Soni_Biostatistics.ppt

INTRODUCTION TO
BIOSTATISTICS
Dr JS SONI FPCPharm.
1

Learning Objectives
Define data and classify the scales of data
measurement
Know the essential elements of
descriptive statistics and compute basic
statistical measures
Know different methods of sampling in
statistical practice
Outline the steps in hypothesis testing
Know how to apply the steps in some
inferential statistical analysis
2

Introduction
Biostatistics - the application of statistical
methods in the life sciences including
medicine, pharmacy, and agriculture.
An understanding is needed in practice
issues requiring sound decisions.
Statistics is a decision science.
Biostatistics therefore deals with data.
Biostatistics is the science of obtaining,
analyzing and interpreting data in order to
understand and improve human health.
3

Applications of Biostatistics
Design and analysis of clinical trials
Quality control of pharmaceuticals
Pharmacy practice research
Public health, including epidemiology
Genomics and population genetics
Ecology
Biological sequence analysis
Bioinformatics etc.
4

Concept of Data
 Data- Set of measurements or observations.
 Used in plural sense as a single datum is not
useful
 Data that can assume different values are
called variables.
 Variables may be discrete(whole numbers or
integers) or continuous(decimals or fractions).
 Accuracy – closeness of a measurement to the
actual value of a variable that is being
measured.
 Precision – closeness of repeated
measurements to one another.
5

Scales or levels of data measurement
• Nominal
• Ordinal Qualitative data
• Interval
• Ratio Quantitative data
6

Scales or levels of data measurement...
 Nominal scale – Data here cannot be measured
in numerical values but rather classified based
on characteristics or attributes such as sex,
colour, genotype. Nominal simply refers to
name. These data are also referred to as
categorical data.
 Ordinal scale – There is a relative difference but
not a quantitative difference between two
observations or measurements. Examples: very
good, good, fair; tall, taller, tallest; potent, more
potent, most potent. Ordinal refers to order or
ranking.
7

Interval scale – Constant interval size exists
between two measurements but no absolute
zero starting point. 60o C is not twice as hot as
30 o C
We can convert ordinal scale to interval scale
with numerical values. The level of patient
satisfaction with a community pharmacy can
be anchored on very satisfied = 5; satisfied =
4; not sure = 3; unsatisfied = 2; very
unsatisfied = 1.
8

Ratio scale – There is always a constant
numerical interval between two successive
measurements based on a true zero point.
80 kg is as twice as heavy as 40 kg.
Converting Celcius temperature
measurements to the kelvin’s scale transforms
the interval data to ratio data.
Measurements at ratio scale also encompass
other levels of data measurement.
9

Types of statistics
Descriptive Statistics- Deals with statistical
measures and data presentation.
Inferential Statistics- Hypothesis testing in
order to draw a conclusion or inference TO
MAKE A DECISION
10

Descriptive Statistics
Statistical measures
Measures of central tendency – mean, median, and
mode.
Measures of spread or variability – range, semi-
interquartile range, variance, standard deviation,
standard error of mean, and coefficient of variation.
Measures of shape – skew and kurtosis.
Data presentation – pie charts, bar charts, histograms,
and frequency polygons (You should review these
methods of data presentation)
11

Measures of central tendency
Arithmetic Mean
Population mean, μ = ΣX/N
Sample mean, M = ΣX/n
The geometric mean is the nth root of the
product of the scores. The geometric mean of:
1, 2, 3, and 10 is the fourth root of 1 x 2 x 3 x 10
which is the fourth root of 60 which equals 2.78.
Geometric mean = (∏X) 1/N
12

Median
The median is the middle of a distribution:
half the scores are above the median and
half are below the median.
The median is the middle term when a set of
data is arranged in either ascending or
descending order.
The median of 4, 7, and 2 is 4. For odd
number
2, 4, 7, 12 is (4+7)/2 = 5.5. For even number
13

Mode
 The mode is the most frequently occurring
score in a distribution.
 The only measure of central tendency that
can be used with nominal data.
 Some distributions have more than one
mode (multi modal).
 In a normal distribution, the mean, median,
and mode are identical.
14

Measures of variability or spread or dispersion
Range- It is equal to the difference between the
largest and the smallest values.
The range of the numbers 1, 2, 4, 6, 12, 15, 19,
26 = 26 -1 = 25
Semi-interquartile range- One half the
difference between the 75th percentile [often
called (Q3)] and the 25th percentile (Q1). The
formula for semi-interquartile range is
therefore: (Q3-Q1)/2.
15

Standard deviation and variance
The variance is computed as the average
squared deviation of each number from its mean.
For example, for the numbers 1, 2, and 3, the
mean is 2 and the variance is:
16

Population and sample variances
Population
Sample
Standard deviation = √ Variance σ² or s²
In a normal distribution, about 68% of the scores are
within one standard deviation of the mean and about
95% of the scores are within two standard deviations of
the mean.
17

