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From Data to Decisions in Music Education Research: Data Analytics and the General Linear Model Using R [Pehme köide]

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(University of Georgia, USA)
  • Formaat: Paperback / softback, 494 pages, kõrgus x laius: 254x178 mm, kaal: 453 g, 92 Line drawings, black and white; 3 Halftones, black and white; 95 Illustrations, black and white
  • Ilmumisaeg: 23-Feb-2022
  • Kirjastus: Routledge
  • ISBN-10: 1032060492
  • ISBN-13: 9781032060491
Teised raamatud teemal:
From Data to Decisions in Music Education Research: Data Analytics and the General Linear Model Using RSuurem pilt
  • Formaat: Paperback / softback, 494 pages, kõrgus x laius: 254x178 mm, kaal: 453 g, 92 Line drawings, black and white; 3 Halftones, black and white; 95 Illustrations, black and white
  • Ilmumisaeg: 23-Feb-2022
  • Kirjastus: Routledge
  • ISBN-10: 1032060492
  • ISBN-13: 9781032060491
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781032060491.html
Märksõnad:
From Data to Decisions in Music Education Research provides a structured and hands-on approach to working with empirical data in the context of music education research. Using step-by-step tutorials with in-depth examples of music education data, this book draws upon concepts in data science and statistics to provide a comprehensive framework for working with a variety of data and solving data-driven problems.

All of the skills presented here use the R programming language, a free, open-source statistical computing and graphics environment. Using R enables readers to refine their computational thinking abilities and data literacy skills while facilitating reproducibility, replication, and transparency of data analysis in the field. The book offers:











A clear and comprehensive framework for thinking about data analysis processes in a music education context.





An overview of common data structures and data types used in statistical programming and data analytics.





Techniques for cleaning, preprocessing, manipulating, aggregating, and mining data in ways that facilitate organization and interpretation.





Methods for summarizing and visualizing data to help identify structures, patterns, and trends within data sets.





Detailed applications of descriptive, diagnostic, and predictive analytics processes.





Step-by-step code for all concepts and analyses.





Direct access to all data sets and R script files through the accompanying eResource.

From Data to Decisions in Music Education Research offers a reference "cookbook" of code and programming recipes written with the graduate music education student in mind and breaks down data analysis processes and skills in an approachable fashion. It can be used across a wide range of graduate music education courses that rely on the application of empirical data analyses and will be useful to all music education scholars and professionals seeking to enhance their use of quantitative data.
List of Figures
