EDITORIAL
SA JOURNAL OF DIABETES & VASCULAR DISEASE
92
VOLUME 7 NUMBER 3 • SEPTEMBER 2010
P
-values: what are they?
J Upton, E McCutcheon
P
-values are commonly included in the results sections of
randomised controlled trials (RCTs), but what is a
p
-value and
how should it be interpreted?
The ‘p’ stands for ‘probability’; the chance of something
happening. If there is a 0% chance of something occurring (i.e.
it is impossible), then the
p
-value is 0. Similarly, if there is a 100%
chance of something occurring (i.e. it is certain), then the
p
-value
is 1. The
p
-value may fall anywhere between these two extremes.
For example, there is a one-in-six chance that if you rolled a dice
you would throw a 1. The
p
-value for this would be 0.1666 (i.e.
1 divided by 6). Further examples of
p
-values are given in Table 1.
P
-values are often included in the results sections of quantitative
research papers to indicate whether a finding was likely to have
occurred by chance. For example, Weekes,
et al
. (2009)
1
conducted
a randomised controlled trial
2
to assess the impact of nutritional
support on patient-centred outcomes in outpatients with COPD at
risk of malnutrition. Patients were randomised to two groups. The
treatment group received dietary counselling and advice on food
fortification; the control group received a dietary advice leaflet.
After six months the researchers compared outcomes between
the two groups to see if there were any statistically significant
differences between them, i.e. to see if nutritional support had
made a greater impact on the outcome measures than the dietary
leaflet. Two of the outcome measures included in the study were
FEV
1
and weight. The average difference in FEV
1
between the two
groups after six months was 0.03 litres; the average difference in
weight between the two groups was 3.1 kg. The authors analysed
the data to ascertain if these differences between the two groups
were statistically significant. The p-value for weight was 0.02 and
the
p
-value for FEV
1
was 0.56.
Researchers traditionally use a cut-off point of
p
=
0.05. If the
p
-value is 0.05 or higher the researcher is likely to conclude that
there is no difference between the two groups. In the above study
the
p
-value of 0.02 for weight was lower than this cut-off point.
The authors therefore concluded that nutritional support had a
significant effect on body weight. There was a very small chance
(2%) that there was really no difference in body weight between
the two groups of patients but the authors were happy to accept
this small chance.
The
p
-value for FEV
1
was 0.56. As this is higher than the 0.05
cut-off point the researchers concluded that ‘nutritional support
had no significant effect on lung function’. The technical way of
saying this is that they ‘failed to reject the null hypothesis’.
3
The smallest
p
-value reported in scientific papers is ‘
<
0.001’.
In an RCT this indicates that there is a one-in-a-thousand chance
that there is no difference between the treatment and control
groups. It is not possible to have a
p
-value of zero in an RCT as
there is always a small chance that the results would have been
different if a different sample of participants had been included or
the randomisation of participants to each of the study groups had
been different.
References
1.
Weekes CE, Emery PW, Elia M. Dietary counselling and food fortification in
stable COPD: a randomised trial.
Thorax
2009 Apr;
64
(4): 326–31. doi:10.1136/
thx.2008.097352.
2.
For further information about randomised controlled trials please see
BJPCN
Respiratory
2007;
1
(3): 109;
BJPCN Respiratory
2008;
2
(2): 13.
3.
For further information about the null hypothesis please see
BJPCN Respiratory
2008;
3
(1): 17;
BJPCN Respiratory
2008;
2
(4): 15.
Jane Upton
Research Project Manager, Education for Health
Ellen McCutcheon
Research Assistant, Education for Health
S Afr J Diabetes Vasc Dis
2010;
7
: 92
Table 1.
Examples of
p
-values
Chance of an event occurring
Percentage
probability
p
-value
Certain
100 times out of 100 (every time)
100% 1 (100/100)
56 times out of 100 (just over
half of the time)
56% 0.56 (56/100)
25 times out of 100 (quarter of
the time)
25% 0.25 (25/100)
5 times in 100
5% 0.05 (5/100)
2 times in 100
2% 0.02 (2/100)
0.1 times in 100
0.01% 0.001 (0.1/100)
Impossible
0 times in 100
0% 0 (0/100)