Standard error of mean (SEM)
While SD measures variability among the data,
the SEM measures how accurately the overall
population is known i.e. how precisely you
know the population mean.
SEM = SD/√N
Coefficient of variation (CV)
This is also called measure of relative
variability or relative dispersion.
CV = S/M x 100%; where S = standard
deviation, M = mean
18

Skew
A distribution is skewed if one of its tails is
longer than the other.
19

Kurtosis
Kurtosis is based on the size of a distribution's
tails. Distributions with relatively large tails are
called "leptokurtic"; those with small tails are
called "platykurtic." A distribution with the
same kurtosis as the normal distribution is
called "mesokurtic." The kurtosis of a normal
distribution is 0.
ege of Pharmacists 20

Normal Distribution
They are symmetric with scores more
concentrated in the middle than in the tails.
Normal distributions are sometimes described
as bell shaped.
The standard normal distribution is a normal
distribution with a mean of 0 and a standard deviation
of 1.
21

Inferential Statistics
Deals with hypothesis testing. It compares
values obtained between two or more
samples/populations and makes an inference or
conclusion. Basic to an understanding of
inferential statistics, is an understanding of the
concepts of population and sample.
The sample is the set of data actually analyzed,
while population is set of all the units under
study. Population may be finite (defined) or
infinite (not defined).
Four different contexts where the terms are
used are:
22

Inferential Statistics…
Quality control – a sample of tablets in a batch
is tested to make a prediction about the quality
of the entire batch (population).
Political polls – A random sample of voters is
pooled to make a conclusion about the entire
population of voters.
Clinical studies – A sample of patients (rarely
random) is studied to draw a conclusion about
the entire population of patients.
Laboratory experiments – An experiment is
performed a few times (sample) as compared to
an infinite number of times (population)
23

Sampling Methods
Probability
Nonprobability
In probability samples, each member of the
population has a known non-zero probability of
being selected.
24

Probability methods
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
Multi-stage sampling
Nonprobability sampling
 Convenience sampling
 Judgment sampling
 Quota sampling and
 Snowball sampling
25

Population parameters versus sample statistics
Comparison of population and sample
Population Sample
(Parameters) (Statistics)
Mean µ M
Variance σ2 s2
Standard deviation σ s
Proportion P p
26

Parametric and Non-parametric tests
Most statistical hypotheses make use of the
above population parameters (parametric tests).
Parametric tests are based on the assumption
that you sampled from a normal distribution.
There is a collection of tests called distribution-
free tests that do not make any assumptions
about the distribution from which the numbers
were sampled. The tests are nonparametric
because they do not assume any of the
population parameters.
27

Basic concepts in hypothesis testing
Hypothesis is an assumption made about a
population parameter or sample statistic.
There are two types
Null hypothesis (no difference hypothesis)
Alternative hypothesis
A statistical hypothesis is stated in a negative
sense to avoid bias.
West African Postgraduate College of Pharmacists 28

Confidence intervals
 Can be calculated for many values including a
mean, the difference between two means, a
proportion, or difference (or ratio) of two
populations.
 If your sample is randomly selected, you can be
95% sure that the true population mean lies
within the confidence interval. This means that
95% of the time, the calculated confidence
interval contains the population mean and 5%
of the time it does not.

P-value and Statistical significance
P-value is the probability of randomly obtaining
samples with a mean difference as large or
larger than you actually observed if the null
hypothesis were true.
Statistical significance of 5% (P< 0.05) means
that if the null hypothesis were true, what is the
probability that random sampling would result
in a difference large enough to result in a
“significant” (P< 0.05) result? The answer is 5%.

Errors
Type I error (alpha) – There is really no
difference or association or correlation in the
overall population but you found “a significant”
difference by chance.
Type II error (beta) – There is really a difference
or association or correlation in the overall
population larger than the hypothetical value,
but you did not find a “significant” difference.
31

Steps in Hypothesis Testing
State the null hypothesis: Ho: µ1 = µ2
State the alternative hypothesis: H1: µ1 ≠ µ2
State the level of significance (α) = 0.05
Select the test statistic i.e. the equation to be used e.g.
Students’ t-test, Z score, X2
Compute the numerical value of the test i.e. solve the
equation above
Compare calculated value with the tabular value (value
from a standard table)
e.g. Z0.05 = 1.645; Z0.025 = 1.96
Decision: If the absolute calculated value (irrespective
of the sign) > the tabular value, Reject the null
hypothesis, otherwise, do not reject (fail to reject). In
case of a problem of equality, withhold decision, take
more observations and run the experiment again.
32

Statistical tests required
You should learn the following tests:
Z score test for large sample, comparing two
population means with known standard
deviation and Z score test of proportions
Students’ t – test for two sample/population
means
Ordinary One way analysis of variance (ANOVA)
Chi- Square test (X2)
Correlation and Regression analysis
33
ts

QUESTIONS
A comparative efficacy evaluation of medications
for diabetes (A) and hypertension (B) with
innovator products reported P> 0.05 for A and
P< 0.05 for B.
Management is confused as to which of the new
products should be included in the hospital
formulary. Advise management.
34

Soni_Biostatistics.ppt

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