introduction

Chapter 1: Prologue
1.
The meaning of statistics
2.
The role of statistics
3.
Meaning of variables
4.
Classification of measurements
4.1 Nominal scale
4.2 Ordinal scale
4.3 Interval scale
4.4 Ratio scale
5.
Complete works and specimens
6.
Descriptive and inferential statistics
7.
Parametric and nonparametric statistics


Chapter 2: Organizing Data
1.
Frequency distribution
1.1 Score range
1.2 Size of the interval
1.3 Score limit for each grade
1.4 Accurate limits
2.
Example of a frequency distribution plot
2.1 Histogram
2.2 Frequency polygon
2.3 Cumulative frequency distribution
2.4 Cumulative percentage curve
2.5 percentiles and percentile scores
■ Practice problems


Chapter 3: Central Tendency
1.
Choi Bin-chi
2.
median
3.
average
3.1 Mathematical properties of the mean
3.2 Comparison of central tendency measures
3.3 Merging of averages
■ Practice problems


Chapter 4: Byeonsando
1.
range
2.
quartile deviation
3.
dispersion
4.
standard deviation
5.
coefficient of variation
■ Practice problems


Chapter 5 Standard Scores and Normal Distribution
1.
standard score
1.1 Characteristics of standard scores
1.2 Converted standard scores
1.3 Weighted average of the inspectors
2.
normal distribution
2.1 Unit normal curve
2.2 Use of the normal distribution curve
3.
Probability and probability distributions
3.1 Some laws of probability theory
3.2 Probability distribution
3.3 Probability distribution and normal distribution curve
■ Practice problems


Chapter 6 Correlation
1.
The concept of correlation coefficient
2.
scale of measurement
2.1 Nominal scale: 2-category discontinuous (Nominal-discrete dichotomy) variables
2.2 Nominal scale: 2-category continuous (Nominal-continuous dichotomy) variable
2.3 Ordinal scale
2.4 Interval/ratio scale
3.
Pearson's product-moment correlation coefficient
3.1 Calculation of the correlation coefficient
3.2 Factors affecting the magnitude of the correlation coefficient
3.3 Interpretation of correlation coefficients
4.
Spearman's rank-order correlation coefficient
5.
Kendall's correlation coefficient
6.
Inter-rater correlation coefficient
7.
Pi coefficient
8.
Correlation coefficient
9.
Bivariate correlation coefficient
10.
Bivariate correlation coefficient
11.
Orthographic correlation coefficient
12.
Correspondence ratio
■ Practice problems


Chapter 7 Inferential Statistics
1.
Sampling method
1.1 Simple random sampling
1.2 Systematic sampling
1.3 Stratified sampling
1.4 Cluster sampling
1.5 Multistage sampling
1.6 Quota sampling
1.7 Purposive sampling
1.8 Random sampling
1.9 Mixed Sampling
2.
Procedures for conducting a sampling survey and determining sample size
3.
Sampling distribution
3.1 Properties of sampling distribution
3.2 Distribution
3.3 Degrees of freedom
3.4 Degrees of freedom and distribution
4.
hypothesis testing
4.1 Hypothesis testing when the characteristics of the complete collection are unknown
Sampling distribution of the sample mean when 4.2 is unknown
4.3 Example of hypothesis testing
4.4 Significance level (level)
5.
Estimation of parameter values
5.1 Estimation by single value (point estimation)
5.2 Estimation by setting confidence intervals (interval estimation)
■ Practice problems


Chapter 8 Inferential Statistics
1.
Hypothesis statement
2.
Errors that can be made in hypothesis testing
3.
Significance level
4.
Areas where the null hypothesis is rejected: Two-tailed verification
5.
Areas where the null hypothesis is rejected: One-sided tests
■ Practice problems


Chapter 9 Hypothesis Testing for Single Samples
1.
Hypothesis testing for the mean of the entire collection ()
2.
Verification of the complete correlation coefficient ()
3.
Hypothesis verification of whether the correlation coefficient of the entire collection is 0
4.
Verification of the ratio of the complete collection ()
5.
Hypothesis testing on the total variance ()
6.
statistical precision
7.
Statistical significance and practical significance
■ Practice problems


Chapter 10: Testing the Difference Between Two Sample Statistics
1.
Assumptions for testing the difference between two sample statistics
1.1 Independent sample assumption
1.2 Homogeneity of variance assumption
1.3 Normality assumption of the collected data distribution
2.
Test for the difference between two means in case of independent samples
2.1 A specific understanding of the null hypothesis testing method: Independent sample case
2.2 Test for differences between means in independent samples
2.3 Test for differences in means in independent samples
3.
For dependent samples, test for difference between two means
4.
Difference test between two proportions for independent samples
5.
For the dependent sample, the test of the difference between two proportions
6.
Test for the difference between two correlation coefficients for independent samples
7.
In the case of dependent samples, the difference test between two correlation coefficients
8.
In case of independent samples, test for difference between two variances
9.
For dependent samples, test for differences between two variances
10.
statistical power
10.1 Factors Affecting Statistical Power
10.2 Calculating statistical power
11.
effect size
11.1 Size of the difference between the means
11.2 Strength of Association
12.
Estimation of sample size
12.1 In the case of hypothesis testing
12.2 For setting confidence intervals
13.
Statistical power and sample size estimation using G*Power
13.1 How to use G*Power
summation
■ Practice problems


