Basic Statistical Concepts – PST06210 Operational Research

NTA Level 6 • Semester 2 • PST06210

Basic Statistical Concepts

Operational Research • Source Session/Topic 1
Full source-text version: all educational wording from the extracted learning source is retained; only presenter/tutor metadata and web-layout noise are removed, while formatting is improved for readability.

Session 1: Basic Statistical Concepts

Total Session Time: 120 minutes

Prerequisites

• None

Learning Tasks

By the end of this session students are expected to be able to:

• Define common terms used in biostatistics
• Explain the importance of different measures in statistics
• Explain the application of statistics in data analysis

Resources Needed

• Flip charts, marker pens, and masking tape
• Black/white board and chalk/whiteboard markers
• Computer and LCD Projector

SESSION OVERVIEW

Activity/

Step Time Content

Method

1 5 minutes Presentation Introduction, Learning Tasks

30 minutes Presentation

2 Definitions of common terms in Biostatistics

Brainstorm

45minutes Presentation Importance of Different Measures in

3

Buzzing Statistics

30minutes Presentation

4 Application of Statistics in Data Analysis

Brainstorming

5 05minutes Presentation Key Points

6 05 minutes Presentation Evaluation

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PST 06210 Operational Research NTA Level 6 Semester 2 Facilitator Guide 1

SESSION CONTENTS

STEP1: Presentation of Session Title and Learning Tasks (5 minutes)

READ or ASK students to read the learning tasks and clarify

ASK students if they have any questions before continuing

STEP 2: Definition of common terms in Biostatistics (30 minutes)

Activity: Buzzing (5 minutes)

ASK students to pair up and buzz on the following question for 2 minutes

• What is biostatistics?

ALLOW few pairs to respond and let other pairs to add on points not mentioned

WRITE their response on the flip chart/board

CLARIFY and SUMMARIZE by using the content below

• Biostatistics can be defined as the application of statistics to biological problems.
• Many biomedical scientists consider it to mean the application of statistics specifically to

medical problems.

• For this group of people, therefore, biostatistics and medical statistics are synonymous

Other terms:

• Statistics can be defined in two forms:

o First ―statistics‖ as a ―noun‖ means a descriptive measure computed from data of a

sample i.e. numerical statement – information that is available in numbers). Examples

of this include:

 Hospital data on the number of admissions for some condition in a period

 How much drug (e.g. Amoxicillin capsules) is distributed to health units –

hospitals, health centers and dispensaries

 This first part of the subject is usually referred to as descriptive statistics

o Secondly ―statistics‖ as a ―discipline‖ is a field of study concerned with:

 Collecting, organizing and summarizing and analysis of data in a systematic way.

 Drawing of inferences about a population on the basis of only a part of the

population targeted.

 This second part, which, provides objective means of drawing conclusions,

constitutes inferential statistics

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PST 06210 Operational Research NTA Level 6 Semester 2 Facilitator Guide 2

• Population

o A collection of entities.

o A statistical population means the largest collection of entities in which we have an

interest.

o Example we may be interested in looking at how may health facilities are given

Amoxil in district X?

• Sample

o Part of a population.

o Example number of health centers given Amoxil capsules.

• Central tendency

o Measures of central tendency provide a summary measure that attempts to describe

data with a single value that represents the middle or center of its distribution.

o There are three main measures of central tendency:

 the mean,

 median and

 mode

Mean, arithmetic mean (X or M):

• The mean of a data set is also known as the average value
• The sum of the scores in a distribution divided by the number of scores in the distribution.

It is the most commonly used measure of central tendency.

• It is often reported with its companion statistic, the standard deviation, which shows how

far things vary from the average.

Median (Mdn):

• The midpoint or number in a distribution having 50% of the scores above it and 50% of

the scores below it.

• The median of a data set is the value that is at the middle of a data set arranged from

smallest to largest

• If there are an odd number of scores, the median is the middle score.

Mode (Mo):

• The number that occurs most frequently in a distribution of scores or numbers
• The mode is the most common observation of a data set, or the value in the data set that

occurs most frequently.

Quartile

• A measure of statistical dispersion which divides a frequency distribution into equal

groups each containing the same fraction of the total population

• The first quartile (designated Q1) is the lower and cuts off the lowest 25% of data (the

25th percentile)

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PST 06210 Operational Research NTA Level 6 Semester 2 Facilitator Guide 3

• The second quartile (Q2), or the median, cuts the data set in half (the 50th percentile)
• The third quartile (Q3) cuts off highest 25% of data, or the lowest 75% (the 75th

percentile)

Variations

• Range (Ra): The difference between the highest and lowest scores in a distribution; a

measure of variability.

