关于t检验、F检验适用性及股票组合收益t检验类型选择的技术问询

1. Applicability of t-tests vs F-tests #

Let’s break down when each test is appropriate:

• t-tests: These are focused on comparing means across groups or against a baseline. The three main types are:

  • One-sample t-test: Verify if a sample mean differs from a known population mean.
  • Independent two-sample t-test: Compare means of two separate, unrelated groups (use the standard version if variances are equal, or Welch’s variant if variances are unequal).
  • Paired t-test: Compare means of linked observations (e.g., same time period for two portfolios, or before/after measurements on the same subjects).
    Key assumptions: For small samples, data (or differences, in paired tests) should be roughly normally distributed; large samples rely on the Central Limit Theorem, so normality becomes less critical. Independence is required except for paired tests.

• F-tests: These are most commonly used to compare variances or test overall group differences in ANOVA:

  • Two-sample F-test: Check if two populations have equal variances (requires normality of both samples).
  • ANOVA F-test: Determine if at least one group mean differs significantly from the others (assumes normality, independence, and homogeneity of variances across groups).

2. Choosing Between Paired t-test and Unequal Variance t-test for Stock Portfolio Returns #

Given your setup—monthly returns for two portfolios over the identical 1990-2017 period—the paired t-test is the correct choice, and here’s why:

• Your observations are paired: Each month has a return for Portfolio A and Portfolio B, and these pairs are dependent (they share the same market conditions, economic events, and time-specific risks that month). The paired t-test accounts for this dependency by analyzing the mean of the differences between each monthly pair (A’s return minus B’s return).
• The unequal variance (Welch’s) t-test is designed for independent samples—scenarios where the two groups have no inherent link (e.g., returns from Portfolio A in 1990-2003 vs Portfolio B in 2004-2017). That doesn’t fit your case.
• Bonus: With 336 monthly observations (28 years × 12 months), your sample size is large enough that even if the monthly return differences aren’t perfectly normal, the Central Limit Theorem ensures the t-test will still produce reliable results.

Content of the question is from Stack Exchange, question author: Statistics_query