xviii
Preface xxii
SECTION I Fundamentals and Principles of the R Programming Language
1(56)
1 The R Programming Environment
3(24)
1.1 Downloading R and RStudio
3(1)
1.2 The Four Panes of RStudio
4(2)
1.3 First Commands in R: A Fancy Calculator
6(1)
1.4 Garbage In, Garbage Out
7(2)
1.5 R Style
9(1)
1.6 Assigning Values to Objects: Object-Oriented Programming
9(3)
1.7 Working in the Syntax Pane and Creating Scripts
12(1)
1.8 An Example of Computational Thinking with Object-Oriented Programming
13(3)
1.9 Functions
16(1)
1.10 Setting Up a Working Directory
17(2)
1.11 Saving Files
19(2)
1.12 Recap of Starting an R Session
21(1)
1.13 Closing Down an R Session
21(1)
1.14 Reopening an R Session
22(1)
1.15 Installing and Loading Packages
22(3)
1.16 Getting Help in R
25(2)
1.16.1 Syntax-Level Help
25(1)
1.16.2 Topic-Level Help
25(1)
1.16.3 Community-Based Help
26(1)
2 Data Types and Data Structures
27(30)
2.1 The Five Atomic Object Classes of R
27(3)
2.1.1 Character Classes
27(1)
2.1.2 Numeric Classes
28(1)
2.1.3 Integer Classes
28(1)
2.1.4 Complex Classes
29(1)
2.1.5 Local Classes
29(1)
2.2 Relational and Logical Operators
30(2)
2.3 `Flic Five Data Structures of R
32(2)
2.3.1 Vectors
32(1)
2.3.2 Matrices
33(1)
2.3.3 Arrays
33(1)
2.3.4 Drf/a Frames
33(1)
2.3.5 L&s
34(1)
2.4 Working with Vectors
34(18)
2.4.1 Kafor Operations
37(4)
2.4.2 Explicit Coercion of Atomic Class Types
41(3)
2.4.3 Nominal Factor Vectors
44(1)
2.4.4 Ordered Factor Vectors
45(2)
2.4.5 Naming Factor Vector Levels: From Integers to Labels
47(2)
2.4.6 Reverse Coding Numeric Vectors
49(1)
2.4.7 Reverse Coding Character Vectors
50(2)
2.5 Working with Data Frames
52(4)
2.5.1 Creating Vectors
52(3)
2.5.2 Creating Data Frames
55(1)
2.5.3 Accessing Variables in a Data Frame
56(1)
2.6 Exporting Data Structures to. csv
56(1)
SECTION II Data Wrangling Techniques
57(56)
3 Data Preprocessing and Data Manipulation
59(33)
3.1
Chapter Preparation
59(1)
3.2 Data Preprocessing Techniques
60(14)
3.2.1 Importing External Datasets into a Data Frame
60(1)
3.2.1.1 Fifes with, csv Extensions
60(1)
3.2.1.2 Files with, txt Extensions
61(1)
3.2.1.3 Files with. xlsx or. xls Extensions
61(1)
3.2.2 Examining the Landscape of the Data
62(3)
3.2.2.1 Missing and Inconsistent Data Elements
65(4)
3.2.2.2 Explicit Coercion of Variables
69(5)
3.3 Data Manipulation Techniques
74(17)
3.3.1 Indexing
74(2)
3.3.2 Subsets
76(3)
3.3.3 Sorting and Ordering
79(3)
3.3.4 Removing Rows from a Data Frame
82(1)
3.3.5 Removing Rows by Condition
83(1)
3.3.6 Creating New Vectors: Creating Composite Variables and Collapsing Levels Using Explicit Coercion
84(1)
3.3.6.1 Categorical to Logical
84(1)
3.3.6.2 Categorical to Categorical
85(1)
3.3.6.3 Numeric to Categorical
85(2)
3.3.7 Adding Vectors to Data Frames
87(1)
3.3.8 Dollar Sign Notation
88(1)
3.3.9 Bracket Notation
88(1)
3.3.10 Column Bind Function
89(1)
3.3.11 Reordering Columns in a Data Frame
89(1)
3.3.11.1 Indexing Columns by Position Number or Variable Name
89(1)
3.3.11.2 Subset
90(1)
3.3.12 Removing Columns from a Data Frame
90(1)
