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Eng.Mosab I. Tabash
Applied StatisticsApplied StatisticsApplied StatisticsApplied Statistics
Eng.Mosab I. Tabash
Session 1 : Lesson 1Session 1 : Lesson 1
Introduction Introduction
to to
StatisticsStatistics
Introduction Introduction
to to
StatisticsStatistics
Eng.Mosab I. Tabash
ObjectivesObjectives
To define statisticsTo define statistics To discuss the wide range of To discuss the wide range of
applications of statistics in businessapplications of statistics in business To understand the branches of To understand the branches of
statisticsstatistics To describe the levels of To describe the levels of
measurement of datameasurement of data
Eng.Mosab I. Tabash
What is Statistics? Science of collecting, organizing,
presenting, analyzing, and interpreting data for the purpose of assisting in making more effective decision
Branch of mathematics Facts and figures A subject or discipline Collections of data A way to get information from data
Eng.Mosab I. Tabash
What is Statistics?
“Statistics is a way to get information from data”
Data
Statistics
Information
Data: Facts, especially numerical facts, collected together for reference or information.
Definitions: Oxford English Dictionary
Information: Knowledge communicated concerning some particular fact.
Statistics is a tool for creating new understanding from a set of numbers.
Eng.Mosab I. Tabash
Example - Stats Anxiety…A business school student is anxious about their statistics course, since they’ve heard the course is difficult. The professor provides last term’s final exam marks to the student. What can be discerned from this list of numbers?
Data
Statistics
Information
List of last term’s marks.
958970657857:
New information about the statistics class.
E.g. Class average,Proportion of class receiving A’sMost frequent mark,Marks distribution, etc.
Eng.Mosab I. Tabash
Applications of Statistics in Business
Accounting – auditing and cost estimation Finance – investments and portfolio
management Human resource – compensation, job
satisfaction, performance measure Operation – quality management, forecasting,
MIS, capacity planning, materials control Marketing - market analysis, consumer
research, pricing Economics – regional, national, and
international economic performance International Business- market and
demographic analysis.
Eng.Mosab I. Tabash
Key Statistical Concepts… Population
— a population is the group of all items of interest to a statistics practitioner.
— frequently very large; sometimes infinite.
E.g. All Blue collar workers in Malaysia
Sample
— A sample is a set of data drawn from the population.
— Potentially very large, but less than the population.
E.g. a sample of 765 blue collar workers
Eng.Mosab I. Tabash
Key Statistical Concepts…
Parameter— A descriptive measure of a population.
Statistic— A descriptive measure of a sample.
Eng.Mosab I. Tabash
Key Statistical Concepts…
Populations have Parameters,Populations have Parameters, Samples have Statistics.Samples have Statistics.
Parameter
Population Sample
Statistic
Subset
Eng.Mosab I. Tabash
Branches of Statistics
Statistics
Descriptive Statistics Inferential Statistics
Non-Parametric StatisticsParametric Statistics
Eng.Mosab I. Tabash
Descriptive Statistics… …are methods of organizing, summarizing, and
presenting data in a convenient and informative way. These methods include: Graphical Techniques Numerical Techniques
The actual method used depends on what information we would like to extract. Are we interested in… measure(s) of central location? and/or measure(s) of variability (dispersion)?
Descriptive Statistics helps to answer these questions…
Eng.Mosab I. Tabash
Inferential Statistics… Descriptive Statistics describe the data set that’s
being analyzed, but doesn’t allow us to draw any conclusions or make any interferences about the data. Hence we need another branch of statistics: inferential statistics.
Inferential statistics is also a set of methods, but it is used to draw conclusions or inferences about characteristics of populations based on data from a sample.
Eng.Mosab I. Tabash
Statistical Inference…Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample.
Parameter
Population
Sample
Statistic
Inference
What can we infer about a Population’s Parametersbased on a Sample’s Statistics?
Eng.Mosab I. Tabash
Statistical Inference…We use statistics to make inferences about parameters.
Therefore, we can make an estimate, prediction, or decision about a population based on sample data.
Thus, we can apply what we know about a sample to the larger population from which it was drawn!
Eng.Mosab I. Tabash
Statistical Inference… Inference… Rationale:
•Large populations make investigating each member impractical and expensive.
•Easier and cheaper to take a sample and make estimates about the population from the sample.
However:Such conclusions and estimates are not always going to be correct.
For this reason, we build into the statistical inference “measures of reliability”, namely confidence level and significance level.
Eng.Mosab I. Tabash
Confidence & Significance Levels…
The confidence level is the proportion of times that an estimating procedure will be correct.
E.g. a confidence level of 95% means that, estimates based on this form of statistical inference will be correct 95% of the time.
