Statistics for terrified biologists

Statistics for Terrified Biologists......Page 2
Preface......Page 14
The text of the chapters......Page 18
What should you do if you run into trouble?......Page 19
Boxes......Page 20
Why go to all that bother?......Page 21
The bibliography......Page 23
Notation......Page 25
Notation for calculating the mean......Page 27
Introduction......Page 29
Mean deviation......Page 30
Variance......Page 31
Why n – 1?......Page 33
Why the squared deviations?......Page 34
The standard deviation......Page 35
Spare-time activities......Page 37
Added squares......Page 38
Avoid being confused by the term “sum of squares”......Page 39
Summary of the calculator method of calculating down to
standard deviation......Page 40
Spare-time activities......Page 41
Frequency distributions......Page 42
The normal distribution......Page 43
What per cent is a standard deviation worth?......Page 44
Are the percentages always the same as these?......Page 46
Other similar scales in everyday life......Page 47
From per cent to probability......Page 48
EXECUTIVE SUMMARY 1
The standard deviation......Page 50
To recap......Page 52
Is our observed distribution normal?......Page 53
Checking for normality......Page 54
Transformation......Page 55
How many samples are needed?......Page 57
Calculating how many samples are needed......Page 58
Is “A” bigger than “B”?......Page 59
The yardstick for deciding......Page 60
Step 1 – from variance of single data to variance of means......Page 62
Step 2 – from variance of single data to “variance of differences”......Page 65
Step 3 – the combination of Steps 1 and 2; the standard error of difference between means (s.e.d.m.)......Page 66
Recap of the calculation of s.e.d.m. from the variance
calculated from the individual values......Page 68
Summary of this chapter......Page 69
EXECUTIVE SUMMARY 2
Standard error of a difference between two means......Page 73
Spare-time activities......Page 74
The principle of the t-test......Page 75
The t-test in statistical terms......Page 76
Why t?......Page 77
Tables of the t-distribution......Page 78
The procedure......Page 81
t-test for means associated with unequal variances......Page 86
The s.e.d.m. when variances are unequal......Page 87
A worked example of the t-test for means associated with unequal variances......Page 90
The paired t-test......Page 92
Pair when possible......Page 95
EXECUTIVE SUMMARY 3
The t-test......Page 97
Spare-time activities......Page 99
Why is the analysis of variance F-test one-tailed?......Page 100
The two-tailed F-test......Page 101
How many tails has the t-test?......Page 103
The final conclusion on number of tails......Page 104
Introduction......Page 105
Some “made-up” variation to analyze by Anova......Page 106
Phase 1......Page 108
Phase 2......Page 109
SqADS – an important acronym......Page 110
How well does the analysis reflect the input?......Page 113
Degrees of freedom in Anova......Page 114
The completion of the End Phase......Page 116
The variance ratio......Page 117
The relationship between “t” and “F”......Page 118
Equality of variance between treatments......Page 120
The element of chance: randomization......Page 121
Comparison between treatment means in the analysis of
variance......Page 124
The least significant difference......Page 125
A caveat about using the LSD......Page 127
EXECUTIVE SUMMARY 4
The principle of the analysis of variance......Page 128
Introduction......Page 132
Fully randomized......Page 133
Prelims......Page 134
Phase 2......Page 135
End Phase......Page 137
Randomized blocks......Page 138
Prelims......Page 140
Phase 1......Page 142
Phase 2......Page 143
Incomplete blocks......Page 144
Latin square......Page 147
Data for the analysis of a Latin square......Page 148
Prelims......Page 149
Phase 2......Page 151
End Phase......Page 152
Further comments on the Latin square design......Page 153
Split plot......Page 154
EXECUTIVE SUMMARY 5
Analysis of a randomized block experiment......Page 156
Spare-time activities......Page 158
What is a factorial experiment?......Page 160
If there is no interaction......Page 162
What if there is interaction?......Page 164
Measuring any interaction between factors is often the
main/only purpose of an experiment......Page 165
Degrees of freedom for interactions......Page 167
The similarity between the “residual” in Phase 2 and the
“interaction” in Phase 3......Page 168
Sums of squares for interactions......Page 169
An example of a 2-factor experiment......Page 171
Prelims......Page 172
Phase 2......Page 173
End Phase (of Phase 2)......Page 174
Phase 3......Page 175
End Phase (of Phase 3)......Page 179
Analysis of factorial experiments with unequal replication......Page 180
EXECUTIVE SUMMARY 6
Analysis of a 2-factor randomized block experiment......Page 183
Spare-time activity......Page 186
Introduction......Page 187
Different “orders” of interaction......Page 188
Example of a 4-factor experiment......Page 189
Prelims......Page 190
Phase 2......Page 192
Phase 3......Page 193
To the End Phase......Page 200
Addendum – additional working of sums of squares calculations......Page 203
Spare-time activity......Page 209
Introduction......Page 211
Deriving the split plot design from the randomized
block design......Page 212
Sub-plots......Page 215
Numerical example of a split plot experiment and its
analysis......Page 218
Calculating the sums of squares......Page 219
End Phase......Page 222
Comparison of split plot and randomized
block experiment......Page 223
Uses of split plot designs......Page 226
Spare-time activity......Page 228
Introduction......Page 230
Brief recap of relevant earlier sections of this book......Page 231
Least significant difference test......Page 232
Multiple range tests......Page 233
Operating the multiple range test......Page 234
Suggested “rules” for testing differences between means......Page 239
Presentation of the results of tests of differences
between means......Page 240
The results of the experiments analyzed by analysis of variance in Chapters 11–15......Page 242
Spare-time activities......Page 253
Introduction......Page 255
Is a straight line appropriate?......Page 256
Regression......Page 261
Independent and dependent variables......Page 262
The regression coefficient (b)......Page 264
Calculating the regression coefficient (b)......Page 265
The regression equation......Page 270
The data (Box 17.2)......Page 272
Calculating the regression coefficient (b) – i.e. the slope of the regression line......Page 273
Drawing the regression line......Page 274
Testing the significance of the slope (b) of the regression......Page 275
How well do the points fit the line? – the coefficient of determination (r2)......Page 279
Derivation of the correlation coefficient (r)......Page 280
An example of correlation......Page 281
Extensions of regression analysis......Page 283
Nonlinear regression......Page 286
Multiple linear regression......Page 287
Analysis of covariance......Page 289
EXECUTIVE SUMMARY 7
Linear regression......Page 291
Spare-time activities......Page 293
Introduction......Page 294
When and where not to use χ2......Page 295
Yates’ correction for continuity......Page 296
The χ2 test for “goodness of fit”......Page 297
The case of more than two classes......Page 299
χ2 with heterogeneity......Page 301
Heterogeneity χ2 analysis with “covariance”......Page 303
2 × 2 contingency table......Page 306
Fisher’s exact test for a 2 × 2 table......Page 308
Larger contingency tables......Page 309
Interpretation of contingency tables......Page 310
Spare-time activities......Page 311
Introduction......Page 313
Where nonparametric methods score......Page 315
Where parametric methods score......Page 316
The sign test......Page 317
The Kruskal–Wallis analysis of ranks......Page 318
Kendall’s rank correlation coefficient......Page 319
The main nonparametric methods that are available......Page 320
Appendix 1
How many replicates......Page 323
Appendix 2
Statistical tables......Page 331
Appendix 3
Solutions to “Spare-time
activities”......Page 338
Appendix 4
Bibliography......Page 354
Index......Page 356