Statistical Analysis

Conrad Carlberg started writing about Excel, and its use in quantitative analysis, before workbooks had worksheets. As a graduate student, he had the great good fortune to learn something about statistics from the wonderfully gifted Gene Glass. He remembers much of that and has learned more since. This is a book he has wanted to rewrite for years, and he is grateful for the opportunity.

Introduction  1
    Using Excel for Statistical Analysis .........1
        About You and About Excel ...........................2
        Clearing Up the Terms .....................3
        Making Things Easier .......................3
        The Wrong Box? ..............................4
        Wagging the Dog ............................6
    What’s in This Book ...............................6
1 About Variables and Values ................. 9
    Variables and Values ..............................9
        Recording Data in Lists ..................10
        Making Use of Lists ........................11
    Scales of Measurement ........................13
        Category Scales ..............................13
        Numeric Scales ..............................15
        Telling an Interval Value from a Text Value ................16
    Charting Numeric Variables in Excel ....18
        Charting Two Variables ..................18
    Understanding Frequency Distributions .................21
        Using Frequency Distributions .......23
        Building a Frequency Distribution from a Sample ...........26
        Building Simulated Frequency Distributions .....................34
2 How Values Cluster Together ..............37
    Calculating the Mean ...........................38
        Understanding Functions, Arguments, and Results ............39
        Understanding Formulas, Results, and Formats ................42
        Minimizing the Spread ..................44
    Calculating the Median ........................49
        Choosing to Use the Median ..........50
        Static or Robust? ............................51
    Calculating the Mode ...........................52
        Getting the Mode of Categories with a Formula ..........56
    From Central Tendency to Variability ...63
3 Variability: How Values Disperse .........65
    Measuring Variability with the Range .66
        Sample Size and the Range ...........67
        Variations on the Range ................69
    The Concept of a Standard Deviation ...70
        Arranging for a Standard ...............71
        Thinking in Terms of Standard Deviations ..............72
    Calculating the Standard Deviation and Variance ..........74
        Squaring the Deviations ................77
        Population Parameters and Sample Statistics ..........78
        Dividing by N ??1 ..........................79
    Bias in the Estimate and Degrees of Freedom ...............81
    Excel’s Variability Functions .................82
        Standard Deviation Functions ........82
        Variance Functions ........................83
4 How Variables Move Jointly: Correlation ..........85
    Understanding Correlation ..................85
        The Correlation, Calculated ............87
        Using the CORREL() Function .........93
        Using the Analysis Tools ................96
        Using the Correlation Tool .............98
        Correlation Isn’t Causation...........101
    Using Correlation ...............................102
        Removing the Effects of the Scale ...............103
        Using the Excel Function..............106
        Getting the Predicted Values .......107
        Getting the Regression Formula ..109
    Using TREND() for Multiple Regression ...............111
        Combining the Predictors ............111
        Understanding “Best Combination” ...........112
        Understanding Shared Variance ..116
        A Technical Note: Matrix Algebra and Multiple Regression in Excel ........ 118
5 Charting Statistics .............121
    Characteristics of Excel Charts ............122
        Chart Axes ...................................122
        Date Variables on Category Axes .123
        Other Numeric Variables on a Category Axis ...........125
    Histogram Charts ...............................127
        Using a Pivot Table to Count the Records ................127
        Using Advanced Filter and FREQUENCY() .....................129
        The Data Analysis Add-in’s Histogram .......................131
        The Built-in Histogram ................132
        Data Series Addresses ..................133
    Box-and-Whisker Plots ......................134
        Managing Outliers .......................137
        Diagnosing Asymmetry ...............137
        Comparing Distributions ..............138
6 How Variables Classify Jointly: Contingency Tables ... 139
    Understanding One-Way Pivot Tables .....................139
        Running the Statistical Test .........143
    Making Assumptions .........................148
        Random Selection ........................148
        Independent Selections ...............150
        The Binomial Distribution Formula .............................150
        Using the BINOM.INV() Function .152
    Understanding Two-Way Pivot Tables ..........................158
        Probabilities and Independent Events .....................161
        Testing the Independence of Classifications ..............163
        About Logistic Regression............168
    The Yule Simpson Effect ....................169
