Statistics

Statistics

David Kilgour

http://www.avyg86.dsl.pipex.com/research.htm

Statistics 2

Learning Objectives

Understand and be able to distinguish different meanings and uses of the word ‘statistics’;

Be able to describe the nature of statistics as a scientific discipline;

Be aware of the fact that statistics can be presented and used in misleading ways, unintentionally or even intentionally;

Appreciate the importance of statistics in science and in society in general;

Appreciate the need for statistics in a business and finance environment.

Statistics 3

Goals

After completing this note, you should be able to:

Explain key definitions: Population vs. Sample Primary vs. Secondary Data

Parameter vs. Statistic Descriptive vs. Inferential Statistics

Describe key data collection methods Describe different sampling methods

Probability Samples vs. Nonprobability Samples

Select a random sample using a random numbers table Identify types of data and levels of measurement Describe the different types of survey error

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Meaning of Statistics

The word ‘statistics’ has a few different (but related) meanings, and is used in different ways, depending on the context.

Most people have heard of statistics in the context of football, cricket or political opinion polls.

Statistics 5

What Is Statistics?

Why? 1. Collecting Data

e.g. Survey

2. Presenting Data e.g., Charts & Tables

3. Characterizing Data e.g., Average

Data Analysis

Decision-Making

© 1984-1994 T/Maker Co.

Statistics 6

Some Application Areas

Accounting Auditing Costing

Finance Financial Trends Forecasting

Management Describe Employees Quality Improvement

Marketing Consumer Preferences Marketing Mix Effects

Statistics 7

Statistical Methods

StatisticalMethods

DescriptiveStatistics

InferentialStatistics

Statistics 8

Descriptive Statistics

1. Involves Collecting Data Presenting Data Characterizing Data

2. Purpose Describe Data

X = 30.5 S2 = 113

0

25

50

Q1 Q2 Q3 Q4

£

Statistics 9

Inferential Statistics

1. Involves Estimation Hypothesis

Testing

2. Purpose Make Decisions About

Population Characteristics

Population?

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Key Terms

1. Population (Universe) All Items of Interest

2. Sample Portion of Population

3. Parameter Summary Measure about Population

4. Statistic Summary Measure about Sample

Statistics 11

Statistical Studies

StatisticalStudies

EnumerativeStudy

AnalyticalStudy

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Enumerative Study

1. Involves Decision Making about a Population Frame is Listing of All

Population Units e.g., Names in Telephone

Book

2. e.g., Political Poll

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Analytical Study

1. Involves Action on a Process

2. Improves Future Performance

3. No Identifiable Universe or Frame

4. e.g., Manufacturing Process

Goods

Services

ProductFocused

ProcessFocused

People

Equip-ment

Material

Infor-mation

OutputProcessInput

Feedback

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StatisticalComputer Packages

1. Typical Software SAS SPSS MINITAB Excel Matlab

2. Need Statistical Understanding

Assumptions Limitations

Statistics 15

Thinking Challenge

Our market share far exceeds all competitors! - VP

30% 32% 34% 36%

Us

Y

X

Statistics 16

Why a Manager Needs to Know about Statistics

To know how to: properly present information

draw conclusions about populations based

on sample information

improve processes

obtain reliable forecasts

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Key Definitions

A population (universe) is the collection of all items or things under consideration

A sample is a portion of the population selected for analysis

A parameter is a summary measure that describes a characteristic of the population

A statistic is a summary measure computed from a sample to describe a characteristic of the population

Statistics 18

Population vs. Sample

a b c d

ef gh i jk l m n

o p q rs t u v w

x y z

Population Sample

b c

g i n

o r u

y

Measures used to describe the population are called parameters

Measures computed from sample data are called statistics

Statistics 19

Two Branches of Statistics

Descriptive statistics Collecting, summarizing, and describing data

Inferential statistics Drawing conclusions and/or making decisions

concerning a population based only on sample data

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Descriptive Statistics

Collect data e.g., Survey

Present data e.g., Tables and graphs

Characterize data e.g., Sample mean =

iX

n

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Inferential Statistics

Estimation e.g., Estimate the population

mean weight using the sample mean weight

Hypothesis testing e.g., Test the claim that the

population mean weight is 120 pounds

Drawing conclusions and/or making decisions concerning a population based on sample results.

