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Terminating Terminology Terror Part 1 – Statistics

Published: Sat February 20, 2010

When shall we three meet
again? In thunder, lightening or in rain? A little awkward, I thought to myself as I sat at my desk in Mr.
Bebbington's Grade 7 English class reading Shakespeare for the first time. When
the hurlyburly's done, when the battle's lost and won. What the heck does "hurly-burly" mean? That will
be ere the set of sun. Huh? Ere?
Okay, time for Coles Notes. Well, 10 years later, I found that if there was
anything more frustrating to read and understand than a Shakespeare tragedy, it
must surely be a medical journal.

Scientists, for better or
worse, love their terminology; scientific publications are scattered with terms
foreign to most native speakers of the English language. This can make it
difficult for clinicians who browse the literature to grasp the message of any
research paper and determine if the results are applicable to the patients they
encounter. Here is Act 1, I mean, Part 1, of a series of "Coles Notes for
prehospital literature." This time, we focus on the "s" word: Statistics. Feel
free to rip this out and stick it in your protocol book.

Normal distribution: All data is distributed across a range. For example,
if we took all the response times in your area, we would find a few really fast
ones (the call was next door to the station) and a few really slow ones (there
was a snow storm and the ambulance had to drive across town). But most of the
calls will be somewhere in the middle. We call this a normal distribution.
Sometime data is not normally distributed. It is skewed away from the middle.
Consider time to backboard. Usually, we can backboard people quickly, within a
few minutes. But sometimes, the fire department will need an hour to extricate
the patient, skewing the distribution in one direction. This creates Outliers. Outliers are results that are far away from the
expected.

Average: This term can be misleading. Here is an example: 2,
4, 6, 8, 40. These are how many
pairs of shoes five people report owning. We have an outlier who owns 40 pairs
of shoes, which skews the distribution of the data. We can report this with a
mean or median, and get drastically different averages.

Mean: Add up all the responses and divide by the number
of responses. The mean of the above example is 12. This is not really
reflective of how many pairs of shoes people in our sample own; the outlier has
skewed the data, and the mean is not representative of the average. Mean is used
when the data is normally distributed. Standard Deviation measures dispersion -
how close or far responses are to the mean. One standard deviation represents
where about 70 per cent of the results fall. A low standard deviation indicates
that the data points tend to be very close to the mean, whereas a high standard
deviation indicates that the data are spread out over a large range of values.

Median: Take the middle response. In our example, the
median is 6. This measure is appropriate when data is not normally distributed.
Range measures the dispersion of
data by reporting the highest and lowest figure. Using our example, the range
is 2-40. Interquartile Range is
the range of the 25th and 75th percentile. It eliminates
high and low outliers that skew the data by showing us where the middle 50 per
cent of values lie.

Type 1 (alpha) error: This is when your conclusion is a false positive,
believing that there is a difference between two findings when in fact there is
no difference. For example, thinking drug A is better than drug B, when in fact
they are equally beneficial (or equally harmful), would be a type 1 error.

Type 2 (beta) error: This is when your conclusion is a false negative,
believing there is no difference when in fact there is. For example, you might
conclude Defibrillator A doesn't save more lives compared to Defibrillator B,
when in fact it does.

P value: the "probability value," also known as
significance, quantifies the probability that an observation is due to chance
and not an actual difference. In other words, it describes the probability of
making a type 1 error. In medicine, a P value of 0.05 is the highest allowable
P for results to be considered "statistically significant." A P of 0.05 means
there is a 95 per cent chance the results are actual and not caused by chance.
Statistically significant results must be analyzed by clinicians for clinical
significance – if fentanyl decreases pain by 30 per cent and morphine decreases
pain by 32 per cent, are we going throw out all the fentanyl? Probably not –
although these results may be statistically significant, with a p value of
<0.05, they (in my mind) don't justify throwing out the fentanyl.

Odds ratio: This value compares the odds of experiencing an
outcome between two groups. For example, the odds of death in smokers compared
to non-smokers, or the odds of survival in a control group compared to an
experimental group would be the odds ratio. An odds ratio of 1 means the two
groups experience the event of interest (death, survival, etc) equally. An odds
ratio greater than 1 means the first group experiences the event more than the
second group. An odds ratio of less than 1 means the first group experiences an
event less often than the second group.