    Summarizing the Chi-Square Functions .......................171
        Using CHISQ.DIST() ......................171
        Using CHISQ.DIST.RT() and CHIDIST() ........................173
        Using CHISQ.INV() ........................174
        Using CHISQ.INV.RT() and CHIINV() .......................175
        Using CHISQ.TEST() and CHITEST() ...........................176
        Using Mixed and Absolute References to Calculate Expected Frequencies ..............177
        Using the Pivot Table’s Index Display .......................178
7 Using Excel with the Normal Distribution .................181
    About the Normal Distribution ..........181
        Characteristics of the Normal Distribution ...................181
        The Unit Normal Distribution .......186
    Excel Functions for the Normal Distribution ...................187
        The NORM.DIST( ) Function ..........187
        The NORM.INV( ) Function ...........190
    Confidence Intervals and the Normal Distribution ..............192
        The Meaning of a Confidence Interval .....................................193
        Constructing a Confidence Interval ............................194
        Excel Worksheet Functions That Calculate Confidence Intervals ...............198
        Using CONFIDENCE.NORM( ) and CONFIDENCE( ) ......................198
        Using CONFIDENCE.T( ) .................201
        Using the Data Analysis Add-In for Confidence Intervals .........202
        Confidence Intervals and Hypothesis Testing .................204
    The Central Limit Theorem ................205
        Dealing with a Pivot Table Idiosyncrasy ................206
        Making Things Easier ...................207
        Making Things Better ..................209
8 Telling the Truth with Statistics ........211
    A Context for Inferential Statistics .....212
        Establishing Internal Validity .......213
        Threats to Internal Validity ..........214
    Problems with Excel’s Documentation ...................218
    The F-Test Two-Sample for Variances 219
        Why Run the Test? .......................220
    Reproducibility ..................................232
    A Final Point ......................................234
9 Testing Differences Between Means: The Basics ............235
    Testing Means: The Rationale ............236
        Using a z-Test ..............................237
        Using the Standard Error of the Mean ...................240
        Creating the Charts ......................244
    Using the t-Test Instead of the z-Test 252
        Defining the Decision Rule ...........254
        Understanding Statistical Power .258
10 Testing Differences Between Means: Further Issues ..........263
    Using Excel’s T.DIST() and T.INV() Functions to Test Hypotheses ...263
        Making Directional and Nondirectional Hypotheses ................264
        Using Hypotheses to Guide Excel’s t-Distribution Functions ....265
        Completing the Picture with T.DIST() .....................273
    Using the T.TEST() Function ...............275
        Degrees of Freedom in Excel Functions....................275
        Equal and Unequal Group Sizes ...276
        The T.TEST() Syntax .....................278
    Using the Data Analysis Add-in t-Tests .................291
        Group Variances in t-Tests ...........291
        Visualizing Statistical Power ........297
        When to Avoid t-Tests .................298
11 Testing Differences Between Means: The Analysis of Variance ........299
    Why Not t-Tests? ...............................299
    The Logic of ANOVA ...........................301
        Partitioning the Scores ................302
        Comparing Variances ...................305
        The F-Test ....................................309
    Using Excel’s F Worksheet Functions .312
        Using F.DIST() and F.DIST.RT() .....312
        Using F.INV() and FINV() ..............314
        The F-Distribution ........................315
    Unequal Group Sizes ..........................316
    Multiple Comparison Procedures .......318
        The Scheffé Procedure .................320
        Planned Orthogonal Contrasts .....324
12 Analysis of Variance: Further Issues...329
    Factorial ANOVA .................................329
        Other Rationales for Multiple Factors ....................330
        Using the Two-Factor ANOVA Tool ..........................333
    The Meaning of Interaction ...............335
        The Statistical Significance of an Interaction ................336
        Calculating the Interaction Effect 338
    The Problem of Unequal Group Sizes .342
        Repeated Measures: The Two Factor Without Replication Tool .............345
    Excel’s Functions and Tools: Limitations and Solutions ..................346
        Mixed Models ..............................347
        Power of the F-Test .....................348
13 Experimental Design and ANOVA.......349
    Crossed Factors and Nested Factors ...349
        Depicting the Design Accurately ..351
        Nuisance Factors ..........................352
    Fixed Factors and Random Factors.....352
        The Data Analysis Add-In’s ANOVA Tools ...........354
        Data Layout .................................356
    Calculating the F Ratios .....................357
        Adapting the Data Analysis Tool for a Random Factor .............357
        Designing the F-Test ....................358
        The Mixed Model: Choosing the Denominator .........................359
