chapter one: introduction to basic statistics

This document states the introduction of statistics, defines the classification of statistics such as descriptive and inferential statistics with examples are clearly written. In addition, measurement scales; nominal, ordinal, interval, ratio scales and some basic statistics terms are neatly stated.

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ASSOSA UNIVERSITY
Department of Statistics
Introduction to StatisticsIntroduction to Statistics
Instructor: Eshetu M.( MSc. in BiostatisticsMSc. in Biostatistics)
E-Mail: [email protected]

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
The objective of this course is to teach the student to
organize and summarize data.

The concepts and methods necessary for achieving
the objective are presented under the heading of
descriptive statistics.
ObjectivesObjectives

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Definition:
The term statistics have two definitions;
–When used in singular senseWhen used in singular sense
–When used in its plural senseWhen used in its plural sense
In Plural SenseIn Plural Sense: Statistics are the raw data themselves , like
statistics of births, statistics of deaths, statistics of students,
statistics of imports and exports, etc.
It is equivalent to numerical facts, figures or measurements.
But all numerical figures are not statistics.
1.1. Definition of STATISTICS1.1. Definition of STATISTICS

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In Singular SenseIn Singular Sense: Statistics is subject that deals with
collecting, organizing, presenting, analyzing and interpreting
numerical data for the purpose of assisting in making a more
effective decision.
Statistics Statistics is a science that helps us make better decisions in business,
health and economics as well as in other fields.
Definition of STATISTICS (cont’d…)Definition of STATISTICS (cont’d…)

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Statistics can be classified in to two broad classes: Descriptive statistics and
Inferential Statistics.
1.1.Descriptive StatisticsDescriptive Statistics: This part of statistics deals only with describing some
characteristics of the data collected (only sample data) without going beyond the
data.
That is without attempting to infer (conclude) anything about the population.
Descriptive statistics deals with collection of data, its presentation in various forms,
such as tables, graphs and diagrams and findings averages and other measures
which would describe the data.
Examples:
•Classification of students in Assosa Campus according to their Department
•The number of female/male students in this class.
1.2. Classification of Statistics

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2.Inferential Statistics: This type of statistics is concerned with drawing
statistically valid conclusions about the characteristics of the population (large
group) based on information obtained from a sample (small group).
It is the part of statistics that is generalizing from sample to population using
probabilities, performing hypothesis testing, determining relationships between
variables, and making predictions.
Example:
–Of 50 randomly selected people in the town of Assosa, 10 people had
the last name Abebe. An example of inferential statistics is the
following statement: "about 20% of all people living in Ethiopia have
the last name Abebe."
1.2. Classification of Statistics(cont’d…)

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1.3. Stages in Statistical Investigation
Stage 1: Data Collection
- The process of obtaining measurements or counts.
Stage 2: Organization
- Editing, coding and classification are the three steps in the organization of data
Stage 3: Presentation of Data
- Overall view of what the data actually looks like.
- The organized data are presented with the help of tables, diagrams and graphs to
facilitate further statistical analysis.
Stage 4: Data Analysis
- extraction of relevant information from the collected data using some
mathematical and statistical tools
Stage 5: Interpretation of the Result
This involves making inferences (drawing conclusions) based on the analysis of
data.

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1.4. Definition of some basic terms
Population vs. SamplePopulation vs. Sample
1.A population consists of the set of all subjects, measurements or individuals possessing
certain common characteristics that are being studied or sample comes from it.
2.While, a sample is a representative subset (subgroup) of a population selected by using
valid statistical procedures (sampling techniques).
Examples of a population:
–All types of rocks in Adama
–All patients in Assosa Hospital
–All households in Assosa with monthly income more than 1500 birr
Examples of a sample:
–A sample of 25 patients in Assosa Hospital
–A sample of 100 students in Assosa Campus

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Basic terms (cont’d…)
Census Vs. Sampling Census Vs. Sampling
3.A census is a complete enumeration of every item in a population.
4.Sampling is the process of taking a sample from a population
There are several reasons why we do not work with populations.
-Expensive
-Time consuming, and
-Difficult
Thus, we study a sample and generalize the properties of the sample to the
entire population.
Parameter Vs. StatisticParameter Vs. Statistic
4.Parameter is a statistical measure obtained from a population data
5.Statistic is a statistical measure obtained from a population data

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Basic terms (cont’d…)
•Examples of parameter:
–The mean age of all students in Assosa Campus
–The mean income of all households in Assosa
•Examples of statistic:
–The mean age of 100 students in Assosa Campus
–The mean income of 25 households in Assosa
5.Variable is a characteristics under study that assumes different values for different
elements

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1.5. Application, Uses and Limitations of of Statistics
Application of statistics:
•Statistics is applied in any field of study which seeks quantitative evidence
•It has become the scientific framework for including education, agriculture,
business and economics, industry and health etc.
•For instance,
•To compare breaking strength of two products
•For quality control of products in a given production process
•To compare the improvement in yield due to application of fertilizer,
pesticide….

