Some Basic Statistical Concepts and Preliminary Considerations

Introduction

(1)

Populations, Samples, and Distributions

(2)

Statistical Inferences and Sampling

(3)

Statistical Inferences

(1)

Random Sampling

(2)

Selection of a Random Sample

(1)

Some Properties of Distributions

(4)

Estimation of m and σ

(1)

Confidence Intervals

(3)

Statistical Tolerance Limits

(1)

Using Statistics to Make Decisions

Approach to a Decision Problem

(1)

Choice of Null and Alternative Hypotheses

(1)

Two Kinds of Errors

(1)

Significance Level and Operating Characteristic (OC) Curve of a Statistical Test

(1)

Choice of the Significance Level

(1)

A Word of Caution

Characterizing the Measured Performance of a Material, Product, or Process

Estimating Average Performance from a Sample

(5)

General

(1)

Best Single Estimate

(1)

Some Remarks on Confidence Interval Estimates

(1)

Confidence Intervals for the Population Mean When Knowledge of the Variability Cannot Be Assumed

(1)

Two-sided Confidence Interval

(1)

One-sided Confidence Interval

(1)

Confidence Interval Estimates When We Have Previous Knowledge of the Variability

(2)

Estimating Variability of Performance from a Sample

(3)

General

(1)

Single Estimates

(1)

s2 and s

(1)

The Sample Range as an Estimate of the Standard Deviation

(1)

Confidence Interval Estimates

(1)

Two-sided Confidence Interval Estimates

(1)

One-sided Confidence Interval Estimates

(1)

Estimating the Standard Deviation When No Sample Data are Available

(1)

Number of Measurements Required to Establish the Mean with Prescribed Accuracy

(3)

General

(1)

Estimation of the Mean of a Population Using a Single Sample

(1)

Estimation Using a Sample Which is Taken In Two Stages

(2)

Number of Measurements Required to Establish the Variability with Stated Precision

(1)

Statistical Tolerance Limits

General

(1)

Two-sided Tolerance Limits for a Normal Distribution

(1)

One-sided Tolerance Limits for a Normal Distribution

(1)

Tolerance Limits Which are Independent of the Form of the Distribution

(1)

Two-sided Tolerance Limits (Distribution-Free)

(1)

One-sided Tolerance Limits (Distribution-Free)

Comparing Materials or Products with Respect to Average Performance

General Remarks on Statistical Tests

(2)

Comparing the Average of a New Product with That of a Standard

(19)

To Determine Whether the Average of a New Product Differs From the Standard

(1)

Does the Average of the New Product Differ From the Standard (σ Unknown)?

(4)

Does the Average of the New Product Differ From the Standard (σ Known)?

(5)

To Determine Whether the Average of a New Product Exceeds the Standard

(1)

Does the Average of the New Product Exceed the Standard (σ Unknown)?

(3)

Does the Average of the New Product Exceed the Standard (σ Known)?

(4)

To Determine Whether the Average of a New Product is Less Than the Standard

(1)

Is the Average of the New Product Less Than the Standard (σ Unknown)?

(1)

Is the Average of the New Product Less Than That of the Standard (σ Unknown)?

(1)

Comparing the Averages of Two Materials, Products, or Processes

(18)

Do Products A and B Differ in Average Performance?

(1)

(Case 1) --- Variability of A and B Is Unknown, But Can Be Assumed to be Equal

(3)

(Case 2) --- Variability of A and B is Unknown, Cannot Be Assumed Equal

(4)

(Case 3) --- Variability in Performance of Each of A and B is Known from Previous Experience, and the Standard Deviations are σA and σB, Respectively

(1)

(Case 4) --- The Observations are Paired

(3)

Does the Average of Product A Exceed the Average of Product B?

(1)

(Case 1) --- Variability of A and B is Unknown, But Can Be Assumed to be Equal

(2)

(Case 2) --- Variability of A and B is Unknown, Cannot Be Assumed Equal

(1)

(Case 3) --- Variability in Performance of Each of A and B is Known from Previous Experience, and the Standard Deviations are σA and σB, Respectively

(1)

(Case 4) --- The Observations are Paired

(2)

Comparing the Averages of Several Products

Comparing Materials or Products with Respect to Variability of Performance

Comparing a New Material or Product with a Standard with Respect to Variability of Performance

(7)

Does the Variability of the New Product Differ From That of the Standard?

