Stat-404
4(4-0)
Biostatistics
Pharmacy Practice IB
What is Statistics?
• “Statistics is a way to get information from data”
Statistics
Data Information
Data: Facts, especially Information:
numerical facts, Communicated
collected together for concerning some
reference or particular facts.
information.
Why study statistics?
1. Data are everywhere
2. Statistical techniques are used to make many decisions
that affect our lives
3. No matter what your career, you will make professional
decisions that involve data. An understanding of statistical
methods will help you make these decisions efectively
Brief history?
• The word statistics is derived from the Latin word status (meaning “state”).
Early uses of statistics involved compilations of data and graphs describing
various aspects of a state or country. In 1662, John Graunt published
statistical information about births and deaths. Graunt’s work was followed
by studies of mortality and disease rates, population sizes, incomes, and
unemployment rates.
• Households, governments, and businesses rely heavily on statistical data
for guidance. For example, unemployment rates, inflation rates, consumer
indexes, and birth and death rates are carefully compiled on a regular basis,
and the resulting data are used by business leaders to make decisions
affecting future hiring, production levels, and expansion into new markets.
Definitions
• Statistics is a collection of methods for planning experiments, obtaining
data, and then processing, summarizing, presenting, analyzing,
interpreting, and drawing scientific conclusions based on the data under
uncertain conditions.
• Statistics is the subject which deals with the variability. No two objects in
a universe are exactly alike. If they were, there would have been no
statistical problem.
• It also deals with uncertainty as every process of getting observations
whether controlled or uncontrolled, involves deficiencies or chance
variation. That is why we have to talk in terms of probability since the
inferences which are made about the population on the basis of sample
evidence cannot be absolutely certain.
Population vs Sample
Statistical
Inference
Population Sample
(have Parameters) (have Statistic)
ഥ , S, r
Statistic: 𝑿
Parameters: µ, σ, ρ
Population: A Population is Sample: A representative
a group of all part/subset of the
object/elements/items population.
under investigation.
Why Sampling?
• A process of drawing a sample from population is called
sampling.
• Reduced cost
• Greater speed
• Greater accuracy
• Some times it is the only option (testing the life of bulbs/bulets)
Branches of Statistics
Statistics
Descriptive Inferential
Involves in Organization,
Using sample information
Summarization, and Display of ഥ , S, r, p to draw
such as 𝑿
Data into Tables, Graphs and
Inference about the
Summary Numbers such as
ഥ , S, r, p Population.
𝑿
Variable Any Characteristics that varies from Object to Object, Place to Place
or Over time is known as Variable. e.g., marks, age, height, sex,
temperature, sales, revenue, time etc.
Variable
Qualitative Quantitative
Characteristic which
varies in quality (not Discrete Continuous
numerically) e.g.,
Eye colour, Height
No. of students
Education level, Weight
No. of chairs
Behaviour, Marks
No. of deaths
Quality, Time
No. of births in a hospital
Design, Distance
No. of accidents
Performance Temperature
Measurement
• The process of assigning numbers or labels to objects, persons, states
or, events in accordance with specific logically accepted rules for
representing quantities or qualities of attributes or characteristics.
• There are actually four levels of measurement: nominal, ordinal,
interval, and ratio [psychologist researcher named Stanley Stevens
1951].
Nominal
• Nominal scales are used for labeling variables, without any
quantitative value.
• “Nominal” scales could simply be called “labels.”
• Nominal scales are mutually exclusive (no overlap) categories where
order of the categories is not important.
Example: Gender, Religion, Marital status, Political affiliation, Eye colour
Ordinal
• With ordinal scales, it is the order of the values is what’s important
and significant, but the differences between each one is not really
known.
Poor Fair Good Very Good Excellent
• Order is important because Very Good is better than Good and
Excellent is better than Very Good etc.
• But, Is the difference between “Very Good” and “Excellent” the same
as the difference between “Good” and “Very Good?” We can’t say.
• Therefore, it is the logical ordering for example, cricket teams
standings in ICC ranking, students’ grades, etc.
Interval
• Interval scales are numeric scales in which we know not only the
order, but also the exact differences between the values.
• Constant interval size
• No “true zero” i.e., there is no such thing as no temperature
• With interval data, we can add and subtract, but cannot multiply or
divide.