3.4 Closing Out the
Chapter
91(1)
4 Data Aggregation
92(21)
4.1
Chapter Preparation
92(1)
4.2 Extending Data Frames
93(16)
4.2.1 Merging Observations to a Data Frame with an Equivalent Column Structure
93(5)
4.2.2 Merging Columns to a Data Frame with an Equivalent Observation Structure
98(1)
4.2.2.1 Scenario 1: Merging on Row Numbers
98(2)
4.2.2.2 Scenario 2: Merging on Columns with the Same Name
100(2)
4.2.2.3 Scenario 3: Merging on Columns with a Different Name
102(1)
4.2.3 Adding Observations with Nonequivalent Column Structures
103(2)
4.2.4 Adding Columns with Nonequivalent Observation Structures
105(4)
4.3 Reshaping Data: Long Versus Wide Formats
109(3)
4.3.1 Wide to Long Format
110(1)
4.3.2 Long to Wide Format
111(1)
4.4 Closing Out the
Chapter
112(1)
SECTION III Descriptive Analytics and Exploratory Data Analysis Techniques
113(98)
5 Summary Operations
115(42)
5.1
Chapter Preparation
115(2)
5.2 The summary() Function
117(1)
5.3 Univariate Data
117(36)
5.3.1 Descriptive Statistics for Univariate Categorical Data
117(1)
5.3.1.1 Frequency
118(1)
5.3.1.2 Proportional Frequency
119(1)
5.3.1.3 Cumulative Frequency
120(1)
5.3.1.4 Cumulative Proportional Frequency
121(1)
5.3.2 Descriptive Statistics for Bivariate Categorical Data
122(1)
5.3.2.1 Frequency
122(1)
5.3.2.2 Proportional Frequency
123(1)
5.3.2.3 Marginals
123(1)
5.3.2.3.1 Frequency Marginals
124(1)
5.3.2.3.2 Proportional Marginals
124(1)
5.3.2.4 The CrossTable() Function
125(2)
5.3.3 Descriptive Statistics for Univariate Continuous Data
127(1)
5.3.3.1 Sampling Theory and the Gaussian Distribution
127(3)
5.3.3.2 Measures of Central Tendency
130(1)
5.3.3.2.1 Mean
130(1)
5.3.3.2.2 Trimmed Mean
131(2)
5.3.3.2.3 Median
133(3)
5.3.3.2.4 Mode
136(1)
5.3.3.3 Measures of Dispersion
137(1)
5.3.3.3.1 Population Variance
137(2)
5.3.3.3.2 Sample Variance
139(1)
5.3.3.3.3 Population Standard Deviation
140(1)
5.3.3.3.4 Sample Standard Deviation
141(1)
5.3.3.3.5 Average Absolute Deviation
141(1)
5.3.3.3.6 Median Absolute Deviation
142(1)
5.3.3.3.7 Range
143(1)
5.3.3.3.8 Skewness
144(2)
5.3.3.3.9 Kurtosis
146(1)
5.3.3.3.10 Standard Error of the Mean
147(1)
5.3.3.4 Five-Number Summaries
148(1)
5.3.3.4.1 Quartiles
148(2)
5.3.3.4.2 Quantiles and Percentile Ranks
150(2)
5.3.3.4.3 The describe() Function
152(1)
5.3.4 Descriptive Statistics for a Continuous Variable Stratified by a Categorical Variable
152(1)
5.4 Coefficient Alpha (Cronbach's Alpha)
153(3)
5.5 Closing Out the
Chapter
156(1)
6 Data Visualization
157(54)
6.1
Chapter Preparation
157(1)
6.2 A Data Visualization Primer in R
158(9)
6.2.1 Creating Multiple Plot Spaces
158(2)
6.2.2 Color Considerations
160(1)
6.2.2.1 R Colors
160(3)
6.2.2.2 Hexadecimal Color Codes
163(1)
6.2.2.3 RGB Values
164(1)
6.2.2.4 Converting between R Colors, Hexadecimal Colors, and RGB Values
164(1)
6.2.2.5 Color Palettes
165(2)
6.3 Visualizing Univariate Data
167(32)
6.3.1 Plotting Univariate Categorical Data
167(1)
6.3.1.1 Bar Plot
167(7)
6.3.1.2 Pareto Chart
174(1)
6.3.2 Plotting of Univariate Continuous Data
175(1)