(2)

Does the Variability of the New Product Exceed That of the Standard?

(2)

Is the Variability of the New Product Less Than That of the Standard?

(3)

Comparing Two Materials or Products with Respect to Variability of Performance

Does the Variability of Product A Differ From That of Product B?

(1)

Does the Variability of Product A Exceed That of Product B?

Characterizing Linear Relationships Between Two Variables

Introduction

(1)

Plotting the Data

(2)

Two Important Systems of Linear Relationships

(8)

Functional Relationships

(2)

Statistical Relationships

(6)

Problems and Procedures for Functional Relationships

(20)

FI Relationships (General Case)

(1)

What Is the Best Line To Be Used for Estimating y From Given Values of x?

(3)

What Are the Confidence Interval Estimates for: the Line as a Whole; a Point on the Line; a Future Value of Y Corresponding to a Given Value of x?

(4)

What Is the Confidence Interval Estimate for β1, the Slope of the True Line y = β0 + β1x?

(1)

If We Observe n' New Values of Y (With Average Y'), How Can We Use the Fitted Regression Line to Obtain an Interval Estimate of the Value of x that Produced These Values of Y?

(1)

Using the Fitted Regression Line, How Can We Choose a Value (x') of x Which We May Expect with Confidence (1 -- α) Will Produce a Value of Y Not Less Than Some Specified Value Q?

(1)

Is the Assumption of Linear Regression Justified?

(2)

FI Relationships When the Intercept Is Known To Be Equal to Zero (Lines Through the Origin)

(1)

Line Through Origin, Variance of Y's Independent of x

(1)

Line Through Origin, Variance Proportional to x (σy2 = Xσ2)

(1)

Line Through Origin, Standard Deviation Proportional to x (σyx = xσ)

(1)

Line Through Origin, Errors of Y's Cumulative (Cumulative Data)

(1)

FII Relationships

(1)

A Simple Method of Fitting the Line In the General Case

(2)

An Important Exceptional Case

(1)

Some Linearizing Transformations

(1)

Problems and Procedures for Statistical Relationships

SI Relationships

(2)

What Is the Best Line To Be Used for Estimating Y x for Given Values of X?

(3)

What Are the Confidence Interval Estimates for: the Line as a Whole; a Point on the Line; a Single Y Corresponding to a New Value of X?

(2)

Give a Confidence Interval Estimate for β1, the Slope of the True Regression Line, Y x = β0 + β1X?

(1)

What Is the Best Line for Predicting X Y From Given Values of Y?

(1)

What Is the Degree of Relationship of the Two Variables X and Y as Measured by ρ, the Correlation Coefficient?

(1)

SII Relationships

(1)

What Is the Best Line To Be Used for Estimating Y x From Given Values of X?

(1)

What Are the Confidence Interval Estimates for: the Line as a Whole; a Point on the Line; a Single Y Corresponding to a New Value of X?

(3)

What Is the Confidence Interval Estimate for β1, the Slope of the True Line Y x = β0 + β1X?

Polynomial and Multivariable Relationships Analysis by the Method of Least Squares

Introduction

(2)

Least Squares Theorem

(1)

Multivariable Functional Relationships

(13)

Use and Assumptions

(1)

Discussion of Procedures and Examples

(1)

Procedures and Examples

(11)

Multiple Measurements at One or More Points

(1)

Polynomial Fitting

(1)

Inequality of Variance

(3)

Discussion of Procedures and Examples

(1)

Procedures and Examples

(2)

Correlated Measurement Errors

(4)

Discussion of Procedures and Examples

(1)

Procedures and Examples

(4)

Use of Orthogonal Polynomials with Equally Spaced x Values

(11)

Discussion of Procedures and Examples

(4)

Procedures and Examples

(7)

Matrix Methods

Formulas Using Triangular Factorization of Normal Equations

(1)

Triangularization of Matrices

(3)

Remarks

Characterizing the Qualitative Performance of a Material, Product, or Process

General

(1)

Best Single Estimate of the True Proportion P

(1)

Confidence Interval Estimates of the True Proportion P

(2)

Two-Sided Confidence Intervals

(1)

Exact Limits for n ≤ 30

(1)

Exact Limits for n > 30

(1)

Approximate Limits for n > 30

(1)

One-Sided Confidence Intervals

(1)

Exact Limits for n ≤ 30

(1)

Exact Limits for n > 30

(1)

