Download - © 2008 Pearson Addison-Wesley. All rights reserved Chapter 5 Statistical Reasoning

© 2008 Pearson Addison-Wesley.All rights reserved

Chapter 5Statistical Reasoning

Copyright © 2008 Pearson Education, Inc. Slide 5-2

Chapter 5Statistical Reasoning

5A Fundamentals of Statistics

5B Should You Believe a Statistical Study?

5C Statistical Tables and Graphs

5D Graphics in the Media

5E Correlation and Causality


Unit 5A

Fundamentals of Statistics


Two Definitions of Statistics

Statistics is the science of collecting, organizing, and interpreting data.

Statistics are the data that describe or summarize something.

5-A


More Definitions

The population in a statistical study is the complete set of people or things being studied.

The sample is the subset of the population from which the raw data are actually obtained.

Population parameters are specific characteristics of the population that a statistical study is designed to estimate.

Sample statistics are numbers or observations that summarize the raw data.

5-A


Elements of a Statistical Study

5-A


Common Sampling Techniques

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Identify the Sampling Method Used

You are conducting a survey of students in a school. You choose your sample by knocking on the every 3rd classroom door.

Choosing every 3rd room makes this a systematic sample. The sample may be representative, as long as students were randomly assigned to rooms.

To survey opinions on a new water line, a research firm randomly draws the addresses or 200 homeowners from a public list of all homeowners.

The records presumably list all homeowners, so drawing randomly from this list produce a simple random sample. It has a good chance of being representative of the population.

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Types of Statistical Study

In an observational study, researchers observe or measure characteristics of the sample members but do not attempt to influence or modify these characteristics.

In an experiment, researchers apply a treatment to some or all of the sample members and then look to see whether the treatment has any effects.

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Treatment and Control Groups

The treatment group in an experiment is the group of sample members who receive the treatment being tested.

The control group in an experiment is the group of sample members who do not receive the treatment being tested.

It is important for the treatment and control groups to be selected randomly and to be alike in all respects except for treatment.

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The Placebo Effect and Blinding

A placebo lacks the active ingredients of a treatment being tested in a study, but is identical in appearance to the treatment. Thus, study participants cannot distinguish the placebo from the real treatment.

The placebo effect refers to the situation in which patients improve simply because they believe they are receiving a useful treatment.

5-A


The Placebo Effect and Blinding

An experiment is single-blind if the participants do not know whether they are members of the treatment group or members of the control group, but the experimenters do know.

An experiment is double-blind if neither the participants nor the experimenters (people administering the treatment) know who belongs to the treatment group and who belongs to the control group.

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Definitions

A case-control study is an observational study that resembles an experiment because the sample naturally divides into two or more groups.

The participants who engage in the behavior under study form the cases.

The participants who do not engage in the behavior are the controls.

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Definitions

The margin of error is used to describe a confidence interval that is likely to contain the true population parameter. The confidence interval is

From (sample statistic − margin of error)

To (sample statistic + margin of error)

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Unit 5B

Should You Believe a Statistical Study?


Should I Believe a Statistical Study?

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1. Identify the goal, population and type of study.

2. Consider the source.3. Look for bias in the sample.4. Look for problems in defining or measuring

the variables of interest.5. Watch out for confounding variables.6. Consider the setting and wording in

surveys.7. Check that results are presented fairly.8. Stand back and consider the conclusions.


Unit 5C

Statistical Tables and Graphs


Frequency Tables

A basic frequency table has two columns: The first column lists the categories of data. The second column lists the number of times

(frequency) each category appears in the data set.

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The relative frequency is the frequency expressed as a fraction or percentage of the total.

The cumulative frequency is the total of frequencies for the given category and all previous categories.


Data Types

Qualitative data describe qualities or nonnumerical categories.

Quantitative data represent counts or measurments.

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Summarizing Raw Data

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20 scores from a 100-point exam76 80 78 76 94 75 98 77 84 8881 72 91 72 74 86 79 88 72 75


Bar and Pie Graphs

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Important Labels for Graphs

Title/caption

5-C

Legend

Vertical scale and title

Horizontal scale


Definitions

Histogram: a bar graph for quantitative data categories. The bars have a natural order and the bar widths have specific meaning.

Line chart: shows the data value for each category as a dot, and the dots are connected with lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the data value for the bin.

Time-series diagram: a histogram or line chart in which the horizontal axis represents time.

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Histogram and Line Chart for Table 5.3

5-C


Reading A Time-Series Diagram

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Unit 5D

Graphics in the Media


Graphics in the Media: Graphics Beyond the Basics

5-D

A stack plot showing trends in death rates from four diseases.


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A perceptual distortion



5-D

Both graphs show the same data, but they look very different because their vertical scales have different ranges.


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It appears that the world population has been rising linearly. However, the time intervals on the horizontal axis are not uniform in size.


Unit 5E

Correlation and Causality


Relationships Between Two Data Variables

No correlation: There is no apparent relationship between the two variables.

Positive correlation: Both variables tend to increase or decrease together.

Negative correlation: One variable increases while the other decreases.

Strength of a correlation: The more closely two variables follow the general trend, the stronger the correlation. In a perfect correlation, all data points lie on a straight line.

5-E



5-E

A scatter diagram for diamond weights and prices: a positive correlation.



5-E

A scatter diagram for life expectancy and infant mortality: a negative correlation


Possible Explanations for a Correlation

1. The correlation may be a coincidence.

2. Both variables might be directly influenced by some common underlying cause.

3. One variable may be a cause of the other.

5-E


Guidelines for Establishing Causality

5-E

1. Look for situations where the effect is correlated with the suspected cause.

2. Check that the effect is present or absent among groups that differ only in the presence or absence of the suspected cause.

3. Look for evidence that larger amounts of the suspected cause produce larger effects.

4. Account for other potential causes.5. Test the suspected cause with an

experiment.6. Try to determine how the suspected cause

produces the effect.

Download - © 2008 Pearson Addison-Wesley. All rights reserved Chapter 5 Statistical Reasoning

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