• Standard deviation (SD): The most stable measure of variability, it takes into account

each and every score in a normal distribution. This descriptive statistic assesses how far

individual scores vary in standard unit lengths from its midpoint of 0. For all normal

distributions, 95% of the area is within 1.96 standard deviations of the mean.

• Variance (SD2): A measure of the dispersion of a set of data points around their mean

value. It is a mathematical expectation of the average squared deviations from the mean.

STEP 3: Importance of Measures in Statistics (45 minutes)

Activity: Buzzing (5 minutes)

ASK students to pair up and buzz on the following questions for 2 minutes

• What are the importance of different measures in statistics

ALLOW few pairs to respond and let other pairs to add on points not mentioned

WRITE their responses on the flipchart or board

CLARIFY and SUMMARIZE by using the content below

• The following are importance of different measures in statistics

o Measures of central tendency (Mean, Median, and Mode) in statistics

are important because of the following reasons:

 To find representative value: Measures of central tendency or averages; give us

one value for the distribution and this value represents the entire distribution

 Central tendency is very useful in psychology. It helps to know what is normal or

'average' for a set of data. It also condenses the data set down to one representative

value, which is useful when working with large amounts of data

 The mean is an important measure because it incorporates the score from every

subject in the research study

o Measures of dispersion (Range of the Data, Variance, Standard Deviation and

Quartiles) in statistics are important because of the following reasons:

 Variation is a measure of statistical dispersion

 Quartile divides a range of data or population into four equal parts

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PST 06210 Operational Research NTA Level 6 Semester 2 Facilitator Guide 4

STEP 4: Application of Statistics in Data Analysis (30Minutes)

• Statistics is the mathematical science involving the collection, analysis and interpretation

of data.

• The following are application of statistics:

o To assess risk in the pharmaceutical industries.

o To study biological phenomena and observations by means of statistical analysis

o To develop new insights and understanding of performance

o Serves as the foundation and logic of interventions made in the interest of public

health and preventive medicine.

o In clinical trials to arrive at optimal or near optimal solutions to complex problems

 To quantify drug use

 Statistics is an important tool in pharmacological research that is used to

summarize (descriptive statistics) experimental data in terms of central tendency

(mean or median) and variance

o It enables us to conduct hypothesis testing (to determine whether the pharmacological

effect of one drug is superior to another)

o Very helpful in formulating experimental design and drawing appropriate inferences

from the collected data

STEP 5: Key Points (5 minutes)

• Biostatistics can be defined as the application of statistics to biological problems
• Common terms in biostatistics are biostatistics, Statistics, mean, mode, median, Quartile

and Variations

• The importance of different measures in statistics is to give one value for the distribution

and this value represents the entire distribution, to know what is normal or 'average' for a

set of data and variations from normal.

STEP 6: Evaluation (5 minutes)

• What is the importance of different measures in statistics (central tendency, quartile and

variations)?

• What is the application of statistics in data analysis?

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PST 06210 Operational Research NTA Level 6 Semester 2 Facilitator Guide 5

References

Anderson, D.R., Sweeney, D.J., Williams, T.A., Freeman, J. & Shoesmith, E. (2007).

Basic Statistics and epidemiology (2001). A practical guide, Radcliffe Medical Press,

United Kingdom

Beaglehole R, Bonita R and Kjellstrom (1993) Basic epidemiology, World Health

Organization, Geneva

Kazaura, M. R., Makwaya, C. K., Masanja, C. M. and Mpembeni, R.C. (1997). Lecture notesin

Biostatistics, manual of biostatistics: Muhimbili University College of Health Sciences,

Dar es Salaam

Polit, D. F and Beck, C. T (2004) Nursing Research – Principles and Methods, 7th Edition:

Lippincott Williams & Wilkins, Philadelphia

Rao, J. S., & Richard, J. (2002). An introduction to biostatistics-a manual for students in

helthsciences (3rd. Ed): New Delhi, India: Prentice-Hall of India Pvt.Ltd

Rosner B (2010): Fundamental of Biostatistics (7th Ed.): Boston, USA: Cengage Learning

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PST 06210 Operational Research NTA Level 6 Semester 2 Facilitator Guide 6

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