Statistical Testing

Statistical Testing covers hypothesis testing, one of the most important methodologies in statistics, and introduces basic theories as well as various tests frequently used in practice. In particular, the content in the Advanced section originated from the complaint “please write down what the null hypothesis and alternative hypothesis are, not just output the test statistic and p-value,” and it is certain that it will be helpful to many statistics students.

• In particular, the posts in the Beginner section carefully explain the derivation process of hypothesis tests that must be accepted without mathematical proof when you are an undergraduate freshman. Even if you advance to higher grades, it is difficult to understand the proof at the undergraduate level, but if you are at the level of a graduate student, it is recommended to review them as you go through.

Beginner

• Simple Definition of Hypothesis Testing
  • How to Set the Null Hypothesis and Alternative Hypothesis
• Rejection Region and Significance Level
  • Difference Between Type I Error and Type II Error
• P-value or Significance Probability
  • What is P-hacking?

Inference on Population Mean

• Large Sample Hypothesis Test for Population Mean
• Small Sample Hypothesis Test for Population Mean
• Large Sample Hypothesis Test for Difference of Two Population Means
• Small Sample Hypothesis Test for Difference of Two Population Means

Chi-squared Test

• Pearson Chi-squared Test Statistic $\mathcal{X}^{2}$
  • Multinomial Experiments and Contingency Tables
  • Goodness-of-fit Test for Groups
  • Independence Test for Groups
  • Homogeneity Test for Groups
• Population Variance Estimation for Groups Following Normal Distribution

ANOVA

• Experimental Design CRD, RBD
• Analysis of Variance or ANOVA?
• ANOVA Table
• F-test in ANOVA
• One-way ANOVA
• Two-way ANOVA

Nonparametric Statistics

• What is Nonparametric Statistics?
• Rank in Statistics
  • Mean and Variance of Ranks in Statistics
• Mann-Whitney $U$ Test
• Wilcoxon Signed-rank Test
  • Sign Test in Statistics
• Kruskal-Wallis $H$ Test
• Friedman $F_{r}$ Test
• Spearman Rank Correlation Coefficient $r$

Advanced

Distribution Testing

• Shapiro-Wilk Test
• Jarque-Bera Test

Regression Analysis

• t-test for Regression Coefficients
• F-test for Regression Coefficients
• Hosmer-Lemeshow Goodness-of-fit Test

Time Series Analysis

• Dickey-Fuller Test
• Box-Cox Transformation
• Durbin-Watson Test
• Ljung-Box Test
• MacLeod-Li Test

Main References

• Mendenhall. (2012). Introduction to Probability and Statistics (13th Edition)
• Department of Statistics, Kyungpook National University. (2008). Statistics Using Excel