted line, as the increase in Y for a unit increase in x. Mark two convenient points, c and d, on the line. Read off the corresponding values for both x and Y.

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