Statistical Test

Statistical Testing deals with hypothesis testing^{Hypothesis Test}, one of the most important methodologies in statistics, introducing everything from the fundamental theory to a variety of tests frequently used in practice. In particular, the contents in the Senior section arise from feedback such as “Don’t just output the test statistic and p-value—please state what the null and alternative hypotheses are,” and I’m confident they’ll be helpful to many statistics students.

• Especially in the Freshman posts, the derivations of hypothesis tests that undergraduates must accept without mathematical proofs are organized in detail. Even as you advance through your years as an undergraduate, these proofs can still be hard to follow—but if you’re roughly at the level of a graduate-program newcomer, I recommend working through them sequentially as a review.

Freshman

• An Easy Definition of Hypothesis Testing
  • How to Determine Null and Alternative Hypotheses
• Rejection Region and Significance Level
  • The Difference Between Type I and Type II Errors
• The p-Value or Significance Probability

Inference for Population Mean

• Hypothesis Test for a Population Mean (Large Sample)
• Hypothesis Test for a Population Mean (Small Sample)
• Hypothesis Test for the Difference of Two Population Means (Large Samples)
• Hypothesis Test for the Difference of Two Population Means (Small Samples)

Chi-Square Tests

• Pearson’s Chi-Square Test Statistic $\mathcal{X}^{2}$
  • Multinomial Experiments and Contingency Tables
  • Goodness-of-Fit Test
  • Test for Independence of Populations
  • Test for Homogeneity of Populations
• Estimation of Population Variance Assuming Normality

ANOVA

• Experimental Designs: CRD and RBD
• What Is Analysis of Variance (ANOVA)?
• The ANOVA Table
• 🔒(25/06/16) The F-Test in ANOVA
• 🔒(25/06/20) One-Way ANOVA
• 🔒(25/06/24) Two-Way ANOVA

Nonparametric Statistics

• 🔒(25/07/06) What Is Nonparametric Statistics?
• 🔒(25/07/10) Ranks in Statistics
  • 🔒(25/07/26) Mean and Variance of Ranks in Statistics
• 🔒(25/07/14) Mann–Whitney U Test
• 🔒(25/07/22) Wilcoxon Signed-Rank Test
  • 🔒(25/07/18) The Sign Test in Statistics
• 🔒(25/08/11) Kruskal–Wallis H Test
• 🔒(25/08/15) Friedman’s $F_r$ Test
• 🔒(25/08/19) Spearman’s Rank Correlation Coefficient $r$

Senior

Distribution Tests

• 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
• McLeod–Li Test

References

• Mendenhall. (2012). Introduction to Probability and Statistics (13th Edition)
• 경북대학교 통계학과. (2008). 엑셀을 이용한 통계학