6.3.2.1 Empirical Cumulative Distribution Function
175(3)
6.3.2.2 Box Plot
178(1)
6.3.2.2.1 Box Plot with Strip Chart Overlay
179(2)
6.3.2.3 Stem-and-Leaf Plot
181(2)
6.3.2.4 Histogram with Frequency Scale
183(2)
6.3.2.4.1 Overlays
185(1)
6.3.2.4.1.1 Frequency Count Overlay
185(2)
6.3.2.4.1.2 Mean and Standard Deviation Overlay
187(1)
6.3.2.4.1.3 Rug Overlay
188(1)
6.3.2.4.1.4 Line Graph Overlay
188(1)
6.3.2.4.1.5 Normal Curve Overlay
189(2)
6.3.2.5 Histogram with Probability Density Function Scale
191(2)
6.3.2.5.1 Overlays
193(1)
6.3.2.5.1.1 Normal Curve Overlay
193(1)
6.3.2.5.1.2 Kernel Probability Density Overlay
193(1)
6.3.2.6 Kernel Density Plot
194(1)
6.3.2.7 Violin Plot
194(3)
6.3.2.8 Quantile-Quantile (Q-Q) Plot
197(2)
6.4 Visualizing Bivariate Data
199(10)
6.4.1 Plotting One Categorical and One Continuous Variable
199(1)
6.4.1.1 Stratified Boxplot
199(1)
6.4.1.2 Stratified Lattice Histograms and Kernel Density Plots
199(4)
6.4.1.3 Stratified Kernel Density Plots Overlapped
203(4)
6.4.1.4 Stratified Violin Plots
207(1)
6.4.2 Plotting Two Continuous Variables
208(1)
6.4.2.1 Scatterplot
208(1)
6.5 Closing Out the
Chapter
209(2)
SECTION IV Diagnostic Analytics and Data Mining Techniques
211(80)
7 Normality Assessment and Anomaly Detection
213(21)
7.1
Chapter Preparation
213(1)
7.2 Broad Considerations
214(1)
7.3 A Starting Paradigm
214(1)
7.3.1 Short-Tailed Distributions
215(1)
7.3.2 Long-Tailed Distributions
215(1)
7.3.3 Large Sample Sizes
215(1)
7.3.4 Ties
215(1)
7.4 Univariate Tests of Normality
215(9)
7.4.1 Shapiro-Wilk Test
216(2)
7.4.2 Anderson-Darling Test
218(1)
7.4.3 Jarque-Bera Test
219(1)
7.4.4 Anscombe-Glynn Test
220(1)
7.4.5 Geary and Bonnet-Seier Tests
221(1)
7.4.6 DAgostino Test
222(1)
7.4.7 Kolmogorov-Smirnov Test
223(1)
7.5 Univariate Outlier Identification Techniques
224(9)
7.5.1 Plotting Data to Identify Outliers
225(2)
7.5.2 Descriptive Statistics Rules of Thumb to Identify Outliers
227(1)
7.5.2.1 Z-scores
227(1)
7.5.2.2 Interquartile Range
228(3)
7.5.3 Formal Hypothesis Testing to Identify Outliers
231(1)
7.5.3.1 Grubbs' Outlier Test
231(1)
7.5.3.2 Rosner's Outlier Test
232(1)
7.6 Closing Out the
Chapter
233(1)
8 Data Re-Expression Techniques
234(27)
8.1
Chapter Preparation
234(2)
8.2 Clarifying Terminology
236(10)
8.2.1 Shifting
238(1)
8.2.2 Centering
239(1)
8.2.3 Scaling
240(2)
8.2.4 Normalization
242(1)
8.2.5 Standardization
243(2)
8.2.6 Transformation
245(1)
8.3 Selecting a Re-Expression Method
246(14)
8.3.1 Communicating Variables to Audiences
246(1)
8.3.1.1 Percentile Ranks
246(1)
8.3.2 Comparing Variables
247(1)
8.3.2.1 Z-Score Normalization
247(2)
8.3.2.2 SS-Score Normalization
249(2)
8.3.3 Equality of Variables
251(1)
8.3.3.1 [ 0, 1} Min-Max Scaling
251(1)
8.3.3.2 Arbitrary Min-Max Scaling
252(1)
8.3.4 Normality
253(1)
8.3.4.1 Addressing Skewness
253(2)
8.3.4.1.1 Reducing Right Skewness
255(1)
8.3.4.1.1.1 Logarithmic Transformation
255(2)
8.3.4.1.1.2 Reciprocal Transformation
257(1)
8.3.4.1.1.3 Cube Root Transformation
258(1)
8.3.4.1.2 Reducing Left Skewness
258(1)
8.3.4.1.2.1 Squares Transformation
