T-Test in Parametric Tests (with Finance Examples)

 The t-test is a parametric statistical test used to determine whether there is a significant difference between the means of two groups, assuming the data follows a normal distribution and the population variance is unknown.

 Types of t-tests:

Type

Purpose

Example in Finance

One-sample t-test

Compares sample mean to a known value

Test if the average return of a mutual fund is significantly different from the market’s average return (e.g., Nifty 50 annual return of 12%).

Two-sample independent t-test

Compares means of two independent groups

Compare the average returns of two different portfolios (e.g., a growth fund vs. a value fund).

Paired-sample t-test

Compares means from the same group at different times

Compare a company's stock return before and after a major policy change or merger.

 Example 1: One-Sample t-test in Finance

Problem:
A financial analyst wants to test if the average return of a new mutual fund is significantly different from the market average of 10% per year.

  • Sample mean return = 12%
  • Population mean = 10%
  • Sample size = 30
  • Standard deviation = 4%

Hypotheses:

  • H₀ (Null): μ = 10%
  • H₁ (Alternative): μ ≠ 10%

T-statistic formula:

 


Compare this t-value with the critical value from the t-distribution table (with df = 29) to decide whether to reject H₀.

 Example 2: Two-Sample t-test in Finance

Problem:
Compare the average monthly returns of two stock portfolios over a 12-month period.

  • Portfolio A average return: 8%, SD = 2%
  • Portfolio B average return: 10%, SD = 3%
  • Sample size = 12 (each)

Hypotheses:

  • H₀: μ₁ = μ₂ (no difference)
  • H₁: μ₁ ≠ μ₂ (there is a difference)

Apply the independent two-sample t-test formula:

 


You’ll calculate the t-value and compare it against the critical t-value at a chosen significance level (e.g., 0.05).

🔍 When to Use a t-Test in Finance

  • Comparing pre- and post-event returns (mergers, earnings announcements, RBI policy decisions).
  • Evaluating fund performance vs. benchmarks.
  • Checking if a trading strategy generates returns significantly different from zero.

📌 Assumptions of t-Test (Parametric Nature)

  • The data is continuous and approximately normally distributed.
  • Scale-level measurement (interval or ratio).
  • Homogeneity of variance (especially in two-sample tests).
  • Independent observations (except in paired t-tests).

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