Relative risk: This calculation compares the probability (rather
than the odds) of experiencing an outcome between two groups. A relative risk
of 1 means there is no difference in risk between the two groups. A RR of less
than 1 means the event is less likely to occur in the experimental group than
in the control group. A RR of more than 1 means the event is more likely
to occur in the experimental group than in the control group.

Confidence interval: This describes the possible variation of a value
within the margin of acceptable alpha error. For example, the odds of death for
patients treated by circus clowns (compared to paramedics) may be 2.0* with a
confidence interval of 1.8 to 2.2. This means that the odds of death are twice
that for people treated by clowns, and any value between 1.8 and 2.2 has a P
value of <0.05 and is considered statistically significant. If a confidence
interval spans 1 (ie 0.8-1.4), the p value is >0.05. *The author has no
evidence to support or refute the claim that clowns are harmful.

Odds ratio vs. relative
risk: What's the difference?<o:p></o:p>

The odds ratio and the
relative risk both compare the likelihood of an event between two groups. Lets
use the Titanic survivors as an example. There were 462 female passengers:
308 survived and 154 died. There were 851 male passengers: 142 survived
and 709 died.

<div align="center">

<table border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;
mso-table-layout-alt:fixed;border:none;mso-padding-alt:0in 5.4pt 0in 5.4pt">
<tbody><tr>
<td width="60" style="width:60.0pt;border:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
 <o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border:solid #171717 1.0pt;border-left:none;
padding:0in 5.4pt 0in 5.4pt">
Alive<o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border:solid #171717 1.0pt;border-left:none;
padding:0in 5.4pt 0in 5.4pt">
Dead<o:p></o:p>
</td>
<td width="83" style="width:83.0pt;border:solid #171717 1.0pt;border-left:none;
padding:0in 5.4pt 0in 5.4pt">
Total<o:p></o:p>
</td>
</tr>
<tr>
<td width="60" style="width:60.0pt;border:solid #171717 1.0pt;border-top:none;
padding:0in 5.4pt 0in 5.4pt">
Female<o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
308<o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
154<o:p></o:p>
</td>
<td width="83" style="width:83.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
462<o:p></o:p>
</td>
</tr>
<tr>
<td width="60" style="width:60.0pt;border:solid #171717 1.0pt;border-top:none;
padding:0in 5.4pt 0in 5.4pt">
Male<o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
142<o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
709<o:p></o:p>
</td>
<td width="83" style="width:83.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
851<o:p></o:p>
</td>
</tr>
<tr>
<td width="60" style="width:60.0pt;border:solid #171717 1.0pt;border-top:none;
padding:0in 5.4pt 0in 5.4pt">
Total<o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
450<o:p></o:p>
</td>
<td width="82" style="width:82.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
863<o:p></o:p>
</td>
<td width="83" style="width:83.0pt;border-top:none;border-left:none;border-bottom:
solid #171717 1.0pt;border-right:solid #171717 1.0pt;padding:0in 5.4pt 0in 5.4pt">
1,313</td></tr></tbody></table></div>

The odds ratio calculates
the odds of death for passengers on board the Titanic as follows. Females faced
odds of 2 to 1 against dying (154/308=0.5). The odds of death for males
was 5 to 1 (709/142=4.993). The odds ratio is 9.986 (4.993/0.5).
There is a ten-fold greater odds of death for males than for females.

The relative risk compares
the probability of death instead of the odds of death. The probability of death
for females is 33 per cent (154/462=0.3333). The probability of death for
males is 83 per cent (709/851=0.8331). The relative risk of death
is 2.5 (0.8331/0.3333), meaning males have a probability of death 2.5
times greater than females.

The choice to use an odds
ratio or a relative risk is complicated and depends on the study design and
question being asked. Think twice about any reported odds ratio or relative
risk before interpreting the findings of a study.

Whether reading The Tragedy
of MacBeth or the Annals of Emergency Medicine, its important to consider the
message of the text and, when in doubt, do a quick dictionary search on the
Internet to make sure you have interpreted the message correctly. After all,
you'd hate to get lost in the plot. Fair is foul and foul is fair: Hover
through the fog and filthy air. I'll
leave the interpretation of that line up to you.

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