Intended for healthcare professionals

Endgames Statistical Question

# Statistical hypothesis testing

BMJ 2010; 340 (Published 21 April 2010) Cite this as: BMJ 2010;340:c2059
1. Philip Sedgwick, senior lecturer in medical statistics
1. 1Centre for Medical and Healthcare Education, St George’s, University of London, London

A randomised controlled trial evaluated the cost and efficacy of community leg ulcer clinics that used four layer compression bandaging. The control treatment was provision of usual care by district nurses.1 Over the 12 months of follow-up, ulcers healed more quickly in the clinic group than in the control group (P=0.03). Statistical tests were two sided.

Which of the following, if any, are true?

• a) Null hypothesis: in the population, over 12 months of follow-up healing times are shorter if leg ulcers are treated in community clinics rather than by district nurses

• b) Null hypothesis: in the population, no difference exists between community clinics and district nurses in the healing times of leg ulcers over 12 months of follow-up

• c) Alternative hypothesis: in the population, over 12 months of follow-up leg ulcers take longer to heal if treated by district nurses rather than in community clinics

• d) The P value represents the strength of evidence in support of the null hypothesis

Answers b and d are true; a and c are false.

Statistical hypothesis testing forms the cornerstone of medical and healthcare research. It was used in the above study to establish whether the healing times of leg ulcers differed between community clinics and district nurses. Statistical hypothesis testing started at the position of equipoise—that in the population no difference exists between community clinics and district nurses in leg ulcer healing times over 12 months of follow-up. The aim was to establish whether the sample data supported this position or provided evidence of a difference between treatment groups.

We start by stating the statistical null and alternative hypotheses; this is done before we collect the data. The null hypothesis specifies no difference; for the above study this would be that in the population where the sample was obtained, over 12 months of follow-up the healing times of leg ulcers for patients treated in community clinics are the same as if treated by district nurses (answer b is true and a is false).

The alternative hypothesis states that a difference exists—that in the population where the sample was obtained, over 12 months of follow-up the healing times for patients treated in community clinics are not the same as those treated by district nurses (answer c is false). No direction is specified and the alternative hypothesis is two sided—the healing times for patients treated in community clinics could be shorter or longer than those treated by district nurses.

We use the P value to establish whether the sample data support the null hypothesis or provide evidence of a difference as specified by the alternative hypothesis. The P value is derived using the sample data, and it represents the strength of evidence in support of the null hypothesis (answer d is true). The P value is the topic of next week’s question.

## Notes

Cite this as: BMJ 2010;340:c2059

## Footnotes

• Competing interests: None declared.

## References

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