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Textbook Notes
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Canada
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York University
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OMIS 2010
(32)

Alan Marshall
(28)

Chapter 1

School

York University
Department

Operations Management and Information System

Course Code

OMIS 2010

Professor

Alan Marshall

Description

Chapter 1
Descriptive Statistics
Deals with methods of organizing, summarizing, and presenting data in a convenient and
informative way
Forms:
graphical techniques for easy extraction of useful information (Histogram)
Numerical techniques to describe different features of data
Actual technique depends on the specific information that we would like to extract
Measure of central location (Mode, mean, median)
Measure of variability (Range)
Inferential Statistics
Is a body of methods used to draw conclusions or inferences about characteristics of population
based on sample data
Asample that is only a small fraction of the size of the population can lead to correct inferences
only a certain percentages of the time
1.1 Key Statistical Concepts
Population
Is the group of all items of interest to a statistics practitioner
Descriptive measure: parameter
represents the information we need (in most applications)
Sample
Set of data drawn from a studied population
Descriptive measure: Statistic
Used to make inferences about parameter
Statistical Inference
Process of making an estimate, prediction, or decision about a population based on sample data
Populations = almost always VERY large, impractical to investigate each member
Easier and cheaper to take sample from population and draw conclusions or make estimates
Not always correct
Thus statistical inference measure of reliability
Confidence level: proportion of times that an estimating procedure will be correct
Significance level: Measures how frequently the conclusion will be wrong Chapter 2
2.1 Types of Data and Information
Variable: Some characteristic of a population or sample
Varies from person to person, thus the name
Values of the variable: Possible observations of the variable
Data: Observed values of a variable (Plural form of datum)
Three types
Interval: Real numbers, referred to as quantitative or numerical
Nominal: Categories, also called qualitative or categorical
Ordinal:Appear to be nominal, but order of their values has meaning, and thus must be
maintained.
Magnitude no important, as long as they are in order
Difference between ordinal and interval:
Intervals or differences between values of interval are consistent and meaningful (can
calculate or interpret), while the intervals or differences between ordinal values hold no
meaning (cannot calculate or interpret)
Calculations for Types of Data
Interval Data
All calculations are permitted
Nominal Data
Cannot perform any calculations
Calculations based on codes used to store this type of data are meaningless
Can only count or compute percentages of the occurrences of each category
Ordinal Data
Most important aspect = order of the values
Only permissible calculations are those involving a ranking process
Hierarchy of Data
Placed in order of permissible calculations
Higher-level data types may be treated as lower-level ones
Conversion leads to loss of information
Do not convert data unless necessary
CANNOT treat lower-level data as higher-level
Summary
Interval
Values are real numbers
All calculations are valid
Data may be treated as ordinal or nominal
Ordinal
Values must represent the ranked order of the data
Calculations based on an ordering process are valid
Data may be treated as nominal but not as interval
Nominal
Values are the arbitrary numbers that represent categories Only calculations based on the frequencies or percentages of occurrences are valid
Data may not be treated as ordinal or interval
Interval, Ordinal, and Nominal Variables
Variables are given the same name as the type of data which they constitute
2.2 Describing a Set of Nominal Data
Frequency Distribution: Summarized data in a table, which presents the categories and their
counts
Relative Frequency Distribution: Lists the categories and the proportion with which each
occurs
Bar Chart and Pie chart are used to present a picture of the data
Bar chart = frequencies
Pie chart = relative frequencies
Used to enhance the readersability to grasp the substance of the data
Describing Ordinal Data
No specific graphical techniques
When describing, treat as if nominal
Only criterion = the bars in bar charts should be arranged in ascending or descending ordinal
values, in pie charts the wedges are typically arranged clockwise
Factors That Identify Where to Use Frequency and Relative Frequency Tables, Bar and Pie Charts
Objective: Describe a single set of data
Data type: Nominal or ordinal
2.3 Describing the Relationship between Two Nominal Variables and Comparing Two or More
Nominal Data Sets
Univariate: Techniques applied to single sets of data
Bivariate: Techniques that depict relationship between variables
Cross-classification table: Used to describe the relationship between two nominal variables
(Table 2.5)
Avariation of bar chart is used to describe the information graphically (Page 35)
Same technique used to compare two or more sets of nominal data
Tabular Methods of Describing the Relationship between Two Nominal Variables
Must remember permitted only to determine the frequency of the values (Table 2.5)
Comparing Two or More Sets of Nominal Data
Consider one category as defining population (variables are different populations)
Then compare the bar charts or individual bars
Data Formats
Several ways to store data to produce a table or a bar/pie chart
1. Data in two columns (Example 2.4)
First column categories for first variable, second column categories for second variable
Each row represents one observation of the two variables Number of observations in each column is the same
Cross-classification Table can be created from this
2. The data are stored in two or more columns, with each column representing the same
variable in a different sample or population
Cross-classification Table can be created from this
3. Cross-classification Table is already given
Factors That Identify When to Use a Cross-Classification Table
Objective: Describe the relationship between two variables and compare two or more sets of
data
Data type: Nominal

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