Example: Temperature, IQ scores, Shoe size
Ratio
• Ratio scales tell us about the order, they tell us the exact value
between units, AND they also have a “true zero” point
Example: height and weight
Qualitative data
Example 1: Consider the data about Gender of 10 students
Gender M F M M F M F M M M
• Make a frequency distribution, relative frequency and % frequency of the
above data and interpret your results? Make an appropriate graph?
Example 2: Suppose we have also collected data of Sections of these 10
students as
Gender M F M M F M F M M M
Section A A A B B B A B A B
• Construct the Cross tabulation of the above data and interpret your results?
Also make an appropriate graph?
Solution
Example 1 Gender f Relative % freq Example 2
Gender Sec A Sec B Total
freq
Male 7 0.7 70 Male 3 4 7
Female 3 0.3 30 Female 2 1 3
Total 10 1.0 100 Total 5 5 10
Bar Chart Multiple Bar chart
8 7 5
7
4
Frequency
Frequency
6
Sec A
5 3
4 3 2 Sec B
3
2 1
1
0 0
Male Female Male Female
Gender Gender
Simple Bar Chart
• A bar chart is a type of chart which shows the values of different
categories of data as rectangular bars with different lengths.
Example: Draw a Simple Bar Chart to represent the Population of 5
cities of the province Punjab.
Bar diagram showing Population of 5 cities
of Punjab
Cities Population (000)
12,000
10,355
Lahore 10,355 10,000
Population in ‘000’
Rawalpindi 4,765 8,000
Faisalabad 3,675 6,000 4,765
3,675
4,000 3,100
Sargodha 1,550 1,550
2,000
Multan 3,100 0
Lahore Rawalpindi Faisalabad Sargodha Multan
Cities
Multiple Bar Chart
Population Multiple Bar Chart showing Population of
Cities (000) Male Female
Males and Females
Lahore 10,355 5385 4,970 6000
5385
4,970
Rawalpindi 4,765 2478 2,287 5000 Males Females
Faisalabad 3,675 1911 1,764 4000
POPULATION
Sargodha 1,550 806 744 3000 2478
2,287
1911
1,764
2000
1000 806 744
0
Lahore Rawalpindi Faisalabad Sargodha
CITIES
Component Bar Chart
Component Bar Chart showing population of
both Males and Females and Total
Cities Pop (000) Male Female
12000
Lahore 10,355 5385 4,970
10000 Males
Rawalpindi 4,765 2478 2,287
8000 Females
4,970
Population
Faisalabad 3,675 1911 1,764
6000
Sargodha 1,550 806 744 4000
2,287
5385 1,764
2000
2478 1911 744
0 806
Lahore Rawalpindi Faisalabad Sargodha
Cities
Discrete data – Frequency Distribution
Example:
• Following data represents the number of infected plants from a
sample of twenty experimental plots. Your task is to present it in
tabular form.
1 2 4 3 0 1 2 3 1 1 0
2 1 0 2 3 0 0 1 3
Discrete Frequency Distribution
No. of infected Tally Frequency Relative
items frequency
f
X
0 |||| 5 5/20 = 0.25
1 |||| | 6 0.30
2 |||| 4 0.20
3 |||| 4 0.20
4 | 1 0.05
Total 20 1.00
Graphical Representation of Discrete Data
Bar Chart representing the infected items
7
6
6
5
5
Frequency
4
4 4
3
1
1
0
0 1 2 3 4
No. of infected items
Pie Chart
• A pie chart is a type of graph in which a circle is divided into sectors
that each represent a proportion of the whole.
Example: The blood group of 70 students were tested and the following
results were obtained.
Blood No. of Blood Groups of Students
Groups Students (f)
17% 11%
A 8
A
B 30 29% 43%
B
O
O 20 AB
AB 12
Pie Chart
Blood No. of Relative Percent Angle
Groups Students frequency frequency rf x 360
(f)
A 8 8/70 = 0.11 0.11*100 = 11 39.6
B 30 0.43 43 154.8
Divide the total
O 20 0.29 29 104.4
angle of the Circle
AB 12 0.17 17 61.2 360 into four
segments as
Total 70 1.00 100 360 calculated
Simple Bar Chart
• Consider the Same example of the blood group of 70 students
Blood Groups
Blood No. of
35
Groups Students (f) 30
30
A 8 25
20
B 30 20
15 12
O 20
10 8
AB 12
5
0
A B O AB