Approximate Limits for n > 30

(1)

Sample Size Required to Estimate the True Proportion

Determining the Sample Size Required to Estimate the True Proportion With a Specified Limit Of Error In Both Directions (i.e., When It Is Required To Estimate P Within ±δ)

(1)

Graphical Method

(1)

Numerical Method

(1)

Determining the Sample Size Required To Estimate the True Proportion With a Specified Limit Of Error In Only One Direction (i.e., When It Is Required To Estimate P Within +δ ; or, To Estimate P Within -- δ)

Comparing Materials or Products with Respect to a Two-Fold Classification of Performance (Comparing Two Percentages)

Comparing an Observed Proportion with a Standard Proportion

(8)

Does the New Product Differ From the Standard With Regard To the Proportion of Items Which Show the Characteristic of Interest? (Does P Differ From P0?)

(1)

Procedure for n ≤ 30

(1)

Procedure for n > 30

(1)

Does the Characteristic Proportion for the New Product Exceed That For the Standard? (Is P > P0?)

(1)

Procedure for n ≤ 30

(1)

Procedure for n > 30

(1)

Is the Characteristic Proportion for the New Product Less Than That for the Standard? (Is P < P0?)

(1)

Procedure for n ≤ 30

(1)

Procedure for n > 30

(1)

Sample Size Required To Detect a Difference Of Prescribed Magnitude From a Standard Proportion When the Sign of the Difference Is Not Important

(1)

Sample Size Required To Detect a Difference Of Prescribed Magnitude From a Standard Proportion When the Sign of the Difference IS Important

(2)

Comparing Two Observed Proportions

(11)

Comparing Two Proportions When the Sample Sizes Are Equal

(1)

Does the Characteristic Proportion for Product A Differ From That for Product B? (Does PA Differ From PB?)

(1)

Does the Characteristic Proportion for Product A Exceed That for Product B? (Is PA Larger Than PB?)

(1)

Comparing Two Proportions When the Sample Sizes Are Unequal and Small (nA ≠ nB ; Both No Greater Than 20)

(1)

Does the Characteristic Proportion for Product A Differ From That for Product B?

(2)

Does the Characteristic Proportion for Product A Exceed That for Product B? (Is PA Larger than PB?)

(2)

Comparing Two Proportions When the Sample Sizes Are Large

(1)

Does the Characteristic Proportion for Product A Differ From That for Product B? (Does PA Differ From PB?)

(2)

Is the Characteristic Proportion for Product A Larger Than That for Product B? (Is PA Larger Than PB?)

(1)

Sample Size Required to Detect a Difference Between Two Proportions

(1)

Sample Size Required to Detect a Difference of Prescribed Magnitude Between Two Proportions When the Sign of the Difference IS Not Important

(2)

Sample Size Required to Detect a Difference of Prescribed Magnitude Between Two Proportions When the Sign of the Difference IS Important

Comparing Materials or Products with Respect to Several Categories of Performance (Chi-Square Tests)

Comparing A Material or Product With a Standard

(4)

When the Comparison Is With a Standard Material or Product

(2)

When the Comparison Is With a Theoretical ``Standard''

(2)

Comparing Two or More Materials or Products

(2)

A Test of Association Between Two Methods of Classification

Sensitivity Testing

Experimental Situation

(2)

Karber Method of Analysis

(5)

General Solution For the Karber Method

(1)

Procedure

(1)

Example

(1)

Simplified Solution (Karber Method) For the Special Case When Test Levels Are Equally Spaced and Equal Numbers of Items Are Tested at Each Level

(1)

Procedure

(1)

Example

(1)

Probit Method of Analysis

(14)

Graphical Probit Solution

(1)

Procedure

(1)

Example

(5)

Exact Probit Solution

(1)

Procedure

(1)

Example

(3)

Testing Whether the Line Is An Adequate Representation of the Data

(1)

Procedure

(1)

Example

(1)

Using the Probit Regression Line For Prediction

(1)

Level of Stimulus x' At Which a Specified Proportion P' of the Individuals Would Be Expected To Respond

(1)

Level of Stimulus x' At Which 50% of the Individuals Would Be Expected To Respond

(1)

Proportion of Individuals Which Would Be Expected To Respond At a Specified Level of Stimulus

(1)

The Up-and-Down Design

(2)

