Essentials of Statistical Analysis andPsychometrics in Human Sciences
Hidetoki Ishii
Translation Supervisor - Aye Aye Myint
Translator - Nu Nu Khaing

Preface
Statistics has been established as a science since the late 19th and early 20th centuries.
Today, the roles of statistics are so wide that it is considered as a language of science or sciencelearning of data. Researchers are using statistics in many fields to organize, analyze, and summarize
data. Today is the Era of Big Data, and thus various new statistical methods have been developedand applied not only in research but also in the society.
However, it is us who collect data, analyze them, and interpret the results. There are many
advanced analysis methods. It becomes easier to use data analysis. But, unless we have thoroughunderstanding about statistical analysis a1l1cepts, it is di fficult to utilize the results efficiently andappropriately. The important point is that we have to understand not only the superficial process ofthe data analysis but the logic behind the statistical analysis methods.
The aim of this book is to provide thoughts and ideas of statistical analysis with various
practical examples to· those who are interested in human science, especially studying human mind.
In studying human mind, we find out constructs such as intelligence or personality which are
abstract and.do not exist physically. Therefore, in order to measure and assess those constructs, acertain theories and techniques are required. In this book, I focus on these theories and techniques
which are not usually considered in most of other statistics textbooks.
The readers are mainly assumed to be undergraduate students, graduate students, andresearchers in psychology, nursing, public health, medical, education, sociology, welfare, and soon. Moreover, this book can also support everyone who is using statistical analysis methods since
the basic ideas of statistics are common in all discipl ines.
This book includes 22 chapters. In Chapters I to 6, introduction about basic concepts andarguments of statistics are provided. We consider why statistical analysis is necessary in studying

human mind, such as psychology whose disciplines are subjective to the human mind in Chapter 1.
After data collection methods and ethical considerations are discussed in Chapter 2, data types anddata structures are introduced in Chapter 3, and summarization of data is explained in Chapter 4. In
Chapter 5, distribution statistics such as mean and standard deviation are introduced. In Chapter' '6,covariances and correlation coefficients are considered.
In Chapter 7, we introduce test theories which concerns about measuring constructs. This
chapter distinguishes this book from other ordinary statistics books. Unlike weight machines orthermometers, there are no standard specifications for scales or tests to measure constructs. Whether
we can measure what we want to is still uncertain just by gathering items. It is necessary to collectevidences which convince us to measure what we want to. In this chapter, these are discussed.
In Chapters 8 to 10, the basic logic of' statistical inferences is provided. Using simple
examples, logical structures of statistical analysis are explained. Chapter 8 is a preparing part of
the following chapters. We require understanding an important term in statistics, that is, standard
error. Some characteristics of probabi1ity distributions which are often utilized in statistical'analysis are algo explained. The logic of statistical testing is introduced in Chapter 9. The logic ofstatistical estimations is provided in Chapter 10. Estimation of sample size using confidence
intervals is also discussed.
In Chapters 11 to 16, several popular analysis meth ods such as t test, analysis of variance,
non-parametric methods, correlation coefficients, contingency tables, and analysis of proportions
are overviewed. In Chapters 17 to 22, multivariate data analysis related to linear regression and·structural equation modeling are discussed. Chapter 17 describes random vector, partial correlatio ncoefficient and single regression analysis. Chapter 18 discusses multiple regression analysis. FromChapters 19 to 22, we consider the structural equation modeling. Basic ideas of structural equation
modeling, path analysis, model evaluation, factor anal ysis, and more complicated models arediscussed.

CONTENTS
CHAPTER 1

Why Statistical Analysis is Necessary

1.1 Necessity of statistical analysis
1.2 Various statistical methods
1.3 Psychometrics

CHAPTER 2

Data Collection

2.1 Population and sample
2.2 Sampling methods
2.3 Data collection methods
2.4 Ethical considerations
2.5 Data collection process
2.6 Development of questionnaires

CHAPTER 3

Types of Data

3.1 Scales of measurement
3.2 Data structures

CHAPTER 4

Statistical Tables and Figures 34

4.1 Summarization of qualitative data
4.2 Summarization of quantitative data

CHAPTER 5

Quantitative Data Distribution

5.1 Population distribution and data distribution
5.2 Average
5.3 Dispersion
5.4 Nature of asymmetry and heaviness of tails
5.S Data standardization

