Chapter One Getting Started

Copyright (C) 2006 Houghton Mifflin Company. All rights reserved. 1

Understandable StatisticsEighth Edition

By Brase and BrasePrepared by: Lynn SmithGloucester County College

Chapter OneGetting Started


Statistics is

The study of how to:• collect• organize• analyze• interpret

numerical information from data


Individuals and Variables

• Individuals: the people or objects included in the study

• Variable: the characteristic of the individual to be measured or observed


Quantitative and Qualitative Data

• Quantitative variable has a value or numerical measurement– example: height

• Qualitative variable places an individual in a category or group– example: gender


Population

Variable is taken from every individual of interest

Example: the data from all individuals who have

climbed Mt. Everest


Sample

Variable is taken from only some of the individuals of interest

Example: the data from just some of the climbers

of Mt. Everest


Levels of Measurement

• Nominal

• Ordinal

• Interval

• Ratio


Nominal Measurement

Applies to data that consists of names, labels or categories.

Example: names of ski resorts


Ordinal Measurement

Data that may be arranged in order. Differences between data values

either cannot be determined or are meaningless.

Example: class rank


Interval Measurement

Data that can be arranged in order. Differences between data values

are meaningful.Example: body temperature


Ratio MeasurementData that can be arranged in order.

Differences between data values and ratios of data values are

meaningful.Example: temperature in degrees

Kelvin


Branches of Statistics

• Descriptive: methods of organizing, picturing, and summarizing information

• Inferential: methods of using information from a sample to draw conclusions regarding the population


Simple Random Sample of n measurements are selected in a

manner such that:• every sample of size n has equal chance of

being selected• every member of the population has an

equal chance of being included


Random sampling:

• drawing cards “from a hat”

• using a random-number table to select a sample

• using a random-number generator


Example 1 of using a random number table

We want to choose a random sample of 8 shirts out of a shipment of 300. We drop a pin on a random number table on page A13 and it fallson Column 3 row 15. Since we have 300 shirts we regroup the digits into groups of three. The digits are:275, 924, 208, 999, 281, 596, 401, 522, 196, 079, 099, 610, 537, 129,553, 184, ...The shirts we use in our sample are:275, 208, 281, 196, 79, 99, 129, 184.


Example 2 using a random number table

We want to use a random number table to simulate rolling a die 10times. We drop a pin on the random number table and it lands on column 7 row 3. Since a die has numbers 1 through 6, we will usesingle digits as our possible rolls. The numbers from the table are:2, 9, 2, 8, 1, 1, 8, 5, 4, 4, 5, 2, 4, ...The simulated outcomes are 2, 2, 1, 1, 5, 4, 4, 5, 2, 4.


Simulation

• A numerical facsimile or representation of a real-world phenomenon

• Random-number table may be used


Sampling with replacement

A number that is selected for the sample is not removed from the

population.


Other sampling techniques

• Stratified Sampling

• Systematic Sampling

• Cluster Sampling

• Convenience Sampling


Stratified Sampling

• Groups or classes inside a population that share a common characteristic (“strata”)

• Random samples are drawn from each stratum


Systematic Sampling

• Members of the population are sequentially numbered.

• Select a random starting point.• Select every “kth” item.


Cluster Sampling

• Population is divided into pre-existing clusters

• Some clusters are randomly selected

• Every member in selected sections is included in the sample


Convenience Sampling

• Use whatever data is readily available.

• Risk of being severe bias.


Which sampling technique is described?

College students are waiting in line for registration. Every eighth person in

line is surveyed.

Systematic sampling



College students are waiting in line for registration. Students are asked to volunteer to respond to a survey.

Convenience sampling



In a large high school, students from every homeroom are randomly

selected to participate in a survey

Stratified sampling



An accountant uses a random number generator to select ten accounts for

audit.

Simple random sampling



To determine students’ opinions of a new registration method, a college randomly selects five majors. All students in the selected majors are

surveyed.

Cluster sampling


Experimental Design

Statistical studies are used to obtain reliable information.


Planning a Statistical Study

• Identify individuals or object of interest• Specify variables and protocols for

observations• Decide whether to use a census or a sample and

determine viable sampling method• Collect data• Make decisions• List concerns and recommendations


Census

Measurements or observations from entire populations are used.


Sample

Measurements or observations from a representative part of the

population are used.


Simulation

A numerical facsimile of real-world phenomena


Experiments and Observation

• Observational Study: no change is made in the responses or variable being studied

• Experiment: a treatment is imposed in order to observe a possible change in the response or variable being measured


Randomized two-treatment experiment

• Subjects are randomly assigned to one of two groups

• One group receives treatment under study• Control group receives placebo• Results are compared• Randomization prevents bias• Replication on many subjects assures changes

not caused by random chance


Surveys

Data is gathered by asking people questions.


Problems with data collection• Some individuals do not respond.• People with strong opinions may be over-

represented in voluntary response samples.• There may be a hidden bias in the data

collection process.• There may be hidden effects of other variables.• There is no guarantee that results can be

generalized.

Chapter One Getting Started

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