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Why We Need Data

To provide input to survey To provide input to study To measure performance of service or

production process To evaluate conformance to standards To assist in formulating alternative courses of

action

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Data Sources

SecondaryData Compilation

Observation

Experimentation

Print or Electronic

Survey

PrimaryData Collection

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Reasons for Drawing a Sample

Less time consuming than a census Less costly to administer than a census Less cumbersome and more practical to

administer than a census of the targeted population

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Nonprobability Sample Items included are chosen without regard to

their probability of occurrence

Probability Sample Items in the sample are chosen on the basis

of known probabilities

Types of Samples Used

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Types of Samples Used

Quota

Samples

Non-Probability Samples

Judgement Chunk

Probability Samples

Simple Random

Systematic

Stratified

ClusterConvenience

(continued)

Statistics 27

Probability Sampling

Items in the sample are chosen based on known probabilities

Probability Samples

Simple Random

Systematic Stratified Cluster

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Simple Random Samples

Every individual or item from the frame has an equal chance of being selected

Selection may be with replacement or without replacement

Samples obtained from table of random numbers or computer random number generators

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Decide on sample size: n Divide frame of N individuals into groups of k

individuals: k=N/n Randomly select one individual from the 1st

group Select every kth individual thereafter

Systematic Samples

N = 64

n = 8

k = 8

First Group

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Stratified Samples

Divide population into two or more subgroups (called

strata) according to some common characteristic

A simple random sample is selected from each subgroup,

with sample sizes proportional to strata sizes

Samples from subgroups are combined into one

Population

Divided

into 4

strata

Sample

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Cluster Samples

Population is divided into several “clusters,” each representative of the population

A simple random sample of clusters is selected All items in the selected clusters can be used, or items can be

chosen from a cluster using another probability sampling technique

Population divided into 16 clusters. Randomly selected

clusters for sample

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Advantages and Disadvantages

Simple random sample and systematic sample Simple to use May not be a good representation of the population’s

underlying characteristics Stratified sample

Ensures representation of individuals across the entire population

Cluster sample More cost effective Less efficient (need larger sample to acquire the

same level of precision)

Statistics 33

Types of Data

Data

Categorical Numerical

Discrete Continuous

Examples:

Marital Status Political Party Eye Colour (Defined categories) Examples:

Number of Children Defects per hour (Counted items)

Examples:

Weight Voltage (Measured characteristics)

Statistics 34

Levels of Measurementand Measurement Scales

Interval Data

Ordinal Data

Nominal Data

Highest Level

Strongest forms of measurement

Higher Level

Lowest Level

Weakest form of measurement

Categories (no ordering or direction)

Ordered Categories (rankings, order, or scaling)

Differences between measurements but no true zero

Ratio DataDifferences between measurements, true zero exists

Statistics 35

Evaluating Survey Worthiness

What is the purpose of the survey? Is the survey based on a probability sample? Coverage error – appropriate frame? No response error – follow up Measurement error – good questions elicit good

responses Sampling error – always exists

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Types of Survey Errors

Coverage error or selection bias Exists if some groups are excluded from the frame and

have no chance of being selected

Non response error or bias People who do not respond may be different from those

who do respond

Sampling error Variation from sample to sample will always exist

Measurement error Due to weaknesses in question design, respondent

error, and interviewer’s effects on the respondent

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Types of Survey Errors

Coverage error

No response error

Sampling error

Measurement error

Excluded from frame

Follow up on no responses

Random differences from sample to sample

Bad or leading question

(continued)

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Summary

Reviewed why a manager needs to know statistics Introduced key definitions:

Population vs. Sample Primary vs. Secondary data types

Categorical vs. Numerical data Time Series vs. Cross-Sectional data

Examined descriptive vs. inferential statistics Described different types of samples Reviewed data types and measurement levels Examined survey worthiness and types of survey

errors