《Probit Analysis》

Chapter 1.INTRODUCTORY1

1.Biological assay1

2.Variability of response3

3.Sta-tistical 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 te？ainology19

Chapter 3.THE ESTIMATION OF THE MEDLAN 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 LIKEIHOOD 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.FACTORLAL 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 kili170

45.The Parker-Rhodes equation172

Chapter 10.GRADED RESPONSES183

46.The linear dosage-response curve183

47.Quantitative responses and the probit transformtion185

48.Semi-quantal 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 per-centage point218

55.Staircase estimation226

56.The meaning of standard errors232

AppendixⅠ.THE COMPUTING OF PROBIT ANALYSES236

AppendixⅡ.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 X3307

Ⅶ.Distribution of ？308

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

Ex.1.Fitting by eye of a probit regression line to the results of an insecticidal test25

Ex.2.The standard error of a nedian lethal dose34

Ex.3.Fiducial limits to the LD50 in the rotenone-Macro-siphoniella sanborni test37

Ex.4.Estimation of the median lethal dose by Behrens’s and Karber’s methods42

Ex.5.Calculation of working probits50

Ex.6.Arithmetical procedure in the fitting of a probit regression line52

Ex.7.Application of probit analysis to heterogeneous data57

Ex.8.Fiducial bands for a probit regression line62

Ex.9.Fiducial limits of the median lethal dose64

Ex.10.Relative potency of rotenone,deguelin concentrate,and a mixture of the two67

Ex.11.Combination of relative potencies73

Ex.12.Comparison of relative potencies75

Ex.13.The relative toxicities of seven dorris roots75

Ex.14.Combination of relative potencies by the method of least squares76

Ex.15.Mean probit difference of rotenone and deguelin concen-trate86

Ex.16.Calculation of weighting coefficients90

Ex.17.Numerical example of the maximum likelihood solution95

Ex.18.The effect of variation in concentration and deposit on the toxicity of a pyrethrum preparation to Tribolium castaneum106

Ex.19.The effect of variations in concentration of hydrocyanic acid and exposure time on the mortality of Calandra granaria117

Ex.20.Similar joint action of rotenone and a deguelin concen-trate126

Ex.21.Standard errors of discrepancies between observation and similar action predictions128

Ex.22.Expression of one mixture in terms of two others130

Ex.23.Similar action between the toxic constituents of derris root132

Ex.24.Independent action between constituents with parallel probit regression lines138

Ex.25.Independent action between constituents with inter-secting probit lines142

Ex.26.Correlated independent action144

Ex.27.The toxicity of rotenone-pyrethrins mixtures to the house-fly148

Ex.28.The use of Table 26 in planning toxicity tests151

Ex.29.Response curves given by equation(8-26)156

Ex.30.The toxicity of ammonia to Tribolium confusum163

Ex.31.Variability of Macrosporium sarcinaeforme to hydrogen sulphide,sodium dithionite,and sodium tetrathionate176

Ex.32.Maximum likelihood estimation of index of variation of Macrosporium sarcinaeforme relative to sodium tetra-thionate180

Ex.33.The repellent effect of lime sulphur on the honeybee188

Ex.34.The effect of temperature on the insecticidal potency of pyrethrms205