《Probit Analysis A Statistical Treatment of The Sigmoid Response Curve Second Edition》

Chapter 1．INTRODUCTORY1

1．Biological assay1

2．Variability of response3

3．Statistical methods5

4．Summary of constants6

Chapter 2．QUANTAL RESPONSES AND THE DOSAGE-RESPONSE CURVE8

5．The frequency distribution of tolerance8

6．Direct measurement of tolerance12

7．The binomial distribution14

8．The median effective dose17

8．1．Notation and terminology19

Chapter 3．THE ESTIMATION OF THE MEDIAN EFFECTIVE DOSE20

9．The probit transformation20

10．The probit regression line22

11．Precision of the estimates31

12．Fiducial probability36

13．Approximate methods of estimation37

14．History of the probit method42

15．Alternative tolerance distributions46

Chapter 4．THE MAXIMUM LIKELIHOOD SOLUTION48

16．Working probits48

17．The regression equation51

18．Heterogeneity55

19．Fiducial limits61

Chapter 5．THE COMPARISON OF EFFECTIVENESS65

20．Relative potency65

21．Combination and comparison of relative potencies73

22．Design of experiments81

23．Precision of assays83

24．Mean probit difference85

25．Unequal tolerance variances86

Chapter 6．ADJUSTMENTS FOR NATURAL MORTALITY88

26．Abbott＇s formula88

27．Approximate estimation of the parameters89

28．The maximum likelihood estimates91

Chapter 7．FACTORIAL EXPERIMENTS100

29．Reasons for factorial design100

30．Qualitative factors103

31．The probit plane103

32．Ostwald＇s equation114

33．The interaction of two factors116

34．Extensions to several factors120

Chapter 8．THE TOXIC ACTION OF MIXTURES OF POISONS122

35．Types of joint action122

36．Similar action124

37．A general test for similar action130

38．Independent action136

39．Synergistic action146

40．Planned tests of synergism and similarity150

41．Compound response curves153

Chapter 9．MISCELLANEOUS PROBLEMS160

42．Variation between batches160

43．Individual mortality records165

44．The average kill170

45．The Parker-Rhodes equation172

Chapter 10．GRADED RESPONSES183

46．The linear dosage-response curve183

47．Quantitative responses and the probit transformation185

48．Semiquantal responses197

Chapter 11．RECENT DEVELOPMENTS199

49．Alternatives to maximum likelihood estimation199

50．Wadley＇s problem203

51．A factorial experiment205

52．Incomplete replication in complex experiments211

53．Theory of independent action215

54．Estimation of a percentage point218

55．Staircase estimation226

56．The meaning of standard errors232

Appendix Ⅰ．THE COMPUTING OF PROBIT ANALYSES236

Appendix Ⅱ．MATHEMATICAL BASIS OF THE PROBIT METHOD246

References255

Tables264

Ⅰ．Transformation of percentages to probits264

Ⅱ．The weighting coefficient and Q/Z268

Ⅲ．Maximum and minimum working probits and range295

Ⅳ．Working probits296

Ⅴ．The probability,P．the ordinate,Z,and Z2306

Ⅵ．Distribution of X2307

Ⅶ．Distribution of i308

Ⅷ．The weighting coefficient in Wadley＇s problem309

Ⅸ．Minimum working probit,range,and weighting coefficient for inverse sampling310

Index of Authors311

Index of Subjects313