Methodology and statistics for clinical
research – Part 1: descriptive statistics
Stanley CN Ha 夏正楠
HK Pract 2018;40:9396
Summary
To begin a clinical research, we need a lot of statistical
knowledge in designing the protocol, selecting the
patients, choosing correct statistical tests and drawing
valid conclusions. Therefore, the purpose of this article
is to give you some basic background knowledge of
statistics and the use of statistics to begin a clinical
research. The major knowledge you will learn after
reading this article includes (1) 4 types of measurement
scales (nominal , ordinal , interval and ratio) , (2)
difference between dependent and independent
variables, (3) normal distribution of a data, population
and sample, variance and standard deviation and (4)
the way to construct confidence interval.
摘要
當我們開始臨床研究時，我們需要大量的統計知識，包括設
計研究大綱，選擇參加者，選擇正確的統計測試和總結有效
結論。因此，本文的目的是為你提供一些基本的背景知識了
解統計數據，並利用統計學來進行臨床研究。閱讀本文後，
你學習的主要知識包括4種數據測量方法（類別(nominal)、
等級(ordinal)、等距(interval)和等比(ratio)），獨立變項(independent
variable)和依變項(dependent variable)的差異，標準常
態分配(normal distribution)，母體(population)和樣本(sample)，
標準差(standard deviation)和變異數(variance)，計算信賴區間
(confidence interval)的方法。
Introduction
Statistics is all about probability and distribution. It
is a tool to help us analysis clinical research in order to
draw a conclusion, which is part of the whole clinical
research design. It tells us the relationship among the
outcomes, whether there is enough evidence to conclude that the outcomes are different among different groups,
how the data distributes, etc. Before going into how to
use statistics to do analysis and draw conclusions, some
basic background knowledge is important to understand
what statistics is and how we can use statistics
correctly.
Steps to do a clinical research
 Formulate a research question
 Formulate protocol and design sampling method
 Recruit suitable participants into the study
 Collect data
 Present data
 Select suitable statistical test and analyse the data
 Draw conclusion
Statistics is of help in step 2, 5, 6 and 7. In this
first article, I would like to introduce the knowledge
you need to know before doing analysis, including scale
of measurement, type of variable, data presentation,
normal distribution, variance and confidence interval.
Statistical Terminologies
Scale of measurement^{1} – nominal, ordinal, interval
and ratio (Table 1)
To choose a statistical test correctly, it is important
to define the scale of measurement of each variable to
be analysed. There are 4 types of measurement scale,
nominal, ordinal, interval and ratio.^{1}
Nominal scale
Nominal scale represents qualitative data.
Sometimes it is referred to as discrete variable. It is
the most unrestricted assignment of numerals. You can
assign anything you want to measure to a number. For
example, usually we assign 1 to represent male and 2
to represent female. In fact, you can assign anything
you want to represent male, like 4 to male and 9 to
female. It depends on your own preference. However,
considering the easiness of interpretation of future
statistical test results, we usually assign the numbers
that help us interpret the results easily. It involves categorical or group information. For example, each
football player is assigned a number. Therefore, each
number represents one player. For example, in school,
we have class A, class B and class C representing
different groups of students. Each number in a
nominal scale, we call it a level. Levels for a nominal
variable have to be mutually exclusive and include all
possibilities. For example, every participant is either a
male or a female. It is not possible to be both a male
and a female or not possible to be classified as any
other kind of gender. And each number represents one
football player and all numbers together represent all
football players. The way we present nominal scale
data can be with the terms; mode – the level with the
highest frequency, frequency – the number of count
in each level and percentage – the percentage of each
level.
