Today,
few professional activities are untouched by statistical thinking, and
most academic disciplines use it to a greater or lesser degree…
Statistics has developed out of an aspect of our everyday thinking to
be a ubiquitous tool of systematic research… Statistical thinking is a
way of recognizing that our observations of the world can never be
totally accurate; they are always somewhat uncertain. Rowntree D (1981). Statistics without tears. A primer for non-mathematicians. Penguin Books Ltd., London, England.
The
term ‘statistics’ refers to the methods used to collect, process and
interpret data. Because these methods are so inherent in the process of
scientific inquiry, there have been multiple references to statistics
throughout our blog, namely, in the posts on study design, methods,
results and display items. However, given the importance of statistics
in most scientific studies, it is worthwhile having a separate post on
how they should be used and presented.
Statistics should first
be considered long before the commencement of any research, during the
initial study design. First, consider what information you need to
collect in order to test your hypothesis or address your research
question. It is important to get this right from the outset because,
while data can be reanalyzed relatively easily if the wrong tests were
used, it is far more difficult and time-consuming to repeat data
collection with a different sample group or obtain additional variables
from the same sample. If you wish to test the efficacy of a treatment
for use in the general population, then your sample needs to be
representative of the general population. If you wish to test its
efficacy in a given ethnicity or age group, then your sample needs to
be representative of that group. If comparing two groups of subjects
separated on the basis of a particular disease or behavior, then other
variables, such as age, sex and ethnicity, need to be matched as
closely as possible between the two groups. This aspect of statistics
relates to the collection of data; get it wrong and you could face
major problems, potentially the need to start the research all over
again, at the peer review stage many months later.
Second, you
need to consider what statistical tests should be applied so that you
can make meaningful statements about your data. This depends on the
type of data you have collected: do you have categorical data, perhaps
describing the presence or absence of a particular marker, or
quantitative data with numerical values? If your data is quantitative,
is it continuous (that is, can it be measured) or discrete (counts)?
For example, age, weight, time and temperature are all examples of
continuous data because they are measured on continuous scales with
units that are infinitely sub-divisible. By contrast, the number of
people in a given group and the number of cells with apoptotic features
are examples of discrete data that need to be counted and are not
sub-divisible. You also need to know how your data is distributed: is
it normally distributed (Gaussian) or skewed? This also affects the
type of test that should be used. It is important that you know what
type of data you are collecting so that you apply the appropriate
statistical tests to analyze the data and so you present them in an
appropriate manner. The following useful website provides a guide to
choosing the appropriate statistical test:
http://www.graphpad.com/www/Book/Choose.htm
Finally, you need to
know how to interpret the results of the statistical tests you have
selected. What exactly does the p (or t or χ2 or other) value mean?
That, after all is the point of statistical analysis: to determine what
you can say about your findings; what they really mean. Statistics
enable us to determine the central tendency (for example, mean and
median) and dispersion (for example, standard deviation, standard
error, and interpercentile range) of a dataset, giving us an idea of
its distribution. Also using statistics, values from two or more
different sample groups can be compared (for example, by t-test,
analysis of variance, or χ2 test) to determine if a difference between
or among groups could have arisen by chance. If this hypothesis, known
as the null hypothesis, can be shown to be highly unlikely (usually
less than 5% chance), then the difference is said to be significant. It
is important to keep in mind that there are two risks associated with
reducing a decision about the ‘reality’ of a difference to
probabilities, and both depend on the threshold set to determine
significance: the first, known as type I error, is the possibility that
a difference is accepted as significant when it is not; the opposite
risk, known as type II error, refers to the possibility that a
significant difference is considered not to be significant because we
demand a larger difference between groups to be certain. Reducing the
risk of type I errors increases the risk of type II errors, but this is
infinitely more preferable than reaching a conclusion that isn’t
justified. Statistics also provides a measure of the strengths of
correlations and enables inferences about a much larger population to
be drawn on the basis of findings in a sample group. In this way,
statistics puts meaning into findings that would otherwise be of
limited value, and allows us to draw conclusions based on
probabilities, even when the possibility of error remains.
Example
Extracts from The Journal of Clinical Investigation (doi:10.1172/JCI38289; reproduced with permission).
Checklist 1. Indicate what parameters are described when listing data; for example, “means±S.D.” 2. Indicate the statistical tests used to analyze data 3. Give the numerator and denominator with percentages; for example “40% (100/250)” 4. Use means and standard deviations to report normally distributed data 5. Use medians and interpercentile ranges to report data with a skewed distribution 6. Report p values; for example, use “p=0.0035” rather than “p<0.05” 7. Only use the word “significant’ when describing statistically significant differences.