Sensitivity Tests When the Stimulus Levels Cannot Be Controlled

General Considerations in Planning Experiments

The Nature of Experimentation

(2)

Experimental Pattern

(1)

Planned Grouping

(1)

Randomization

(1)

Replication

(1)

The Language of Experimental Design

Factorial Experiments

Introduction

(2)

Some General Remarks and Terminology

(2)

Estimates of Experimental Error for Factorial-Type Designs

(1)

Internal Estimates of Error

(1)

Estimates of Error from Past Experience

(1)

Factorial Experiments (Each Factor at Two Levels)

(6)

Symbols

(2)

Analysis

(1)

Estimation of Main Effects and Interactions

(3)

Testing for Significance of Main Effects and Interactions

(1)

Factorial Experiments When Uniform Conditions Cannot Be Maintained Throughout The Experiment (Each Factor at Two Levels)

(5)

Some Experimental Arrangements

(4)

Analysis of Blocked Factorial Experiments When Each Factor Is at Two Levels

(1)

Estimation of Main Effects and Interactions

(1)

Testing for Significance of Main Effects and Interactions

(1)

Fractional Factorial Experiments (Each Factor at Two Levels)

The Fractional Factorial Designs

(5)

Analysis

(1)

Estimates of Main Effects and Interactions

(2)

Testing for Significance of Main Effects and Interactions

Randomized Blocks, Latin Squares, and Other Special-Purpose Designs

Introduction

(1)

Completely-Randomized Plans

(1)

Planning

(1)

Analysis

(1)

Randomized Block Plans

(4)

Planning

(1)

Analysis

(1)

Estimation of the Treatment Effects

(1)

Testing and Estimating Differences in Treatment Effects

(1)

Estimation of Block Effects

(1)

Testing and Estimating Differences in Block Effects

(1)

Incomplete Block Plans

(24)

General

(1)

Balanced Incomplete Block Plans

(1)

Planning

(7)

Analysis

(1)

Estimating Treatment Effects

(1)

Testing and Estimating Differences in Treatment Effects

(1)

Estimating Block Effects

(1)

Testing and Estimating Differences in Block Effects

(1)

Chain Block Plans

(1)

Planning

(2)

Analysis

(3)

Estimating Treatment and Block Effects

(4)

Testing and Estimating Differences in Treatment Effects

(2)

Latin Square Plans

(6)

Planning

(2)

Analysis

(1)

Estimation of Treatment Effects

(1)

Testing and Estimating Differences in Treatment Effects

(1)

Estimation of Row (or Column) Effects

(1)

Testing and Estimating Differences in Row (or Column) Effects

(1)

Youden Square Plans

Planning

(4)

Analysis

(1)

Estimation of Treatment Effects

(2)

Testing and Estimating Differences in Treatment Effects

(1)

Estimation of Column Effects

(1)

Testing and Estimating Differences in Column Effects

(1)

Estimation of Row Effects

(1)

Testing and Estimating Differences in Row Effects

Experiments to Determine Optimum Conditions or Levels

Introduction

(1)

The Response Function

(2)

Experimental Designs

(1)

Finding the Optimum

(1)

Recommended Sources for Further Study

Some Shortcut Tests for Small Samples from Normal Populations

General

(1)

Comparing the Average of a New Product with That of a Standard

(3)

Does the Average of the New Product Differ From the Standard?

(1)

Does the Average of the New Product Exceed the Standard?

(1)

Is the Average of the New Product Less Than the Standard?

(1)

Comparing the Averages of Two Products

(2)

Do the Products A and B Differ in Average Performance?

(1)

Does the Average of Product A Exceed the Average of Product B?

(1)

Comparing the Averages of Several Products, Do the Averages of t Products Differ?

(1)

Comparing Two Products with Respect to Variability of Performance

Does the Variability of Product A Differ From that of Product B?

(1)

Does the Variability of Product A Exceed that of Product B?

Some Tests Which Are Independent of the Form of the Distribution

General

(1)

Does the Average of a New Product Differ from a Standard?

(2)

Does the Average of a New Product Differ From a Standard? The Sign Test

(1)

Does the Average of a New Product Differ From a Standard? The Wilcoxon Signed-Ranks Test

(1)

Does the Average of a New Product Exceed That of a Standard?

(2)

Does the Average of a New Product Exceed that of a Standard? The Sign Test

(1)

Does the Average of a New Product Exceed that of a Standard? The Wilcoxon Signed-Ranks Test

(1)

Is the Average of a New Product Less Than That of a Standard?

