Preface .

Statistical packages.

**PART 1. DATA TYPES.**

**1. Data types.**

1.1Does it really matter?

1.2 Interval scale data.

1.3 Ordinal scale data.

1.4 Nominal scale data.

1.5 Structure of this book.

1.6 Chapter summary.

**PART 2. INTERVAL-SCALE DATA.**

**2. Descriptive statistics.**

2.1 Summarizing data sets.

2.2 Indicators of central tendency. mean, median and mode.

2.3 Describing variability. standard deviation and coefficient of variation.

2.4 Quartiles. another way to describe data .

2.5 Using computer packages to generate descriptive statistics.

2.6 Chapter summary.

**3. The normal distribution.**

3.1 What is a normal distribution? .

3.2 Identifying data that are not normally distributed.

3.3 Proportions of individuals within one or two standard deviations of the mean.

3.4 Chapter summary.

**4. Sampling from populations. the SEM.**

4.1 Samples and populations.

4.2 From sample to population.

4.3 Types of sampling error.

4.4 What factors control the extent of random sampling error?

4.5 Estimating likely sampling error. The SEM.

4.6 Offsetting sample size against standard deviation.

4.7Chapter summary.

**5. Ninety-five per cent confidence interval for the mean.**

5.1 What is a confidence interval?

5.2 How wide should the interval be?

5.3 What do we mean by ‘95 per cent’ confidence?

5.4 Calculating the interval width.

5.5 A long series of samples and 95 per cent confidence intervals.

5.6 How sensitive is the width of the confidence interval to changes in the SD, the sample size or the required level of confidence?

5.7 Two statements.

5.8 One-sided 95 per cent confidence intervals.

5.9 The 95 per cent confidence interval for the difference between two treatments.

5.10 The need for data to follow a normal distribution and data transformation.

5.11 Chapter summary.

**6. The two-sample t-test(1).Introducing hypothesis tests.**

6.1 The two-sample t-test. an example of a hypothesis test.

6.2 ‘Significance’.

6.3 The risk of a false positive finding.

6.4 What factors will influence whether or not we obtain a significant outcome?

6.5 Requirements for applying a two-sample t-test.

6.6 Chapter summary.

**7. The two-sample t-test(2).The dreaded P value.**

7.1 Measuring how significant a result is.

7.2 P values.

7.3 Two ways to define significance?

7.4 Obtaining the P value.

7.5 P values or 95 per cent confidence intervals?

7.6 Chapter summary.

**8. The two-sample t-test(3).False negatives, power and necessary sample sizes.**

8.1 What else could possibly go wrong?

8.2 Power.

8.3 Calculating necessary sample size.

8.4 Chapter summary.

**9. The two-sample t-test(4).Statistical significance, practical significance and equivalence.**

9.1 Practical significance. is the difference big enough to matter?

9.2 Equivalence testing.

9.3 Non-inferiority testing.

9.4 P values are less informative and can be positively misleading.

9.5 Setting equivalence limits prior to experimentation.

9.6 Chapter summary.

**10. The two-sample t-test(5).One-sided testing.**

10.1 Looking for a change in a specified direction.

10.2 Protection against false positives.

10.3 Temptation!.

10.4 Using a computer package to carry out a one-sided test.

10.5 Should one-sided tests be used more commonly?

10.5 Chapter summary.

**11. What does a statistically significant result really tell us?**

11.1 Interpreting statistical significance.

11.2 Starting from extreme scepticism.

11.3 Chapter summary.

**12. The paired t-test. comparing two related sets of measurements.**

12.1 Paired data.

12.2 We could analyse the data using a two-sample t-test.

12.3 Using a paired t-test instead.

12.4 Performing a paired t-test.

12.5 What determines whether a paired t-test will be significant?

12.6 Greater power of a paired t-test.

12.7 The paired t-test is only applicable to naturally paired data.

12.8 Choice of experimental design.

12.9 Requirements for applying a paired t-test .

12.10 Sample sizes, practical significance and one-sided tests.

12.11 Summarizing the differences between the paired and two-sample t-tests.

12.12 Chapter summary.

**13. Analyses of variance. going beyond t-tests.**

13.1 Extending the complexity of experimental designs.

13.2 One-way analysis of variance.

13.3 Two-way analysis of variance.

13.4 Multi-factorial experiments.

13.5 Keep it simple. Keep it powerful.

13.6 Chapter summary.

**14. Correlation and regression. relationships between measured values.**

14.1 Correlation analysis.

14.2 Regression analysis.

14.3 Multiple regression.

14.4 Chapter summary.

**PART 3. NOMINAL-SCALE DATA.**

**15. Describing categorized data.**

15.1 Descriptive statistics.

15.2 Testing whether the population proportion might credibly be some pre-determined figure.

15.3 Chapter summary.

**16. Comparing observed proportions. the contingency chi-square test.**

16.1 Using the contingency chi-square test to compare observed proportions.

16.2 Obtaining a 95 per cent CI for the change in the proportion of expulsions. is the difference large enough to be of practical significance?

16.3 Larger tables. attendance at diabetic clinics.

16.4 Planning experimental size.

16.5 Chapter summary.

**PART 4. ORDINAL-SCALE DATA.**

**17. Ordinal and non-normally distributed data.Transformations and non-parametric tests.**

17.1 Transforming data to a normal distribution.

17.2 The Mann-Whitney test. a non-parametric method.

17.3 Dealing with ordinal data.

17.4 Other non-parametric methods.

17.5 Chapter summary.

Appendix to Chapter 17.

**PART 5. SOME CHALLENGES FROM THE REAL WORLD.**

**18. Multiple testing.**

18.1 What is it and why is it a problem?

18.2 Where does multiple testing arise?

18.3 Methods to avoid false positives.

18.4 The role of scientific journals.

18.5 Chapter summary.

**19. Questionnaires.**

19.1 Is there anything special about questionnaires?

19.2 Types of questions.

19.3 Designing a questionnaire.

19.4 Sample sizes and return rates.

19.5 Analysing the results.

19.6 Confounded epidemiological data.

19.7 Multiple testing with questionnaire data.

19.8 Chapter summary.

**PART 6. CONCLUSIONS.**

**20. Conclusions.**

20.1 Be clear about the purpose of the experiment.

20.2 Keep the experimental design simple and therefore clear and powerful.

20.3 Draw up a statistical analysis plan as part of the experimental design. it is not a last minute add-on.

20.4 Explore your data visually before launching into statistical testing.

20.5 Beware of multiple analyses.

20.6 Interpret both significance and non-significance with care.

Index.