Chapter 11 One-Way ANOVA
1.
Independent and dependent variables in ANOVA
2.
Basic concepts of analysis of variance
3.
Mathematical model of one-way ANOVA
4.
Division of the square root
5.
Estimate of total variance
6.
Null hypothesis testing
7.
Basic assumptions of analysis of variance
7.1 Verification of homoscedasticity for three or more groups
7.2 Problems when basic assumptions are violated
8.
Relationship between ANOVA and validation
9.
Relationship strength
■ Practice problems


Chapter 12 Individual Comparison of Averages
1.
Post hoc comparison
1.1 Tukey method
1.2 Newman-Keuls method
1.3 Scheff method
1.4 Bonferroni method
2.
A priori comparisons
2.1 Planned orthogonal contrasts
2.2 Trend analysis
summation
■ Practice problems


Chapter 13 Two-Way ANOVA
1.
Meaning of two-way ANOVA
2.
Data structure for two-way ANOVA
3.
Partitioning of variance in two-way ANOVA
4.
Division of the square root
5.
Testing the null hypothesis
6.
Calculation formula and application examples
7.
Interaction effect
8.
Reduction of error variance in two-way analysis of variance
9.
Basic assumptions of two-way ANOVA
10.
Mathematical model of two-way analysis of variance
11.
Special model of two-way ANOVA
12.
Individual comparison of means in two-way ANOVA
13.
Relationship strength
14.
When the sample size of each group is not the same
15.
Randomized block design
16.
Repeated measures design
summation
■ Practice problems


Chapter 14 Analysis of Covariance
1.
Understanding ANCOVA using graphics
2. Advantages and disadvantages of ANCOVA
3.
Method of selecting covariates
4. What method is preferable when ANCOVA is not possible?
5. Things to check in advance for ANCOVA
5.1 Unequal Cases and Missing Data
5.2 Outliers
6. Basic assumptions of ANCOVA
6.1 Multicollinearity and singularity
6.2 Normality of distribution
6.3 Homogeneity of variance
6.4 Linearity
6.5 Homogeneity of regression lines
6.6 Covariate Reliability
7.
Calculation formula and application examples
8.
Relationship strength
9.
Adjusted average
10. Example of describing ANCOVA results
summation
■ Practice problems


Chapter 15 Nonparametric Testing
1.
distribution
2.
Verification of nominal dates
2.1 Validation on a Single Sample: Validation of Goodness of Fit
2.2 Comparing Two Independent Samples: Testing Independence
2.3 Comparison of Independent Samples: Testing Independence
2.4 Comparing Two Dependent Samples: McNemar's Test
3.
Verification of ordinal data
3.1 Comparing Two Independent Samples: Median Test
3.2 Comparison of two independent samples: Mann-Whitney test
3.3 Comparison of Independent Samples: Kruskal-Wallis One-Way ANOVA
3.4 Comparison of Independent Samples: Median Test
3.5 Comparing Two Dependent Samples: Wilcoxon Test
3.6 Comparison of Dependent Samples: Friedman's Two-Way ANOVA
summation
■ Practice problems


Chapter 16: Linear Regression: Predictions and Regression Equations

1.
Prophecy and Prophecy
2.
Regression line
3.
Regression equation
3.1 Derivation of the regression equation
3.2 Deriving regression equations from raw data
3.3 Prophecy scores and their distribution
4.
Prophetic error
4.1 Standard error of estimate
4.2 Error variance
4.3 Correcting the standard error of estimation
4.4 Accuracy of regression coefficients
4.5 Interpreting the standard error of the estimate
4.6 Basic assumptions of regression lines
5.
Accuracy of prophecy
5.1 Coefficient alienation
5.2 Index of forecasting efficiency
5.3 Coefficient of determination
6.
The relationship between correlation and prophecy
6.1 Variance partitioning of predictor variables ()
6.2 Correlation coefficients and regression coefficients
6.3 Prediction of standard scores by standard scores
6.4 Probability of Regression and Prediction
summation
■ Practice problems


Chapter 17: Polycorrelation and Prophecy
1.
The concept of multiple prophecies
1.1 Multiple predictions based on standard scores
1.2 Multiple correlation coefficient
1.3 Standard error of estimation
2.
Purpose of application of multiple regression analysis
2.1 Standard regression analysis
2.2 Hierarchical regression analysis
2.3 Statistical regression analysis
3.
Selection of independent variables in statistical regression analysis
3.1 Methods for selecting independent variables in statistical regression analysis
3.2 Suppressor variable
3.3 Number of independent variables
4.
Things to check for multiple regression analysis
4.1 Ratio of number of cases to number of independent variables
4.2 Outliers
5.
Basic assumptions of multiple regression analysis
5.1 Multicollinearity and singularity
5.2 Normality, linearity, homoscedasticity, and independence of residuals
6.
Multiple regression analysis using the Doolittle method
7.
Test of the difference between two multiple correlation coefficients
8.
Relationship between multiple regression analysis and ANOVA
9.
Partial correlation and semi-partial correlation
10.
Relationship between correlation coefficients, partial correlation coefficients, and semi-partial correlation coefficients by multiple regression analysis method
■ Practice problems


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References

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