        Adapting the Data Analysis Tool for a Nested Factor ...............361
        Data Layout for a Nested Design..362
        Getting the Sums of Squares .......363
        Calculating the F Ratio for the Nesting Factor ................363
    Randomized Block Designs ................364
        Interaction Between Factors and Blocks .......................366
        Tukey’s Test for Nonadditivity .....368
        Increasing Statistical Power .........369
        Blocks as Fixed or Random ..........370
    Split-Plot Factorial Designs ................371
        Assembling a Split-Plot Factorial Design ....................371
        Analysis of the Split-Plot Factorial Design .......................372
14 Statistical Power ..................377
    Controlling the Risk ...........................377
        Directional and Nondirectional Hypotheses ...........378
        Changing the Sample Size ...........378
        Visualizing Statistical Power ........378
    The Statistical Power of t-Tests ..........382
        Nondirectional Hypotheses ..........382
        Making a Directional Hypothesis .385
        Increasing the Size of the Samples .......................387
        The Dependent Groups t-Test ......387
    The Noncentrality Parameter in the F-Distribution ................389
        Variance Estimates ......................389
        The Noncentrality Parameter and the Probability Density Function ............393
    Calculating the Power of the F-Test ...395
        Calculating the Cumulative Density Function ..........396
        Using Power to Determine Sample Size ...............397
15 Multiple Regression Analysis and Effect Coding: The Basics ............401
    Multiple Regression and ANOVA ........402
        Using Effect Coding .....................404
        Effect Coding: General Principles .404
        Other Types of Coding .................406
    Multiple Regression and Proportions of Variance ..........................406
        Understanding the Segue from ANOVA to Regression .............409
        The Meaning of Effect Coding ......411
    Assigning Effect Codes in Excel ..........414
    Using Excel’s Regression Tool with Unequal Group Sizes ...............416
    Effect Coding, Regression, and Factorial Designs in Excel ..............418
        Exerting Statistical Control with Semipartial Correlations .......420
        Using a Squared Semipartial to Get the Correct Sum of Squares ................421
    Using TREND() to Replace Squared Semipartial Correlations .........422
        Working with the Residuals .........424
        Using Excel’s Absolute and Relative Addressing to Extend the Semipartials ..............426
16 Multiple Regression Analysis and Effect Coding: Further Issues .......431
    Solving Unbalanced Factorial Designs Using Multiple Regression .431
        Variables Are Uncorrelated in a Balanced Design ....................433
        Variables Are Correlated in an Unbalanced Design ..................434
        Order of Entry Is Irrelevant in the Balanced Design..................435
        Order Entry Is Important in the Unbalanced Design ................437
        Proportions of Variance Can Fluctuate .....................................439
    Experimental Designs, Observational Studies, and Correlation ......440
    Using All the LINEST() Statistics .........443
    Looking Inside LINEST() .....................450
        Understanding How LINEST() Calculates Its Results .................450
        Getting the Regression Coefficients .........................................452
        Getting the Sum of Squares Regression and Residual..............456
        Calculating the Regression Diagnostics ...................................458
        Understanding How LINEST() Handles Multicollinearity ..........462
        Forcing a Zero Constant ...............466
        The Excel 2007 Version ................467
        A Negative R2? .............................470
    Managing Unequal Group Sizes in a True Experiment ...................474
    Managing Unequal Group Sizes in Observational Research ...........476
17 Analysis of Covariance: The Basics .....479
    The Purposes of ANCOVA ...................480
        Greater Power .............................480
        Bias Reduction .............................480
    Using ANCOVA to Increase Statistical Power ..................................481
        ANOVA Finds No Significant Mean Difference ..........................482
        Adding a Covariate to the Analysis ..........................................483
    Testing for a Common Regression Line ..........................................490
    Removing Bias: A Different Outcome .493
18 Analysis of Covariance: Further Issues ..................499
    Adjusting Means with LINEST() and Effect Coding .........................499
    Effect Coding and Adjusted Group Means ......................................504
    Multiple Comparisons Following ANCOVA .....................................507
        Using the Scheffé Method ...........507
        Using Planned Contrasts ..............512
    The Analysis of Multiple Covariance ...514
        The Decision to Use Multiple Covariates ..................................514
        Two Covariates: An Example ........515
    When Not to Use ANCOVA .................517
        Intact Groups ...............................517
        Extrapolation ...............................519
TOC, 9780789759054, 11/2/2017