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Understandable StatisticsEighth Edition

By Brase and BrasePrepared by: Lynn SmithGloucester County College

Chapter OneGetting Started

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Statistics is

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

numerical information from data

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Individuals and Variables

• Individuals: the people or objects included in the study

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

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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

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Population

Variable is taken from every individual of interest

Example: the data from all individuals who have

climbed Mt. Everest

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Sample

Variable is taken from only some of the individuals of interest

Example: the data from just some of the climbers

of Mt. Everest

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Levels of Measurement

• Nominal

• Ordinal

• Interval

• Ratio

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Nominal Measurement

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

Example: names of ski resorts

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Ordinal Measurement

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

either cannot be determined or are meaningless.

Example: class rank

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Interval Measurement

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

are meaningful.Example: body temperature

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Ratio MeasurementData that can be arranged in order.

Differences between data values and ratios of data values are

meaningful.Example: temperature in degrees

Kelvin

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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

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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

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Random sampling:

• drawing cards “from a hat”

• using a random-number table to select a sample

• using a random-number generator

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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.

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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.

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Simulation

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

• Random-number table may be used

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Sampling with replacement

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

population.

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Other sampling techniques

• Stratified Sampling

• Systematic Sampling

• Cluster Sampling

• Convenience Sampling

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Stratified Sampling

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

• Random samples are drawn from each stratum

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Systematic Sampling

• Members of the population are sequentially numbered.

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

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Cluster Sampling

• Population is divided into pre-existing clusters

• Some clusters are randomly selected

• Every member in selected sections is included in the sample

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Convenience Sampling

• Use whatever data is readily available.

• Risk of being severe bias.

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Which sampling technique is described?

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

line is surveyed.

Systematic sampling

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Which sampling technique is described?

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

Convenience sampling

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Which sampling technique is described?

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

selected to participate in a survey

Stratified sampling

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Which sampling technique is described?

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

audit.

Simple random sampling

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Which sampling technique is described?

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

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Experimental Design

Statistical studies are used to obtain reliable information.

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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

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Census

Measurements or observations from entire populations are used.

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Sample

Measurements or observations from a representative part of the

population are used.

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Simulation

A numerical facsimile of real-world phenomena

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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

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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

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Surveys

Data is gathered by asking people questions.

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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.