258(2)
8.3.4.1.2.2 Cubes Transformation
260(1)
8.4 Closing Out the
Chapter
260(1)
9 Covariance and Correlation
261(30)
9.1
Chapter Preparation
261(1)
9.2 Covariance
262(1)
9.3 Assumptions based on the Design of the Stored Data
263(2)
9.4 Calculating and Examining Covariance
265(4)
9.5 Correlation
269(1)
9.6 Properties of the Correlation Coefficient
270(1)
9.7 Attributes and Structure of the cor.test() Function
271(1)
9.8 Test of Significance Using the t-Statistic
272(5)
9.9 Inference and Correlation: Test of Significance Using p-values
277(1)
9.10 Confidence Intervals for Population Pearson's p
278(1)
9.11 Multiple Correlation
279(10)
9.12 Closing Out the
Chapter
289(2)
SECTION V Predictive Analytics and the General Linear Model
291(195)
10 The Mean Model and Simple Linear Regression
293(60)
10.1
Chapter Preparation
293(1)
10.2 Beyond Correlation
294(1)
10.3 Modeling One Variable: The Mean Model
295(19)
10.3.1 Expressing the Mean Line
296(2)
10.3.2 Making Inferences
298(1)
10.3.3 Calculating Residuals
298(1)
10.3.3.1 Summing the Residuals
299(1)
10.3.4 Distribution of the Residuals
300(2)
10.3.5 Standard Error of the Mean
302(1)
10.3.6 Confidence Intervals
302(3)
10.3.7 Mean Square Error and Root Mean Square Error
305(2)
10.3.8 Formally Expressing the Mean Model
307(1)
10.3.9 Specifying the Mean Model in R
308(6)
10.3.9.1 Calculating Confidence Intervals for b()
314(1)
10.3.10 The Mean Model as a Foundation
314(1)
10.4 Modeling Two Variables: Simple Linear Regression
314(38)
10.4.1 Estimating a Line of Best Fit
315(1)
10.4.1.1 Calculating Ordinary Least Squares
315(4)
10.4.1.2 Expressing the Least Squares Line of Best Fit
319(2)
10.4.2 Decomposing Residuals of the Bivariate Model
321(1)
10.4.2.1 Unexplained Variance: Residual Sum of Squares (RSS)
321(2)
10.4.2.2 Explained Variance: Explained Sum of Squares (ESS)
323(3)
10.4.2.3 Total Variance: Total Sum of Squares (TSS)
326(1)
10.4.3 Quantifying the Quality of the Line of Best Fit: RJ and Adjusted R2
327(3)
10.4.4 Examining the Distribution of the Residuals'
330(1)
10.4.5 Examining the Precision of the Model: Standard Errors
331(2)
10.4.6 Statistical Significance: F-tests and p-values
333(4)
10.4.7 Specifying the Simple Linear Regression Model in R
337(7)
10.4.7.1 Calculating Confidence Intervals for b0 and b1
344(2)
10.4.8 Forecasting
346(4)
10.4.9 Calculating Standardized Coefficients and Effect Size
350(2)
10.5 Closing Out the
Chapter
352(1)
11 Multiple Linear Regression
353(58)
11.1
Chapter Preparation
353(1)
11.2 Continuous by Continuous Multiple Regression
354(7)
11.2.1 Preprocessing the Predictor Variables
355(1)
11.2.2 The Additive Multiple Linear Regression Model
356(2)
11.2.2.1 Analysis of Residuals
358(1)
11.2.2.2 Plotting the Main Effects
359(2)
11.2.2.3 Forecasting
361(1)
11.3 Continuous by Continuous Multiple Regression with a Moderator Variable
361(12)
11.3.1 Preprocessing the Predictor Variables
362(2)
11.3.2 The Multiplicative Multiple Linear Regression Model
364(3)
11.3.2.1 Analysis of Residuals
367(1)