(2)

Is the Average of a New Product Less Than that of a Standard? The Sign Test

(1)

Is the Average of a New Product Less Than that of a Standard? The Wilcoxon Signed-Ranks Test

(1)

Do Products A and B Differ in Average Performance?

(2)

Do Products A and B Differ in Average Performance? The Sign Test For Paired Observations

(1)

Do Products A and B Differ in Average Performance? The Wilcoxon-Mann-Whitney Test For Two Independent Samples

(1)

Does the Average of Product A Exceed That of Product B?

(3)

Does the Average of Product A Exceed that of Product B? The Sign Test For Paired Observations

(1)

Does the Average of Product A Exceed that of Product B? The Wilcoxon-Mann-Whitney Test For Two Independent Samples

(2)

Comparing the Averages of Several Products, Do the Averages of t Products Differ?

The Treatment of Outliers

The Problem of Rejecting Observations

(1)

Rejection of Observations in Routine Experimental Work

(1)

Rejection of Observations in a Single Experiment

When Extreme Observations In Either Direction are Considered Rejectable

(1)

Population Mean and Standard Deviation Unknown --- Sample in Hand is the Only Source of Information

(1)

Population Mean and Standard Deviation Unknown --- Independent External Estimate of Standard Deviation is Available

(1)

Population Mean Unknown --- Value for Standard Deviation Assumed

(1)

Population Mean and Standard Deviation Known

(1)

When Extreme Observations In Only One Direction are Considered Rejectable

(1)

Population Mean and Standard Deviation Unknown --- Sample in Hand is the Only Source of Information

(1)

Population Mean and Standard Deviation Unknown --- Independent External Estimate of Standard Deviation is Available

(1)

Population Mean Unknown --- Value for Standard Deviation Assumed

(1)

Population Mean and Standard Deviation Known

The Place of Control Charts in Experimental Work

Primary Objective of Control Charts

(1)

Information Provided by Control Charts

(1)

Applications of Control Charts

Statistical Techniques for Analyzing Extreme-Value Data

Extreme-Value Distributions

(1)

Use of Extreme-Value Techniques

(1)

Largest Values

(2)

Smallest Values

(1)

Missing Observations

The Use of Transformations

General Remarks on the Need for Transformations

(1)

Normality and Normalizing Transformations

(3)

Importance of Normality

(1)

Normalization By Averaging

(1)

Normalizing Transformations

(2)

Inequality of Variances, and Variance-Stabilizing Transformations

(5)

Importance of Equality of Variances

(1)

Types of Variance Inhomogeneity

(1)

Variance-Stabilizing Transformations

(3)

Linearity, Additivity, and Associated Transformations

(2)

Definition and Importance of Linearity and Additivity

(2)

Transformation of Data To Achieve Linearity and Additivity

(1)

Concluding Remarks

The Relation Between Confidence Intervals and Tests of Significance

Introduction

(1)

A Problem in Comparing Averages

(1)

Two Ways of Presenting the Results

(2)

Advantages of the Confidence-Interval Approach

(2)

Deductions from the Operating Characteristic (OC) Curve

(1)

Relation to the Problem of Determining Sample Size

(1)

Conclusion

Notes on Statistical Computations

Coding in Statistical Computations

(1)

Rounding in Statistical Computations

Rounding of Numbers

(1)

Rounding the Results of Single Arithmetic Operations

(1)

Rounding the Results of a Series of Arithmetic Operations

Expression of the Uncertainties of Final Results

Introduction

(1)

Systematic Error and Imprecision Both Negligible (Case 1)

(1)

Systematic Error Not Negligible, Imprecision Negligible (Case 2)

(1)

Neither Systematic Error Nor Imprecision Negligible (Case 3)

(1)

Systematic Error Negligible, Imprecision Not Negligible (Case 4)

Rent More, Save More! Use code: ECRENTAL

Rent More, Save More! Use code: ECRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Experimental Statistics

9780486439372

0486439372

How To: Textbook Rental

Summary

Table of Contents

Supplemental Materials

Rewards Program

Rent More, Save More! Use code: ECRENTAL

Rent More, Save More! Use code: ECRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Experimental Statistics

9780486439372

0486439372

How To: Textbook Rental

Summary

Table of Contents

Supplemental Materials

Rewards Program

Digital License