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Uses of Statistics
It’s uses include, but not limited It’s uses include, but not limited
•Presents facts in a summarized and precise form
•Simplifies complex data (data reduction)
•Facilitates comparisons
•Helps in estimating unknown population characteristics
•Helps in studying the relationship between two or more variables
•Helps in prediction and forecasting future values and formulating
policies

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Limitation of Statistics
As a science statistics has its own limitations. The following are some
of the limitations:
•It does not study qualitative characteristics directly
•It doesn’t deals with a single individuals but deals with aggregate
of facts
•Statistical findings are approximate
•It is sensitive to misuse

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1.7. Types of Variables
Qualitative/Categorical Variables: are data which are non-numeric
in nature and can’t be measured. A qualitative data is a data that
cannot be described numerically.
- Example: eye color, nationality, sex of patient, gender…
Quantitative variables: are data that can be expressed numerically
or are data that are numeric in nature.
Quantitative data can be further classified as discrete or continuous.

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Types of continuous variables (cont’d…)
Discrete Data: A data that assumes a finite or countable number of possible values.
Discrete data are usually obtained by counting.
- Example: Number of customers; number of tourists in Assosa; number of
children in a family, number of students in a class; number of cars in a parking lot
etc.
Continuous Data: A data that can theoretically assume infinite number of possible
values. Continuous data are obtained by measuring.
- Examples: amount of money in a certain account, Yield of wheat from
certain farm, area of crop land in m
2
, weight, height, length, temperature etc.

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1.8. Scales of Measurement
Proper knowledge about the nature and type of data to be dealt with is
essential inin order to specify and apply the proper statistical method for order to specify and apply the proper statistical method for
their analysis and inferences. their analysis and inferences.
Measurement scale refers to the property of value assigned to the data
based on the properties of order, distance and fixed zeroproperties of order, distance and fixed zero.
According to scale of measurement data can be classified as:
1.1.Nominal Scale data Nominal Scale data
2.2.Ordinal Scale dataOrdinal Scale data
3.3.Interval Scale dataInterval Scale data
4.4.Ratio Scale dataRatio Scale data

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1.8. Scales of Measurement(cont’d…)
1.Nominal Scale: are measurement systems that possess none of the three
properties stated above.
In nominal scale of measurement data are classified into categories in
which no order or ranking can be imposed on the data.
AO: +, -, *, / are impossible
Comparison is impossible
Examples:
–Sex of a person (male and female could be coded as 0 and 1).
–Marital status (Single, married, divorced and widowed as 1, 2, 3 and 4).
–Color ( for example eye color of a given species of fish in a lake)
–Political preference (Republican, Democrat, Federalism etc )

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1.8. Scales of Measurement(Cont’d…)
2.Ordinal Scale: are measurement systems that possess the property of order.
Level of measurement which classifies data into categories that can be ranked.
The magnitude b/n the values is not clearly known. With ordinal scale data
there is qualitative difference but the space or interval between ranks are not
always constant (i.e. no exact difference between the ranks or ordersi.e. no exact difference between the ranks or orders).
Example:
–Economic status (poor, medium, higher),
–military ranks
–Letter grades (A, B, C, D, F)
– Rating scales (Excellent, Very good, Good, Fair, poor)

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1.8. Scales of Measurement(Cont’d…)
3.Interval Scale: are measurement systems that possess the properties of Order
and distance, but not the property of fixed zero.
Level of measurement which classifies data that can be ranked and differences
are meaningful.
However, there is no meaningful zero (i.e. zero does not indicate absence of
the characteristics), so ratios are meaningless.
AO: + & - are possible but * & / are impossible
Example:
-IQ
-Temperatures (0F, 0C)

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1.8. Scales of Measurement(Cont’d…)
4.Ratio Scales: are measurement systems that possess all three properties: order,
distance, and fixed zero.
Level of measurement which classifies data that can be ranked, differences are
meaningful, and there is a true zero.
True ratios exist between the different units of measurements
AO: +, -, *, / are possible
Example:
-Income is a ratio data because zero dollars is truly “no income”
- weight
-Height
-Age
-Numbers of students