11.3.2.2 Plotting the Interaction Effect
367(1)
11.3.2.3 Plotting the Simple Slopes
367(4)
11.3.2.4 Testing the Simple Slopes
371(2)
11.4 Continuous by Categorical Multiple Regression
373(13)
11.4.1 Preprocessing the Predictor Variables
375(4)
11.4.2 The Additive Multiple Linear Regression Model
379(2)
11.4.2.1 Analysis of Residuals
381(1)
11.4.2.2 Plotting the Main Effects
382(3)
11.4.2.3 Forecasting
385(1)
11.5 Continuous by Categorical Multiple Regression with a Moderator Variable
386(9)
11.5.1 Preprocessing the Predictor Variables
386(1)
11.5.2 The Multiplicative Multiple Linear Regression Model
387(2)
11.5.2.1 Analysis of Residuals
389(1)
11.5.2.2 Plotting the Interaction Effect
390(1)
11.5.2.3 Plotting the Simple Effects
390(4)
11.5.2.4 Testing the Simple Effects
394(1)
11.6 Categorical by Categorical Multiple Regression
395(9)
11.6.1 Preprocessing the Predictor Variables
396(3)
11.6.2 The Additive Multiple Linear Regression Model
399(2)
11.6.2.1 Analysis of Residuals
401(1)
11.6.2.2 Plotting and Testing the Effects
401(3)
11.6.2.3 Forecasting
404(1)
11.7 Categorical by Categorical Multiple Regression with a Moderator Variable
404(6)
11.7.1 The Multiplicative Multiple Regression Model
404(2)
11.7.1.1 Analysis of Residuals
406(1)
11.7.1.2 Plotting Interaction Effect
407(2)
11.7.1.3 Testing the Effects
409(1)
11.8 Closing Out the
Chapter
410(1)
12 Special Cases of The General Linear Model
411(39)
12.1
Chapter Preparation
411(1)
12.2 Special Case of the Mean Model
412(4)
12.2.1 One-Sample t-test
412(4)
12.3 Special Cases of the Simple Linear Regression Model
416(10)
12.3.1 Two-Sample t-test
416(5)
12.3.2 Paired-Samples t-lest
421(5)
12.4 Special Cases of the Multiple Linear Regression Model
426(23)
12.4.1 One-Way Between-Subjects Analysis of Variance
426(5)
12.4.2 One-Way Within-Subjects Analysis of Variance
431(4)
12.4.3 Two-Way Between-Subjects Analysis of Variance
435(7)
12.4.4 Two-Way Within Subjects Analysis of Variance
442(7)
12.5 Closing Out the
Chapter
449(1)
13 Model Diagnostics
450(36)
13.1
Chapter Preparation
450(3)
13.2 Assumption: The Relationship Between the Predictor and Response Variables is Linear
453(3)
13.3 Assumption: Independence of Residual Error Terms
456(10)
13.3.1 Identifying Outlier Cases
456(1)
13.3.2 Identifying Cases with High Leverage Values
457(3)
13.3.3 Identifying Influential Cases
460(6)
13.4 Assumption: Residual Errors Are Normally Distributed
466(4)
13.5 Assumption: Homogeneity of Residuals' Variance (i.e., Homosccdasticity)
470(3)
13.6 Global Test of Model Assumptions
473(2)
13.7 Assumption: Multicollinearity Does Not Exist between Predictor Variables
475(6)
13.8 Assumption: Homogeneity of Variances
481(4)
13.8.1 Two Levels
481(1)
13.8.2 Three or More Levels
482(1)
13.8.3 Within-Subjects Designs
483(2)
13.9 Data Remedies for Failing to Meet Assumptions
485(1)
13.10 Closing Out the
Chapter
485(1)
References 486(3)
Index 489
Brian C. Wesolowski is an Associate Professor of Music Education at the University of Georgia. He received his PhD from the University of Miami, Coral Gables, FL.