Ordinal scale
Ordinal scale represents qualitative data, similar
with nominal scale. The difference is ordinal scale
involves rankordering. It can also involve categorical
or group information with a restriction of ordering in
each level of ordinal scale. For example, pain with 4
levels, 0 = no pain, 1 = slightly pain, 2 = moderate pain
and 3 = very painful. As the number increases, there
is an increase in the painfulness but the magnitude of
change in painfulness may not be the same between
“1 = slightly pain” and “2 = moderate pain” as between
“2 = moderate pain” and “3 = very painful”. Each
number or level represents a subjective feeling on a
limited scale. When there are many levels in an ordinal
scale data, we can make use of statistical tests that
are appropriate for interval scale and ratio scale data.The way we present ordinal scale data can be median
– the “middle” outcome in a sorted list of numbers;
mode – the level with the highest frequency, frequency
– the number of count in each level, percentage – the
percentage of each level and percentile – the value
below which a percentage of data falls.
Interval scale
Interval scale represents quantitative data. The
difference between each measurement unit is equally
distant. For example, the difference between 1 and 2 is
the same as the difference between 5 and 6. However,
there is no true meaning for “zero”. For example,
temperature in degree Celsius. Each equal interval of
measurement represents the same volume of expansion
of alcohol. 0^{o}C is an arbitrary zero agreed by the
public and it is not meaningful to say “zero” volume of
expansion. Also, 40^{o}C does not mean it is twice hotter
than 20^{o}C. The way we present interval scale data can
be with the mean – the average of the interval scale
data and standard deviation  the measure of how spread
out the data is.
Ratio scale
Ratio scale represents quantitative data, similar
with interval scale. The difference is ratio scale has a
true meaning to “zero” and the ratio of the measurement
is meaningful. For example, length in meters. Zero
meters is a true zero measurement. 40 meters is twice as
long as 20 meters. The way we present ratio scale data
can be with mean – the average of the ratio scale data
and standard deviation  the measure of how spread out
the data is.
Types of variable  Independent vs dependent
variable
To choose a statistical test correctly, the second
thing we need to know is what the dependent variables
and independent variables are to be analysed in our
research. To classify each variable into dependent and
independent variables, it depends on the design and
outcomes of our research.
Independent variables
Independent variables are variables that can be
controlled or determined by researchers in the research.
The independent variables can also be called as
predictors, explanatory variables and exposure variables.
The independent variables are usually used to predict
the values of the dependent variables in a statistical
model.
Dependent variables
Dependent variables are variables that cannot
be controlled or determined by researchers in the
research. The dependent variables can also be called as
predicted variables and observed variables. In a clinical
study, dependent variables are the outcomes that the
researchers would like to look into or the outcomes
that can answer the research question formulated by the
researchers. We look at the difference in the changes in
dependent variables in different levels or measurements
of independent variables.
For example, we want to find out the factors that
can affect intelligence of a student or, in other words,
we want to look into the difference in intelligence with
the different aspects of variables collected. Therefore,
an intelligence score of a student could be a dependent
variable because it can be changed depending on several
factors, such as the school the student is attending,
father and mother intelligence, gender, age, the time the
student spent in doing intelligence related exercise or
even the sleep quality before he does the intelligence
test. All the factors, that we think or have been shown
by past literature that can affect the intelligence of a
student can be collected and classified as independent
variables.
Normal distribution (mean, variance and
standard deviation)
Normal distribution is an important concept in doing statistical analysis since many statistical tests are
done based on the assumption of normal distribution.
If the data is not normally distributed, the choice of
statistical tests will be largely reduced. However, we
can transform the data to make it normally distributed
in some circumstances.
Before we go into normal distribution, we need to
understand the concept of population, sample, variance
and standard deviation. Population is a complete
set of elements (persons or objects). Sample is one
or more persons or objects from the population. For
example, we conduct a study on a drug effect on lung
cancer patients in Hong Kong. The population is all
lung cancer patients in Hong Kong and the sample
is, say 100, patients in a public hospital. Variance,
denoted as σ^{2} for population variance and S^{2} for sample
variance, measures how far a data set is spread out. It
is defined as “the average of the squared differences
from the mean”, which gives you a very general idea
of the spread of the data. If every input is the same,
the variance is equal to zero which means that there
is no variability. Standard deviation, denoted as σ for
population standard deviation and S for sample standard
deviation, is the square root of the variance.