When the purpose of the statistical inference is to draw a conclusion about a population, the significance level measures how frequently the conclusion will be wrong in the long run.
E.g. a 5% significance level means that, in the long run, this type of conclusion will be wrong 5% of the time.
Eng.Mosab I. Tabash
Process of Inferential Process of Inferential StatisticsStatistics
Process of Inferential Process of Inferential StatisticsStatistics
Population
(parameter)
Sample
x
(statistic)
Calculate x
to estimate
Select a
random sample
Eng.Mosab I. Tabash
Types of Data and InformationTypes of Data and Information
Definitions…A variable is some characteristic of a population or sample.E.g. student grades; workers salaryTypically denoted with a capital letter:A,A-, B+, B, B-…The values of the variable are the range of possible values for a variable.E.g. student marks (0..100)Data are the observed values of a variable.E.g. student marks: {67, 74, 71, 83, 93, 55, 48}
Eng.Mosab I. Tabash
Types of Data & Information
Data (at least for purposes of Statistics) fall into three main groups:
Interval Data Nominal Data
Ordinal Data
Eng.Mosab I. Tabash
Interval Data…Interval data
• Real numbers, i.e. heights, weights, prices, etc.
• Also referred to as quantitative or numerical.
Arithmetic operations can be performed on Interval Data, thus its meaningful to talk about 2*Height, or Price + $1, and so on.
Eng.Mosab I. Tabash
Nominal Data…Nominal Data…Nominal Data
• The values of nominal data are categories.
E.g. responses to questions about marital status, coded as:
Single = 1, Married = 2, Divorced = 3, Widowed = 4
Because the numbers are arbitrary, arithmetic operations don’t make any sense (e.g. does Widowed ÷ 2 = Married?!)
Nominal data are also called qualitative or categorical.
Eng.Mosab I. Tabash
Ordinal Data…Ordinal Data…Ordinal Data appear to be categorical in nature, Ordinal Data appear to be categorical in nature, but their values have an but their values have an orderorder; a ranking to them:; a ranking to them:
E.g. College course rating system:E.g. College course rating system:
poor = 1, fair = 2, good = 3, very good = 4, poor = 1, fair = 2, good = 3, very good = 4, excellent = 5excellent = 5
While its still not meaningful to do arithmetic on While its still not meaningful to do arithmetic on this data (e.g. does 2*fair = very good?!), we can this data (e.g. does 2*fair = very good?!), we can say things like:say things like:
excellent > poorexcellent > poor oror fair < very goodfair < very good
That is, order is maintained no matter what That is, order is maintained no matter what numeric values are assigned to each category.numeric values are assigned to each category.
Eng.Mosab I. Tabash
Types of Data & Information…
Categorical?DataInterval
Data
Nominal Data
Ordinal Data
N
Ordered?
Y
Y
N
Categorical Data
Eng.Mosab I. Tabash
E.g. Representing Student Grades…
Categorical?DataInterval Datae.g. {0..100}
Nominal Datae.g. {Pass | Fail}
Ordinal Datae.g. {F, D, C, B,
A}
N
Ordered?
Y
Y
N
Categorical Data
Rank order to data
NO rank order to data
Eng.Mosab I. Tabash
Calculations for Types of DataAs mentioned above,
• All calculations are permitted on interval data.
• Only calculations involving a ranking process are allowed for ordinal data.
• No calculations are allowed for nominal data, only counting the number of observations in each category is possible.
This lends itself to the following “hierarchy of data”…
Eng.Mosab I. Tabash
Hierarchy of Data…IntervalInterval
Values are real numbers.Values are real numbers.
All calculations are valid.All calculations are valid.
Data may be treated as ordinal or nominal.Data may be treated as ordinal or nominal.
OrdinalOrdinal
Values must represent the ranked order of the data.Values must represent the ranked order of the data.
Calculations based on an ordering process are valid.Calculations based on an ordering process are valid.
Data may be treated as nominal but not as interval.Data may be treated as nominal but not as interval.
Nominal Nominal
Values are the arbitrary numbers that represent Values are the arbitrary numbers that represent categories.categories.
Only calculations based on the frequencies of Only calculations based on the frequencies of occurrence are valid.occurrence are valid.
Data may not be treated as ordinal or interval.Data may not be treated as ordinal or interval.
Eng.Mosab I. Tabash
Data Level, Operations, and Statistical MethodsData Level, Operations, and Statistical Methods
Data Level
Nominal
Ordinal
Interval
Meaningful Operations
Classifying and Counting
All of the above plus Ranking
All of the above plus Addition, Subtraction, Multiplication, and Division
StatisticalMethods
Nonparametric
Nonparametric
Parametric