CHAPTER 6

Correlations between Quantitative Variables

6.1 Composite scores and covariance
6.2 Characteristics of covariance
6.3 Correlation coefficients
6.4 Considerations on correlation coefficients

CHAPTER 7

Test Theory

7.1 Validity
7.2 Reliability
7.3 Reliability coefficient
7.4 Estimations of reliability coefficient
7.5 Considerations on reliability coefficient
7.6 Item analysis

CHAPTER 8

Foundation for Understanding Statistical Inference

8.1 Why statistical inference is necessary
8.2 Standard error
8.3 Probability distribution
8.4 Consideration on probability and statistics

CHAPTER 9

The Logic of Statistical Tests

9.1 Preparation for statistical tests
9.2 Statistical tests
9.3 Considerations on statistical tests

CHAPTER 10

The Logic of Statistical Estimation

10.1 Point estimation
10.2 Interval estimation
10.3 Relationship between confidence intervals and statistical tests
10.4 Estimation of sample sizes using confidence intervals

CHAPTER 11

Inferences for Two-Group Means

11.1 Paired two-group means
11.2 Independent two-group means
11.3 Non-inferiority and equivalency of means
11.4 Effect sizes

CHAPTER 12

Inferences for More than Two Means

12.1 Analysis of variance (ANOVA)
12.2 Inference on one between-subject factor
12.3 Inference on one within-subject factor12.4 Inference on two between-subject factors
12.5 Inference on two within-subject factors
12.6 Inference on one between-subject and. one within-subject factors
12.7 Data transformations
CHAPTER 13

Inference on Locations of Distributions

13.1 Comparison of paired two-group distributions
13.2 Comparisons of paired multi-group distributions
13.3 Comparison of independent two-group distributions
13.4 Comparisons of independent, multi-group distributions

CHAPTER 14

Inference on Correlation Coefficients

14.1 Inference on a single group's correlation coef ficient14.2 Inference on the difference between correlation coefficients of two groups
14.3 Inference on homogeneity of multi-group

CHAPTER 15

correlation coefficientsInference on Contingency Tables

15.1 Independence between variables
15.2 Contingency coefficient15.3 Test for independence
15.4 Analysis of residuals
15.5 Agreement coefficient15.6 Considerations on contingency tables

CHAPTER 16

Inference Oft Proportions

16.1 Inference on a single group proportion
16.2 Inference on paired two-group proportions
16.3 Inference on paired, multi-group proportions
16.4 Prospective, retrospective, and -cross-sectional studies
16.5 Risk difference, risk ratio and odds ratio
16.6 Inference on independent two-group proportions
16.7 Inference on non-inferiority and equivalency of proportions
16.8 Inference on independent, multi-group proportions

CHAPTER 17

Preparations for Multivariate Data Analysis

17.1 Data matrix
17.2 Random vectors
17.3 Elimination of components
17.4 Simple linear regression analysis
17.5 Fundamental understanding of regression analysis

CHAPTER 18

Multiple Regression Analysis

18.1 Multiple regression analysis
18.2 Precision of predictions
18.3 Understanding partial regression coefficients
18.4 Several discussions on explanatory variables

CHAPTER 19

Introduction to Structural Equation Modeling19.1 Fundamental ideas of structural equation modeling19.2 Multiple regression analysis
19.3 Path analysis

CHAPTER 20

Evaluation of Structural Equation Models

20.1 Degrees of freedom of models
20.2 Identification problems
20.3 Indices of goodness of fit
20.4 Considerations on goodness of fit of models
20.5 Improper solutions

CHAPTER 21

Factor Analysis

21.1 Latent variables
21.2 Confirmatory factor analysis
21.3 Exploratory factor analysis
21.4 Factor analysis tables
21.5 Considerations on scale development utilizing factor analysis

CHAPTER 22Expansion of the Structural Equation Model

22.1 Subscale models.
22.2 Models assuming structures among latent variables
22.3 Multiple group analysis

APPENDICES
322 pages