Normal distribution
A normal distribution (Figure 1) is a distribution
of a variable in a bell shape with most of the data in the
middle and an equal spread out of data to the left and
the right. The middle of value of the normal distribution
is equal to the mean, median and mode of the data.
Also, around 68%, 95% and 99.5% of the values lie
within one, two and three standard deviations of the
mean, respectively. Therefore, the value of mean and
standard deviation of the data confirm the shape of the
normal distribution.
Standard normal distribution is a normal
distribution with mean=0 and standard deviation=1.
Every data with normal distribution can be transformed
into standard normal distribution by deducting the mean
of the data and divided by the standard deviation of the
data, like the formula below.
Central Limit Theorem
Central Limit Theorem(CLT)^{2} tells us that
the distribution of the mean of the data is, at least
approximately, normally distributed, regardless of the
distribution of the underlying distribution of the data
when the data has sufficiently large samples. Usually,
sufficiently large means 2530 samples. When the data
is more skewed to the right or the left, more samples are
required to make use of CLT. In reality, it is impossible
to find a data to follow normal distribution precisely.
However, most of the statistical tests have the assumption
of normal distribution of the data. Therefore, it is
impossible to make use of any statistical tests. However,
based on this theorem, we can assume the data mean is
approximately normally distributed with a sample more
than 25. Therefore, we can make use of most statistical
tests with the normal distribution assumption.
Confidence interval
In doing a study, we draw a sample from the
population and draw conclusions. Therefore, the mean
we get from the sample is not the same as the mean
from the population. So, confidence interval, a range
of value that we are, for example 95%, confident that
the true value is within this range, is established. In
other words, when you repeat the same study 100 times
targeting the same population, we expect there are 95
times the mean is within this 95% confidence interval.
To construct a confidence interval, for example
95% confidence interval for mean, we require the mean
and the standard deviation of the mean by the formula
below.  Lower bound: Mean – Z * SD(mean)
 Upper bound: Mean + Z * SD(mean)
where, Z=1.96 for 95% confidence interval, SD
(mean) = where = S is standard deviation of the
sample and n is the number of participant in the sample.
The value of Z will increase when you to have a
higher percentage of confidence interval, for example
Z=2.24 for 97.5% confidence interval, and decrease
when you have a lower percentage of confidence
interval, for example Z=1.645 for 90% confidence
interval.
For example:
We want to look at the 95% confidence interval
of a sample of 100 primary students with an average
height of 150cm and the standard deviation of the
sample height of 20.
Lower bound: 150 – 1.96 * = 146.08cm,
Z=1.96 for 95% confidence interval
Upper bound: 150 + 1.96 * = 153.92cm,
Z=1.96 for 95% confidence interval
Conclus ion: We ar e 95% conf ident that the
true mean of the studied primary student is between
146.08cm and 153.92cm.
Conclusion
When we make use of statistics to help us draw
conclusion, we always need to bear in mind that it is
a probability only. We can never be 100% certain to
conclude or reject one thing.
Further reading suggestion
 Online book : Statistical Methods in Water
Resources by D.R. Helsel and R.M. Hirsch;
Chapter 3. Describing Uncertainty https://pubs.
usgs.gov/twri/twri4a3/html/toc.html
 Online reading : Basics of Statistics by Jarkko
Isotalo; Chapter 25, page 937
http://www.mv.helsinki.fi/home/jmisotal/BoS.pdf
Stanley CN Ha, BSc (STAT), MPH
Hospital Research Manager / Unit Chief of Sleep Technology
United Christian Hospital, Kowloon East Cluster, Hospital Authority
Correspondence to: Mr Stanley CN Ha, Ear, Nose & Throat (ENT) Office, 1/F,
Kowloon East Cluster Admin Building, Tseung Kwan O Hospital,
Hong Kong SAR.
References:
 Stevens SS. On the theory of scales of measurement. Science. 1946 Jun
7;103(2684):677680.
 Le Cam, L. The Central Limit Theorem around 1935, Statistical Science.
1986;1(1):7896.
