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Statistics for finance · level 2

t-statistics and significance

Regression output is read with one division. Coefficient over standard error gives t; anything past 2 in absolute value is significant at the usual 5% bar.

Theory: Statistical Inference

Worked example: Coefficient 0.6, standard error 0.25. t-statistic?

coefficient0.6
standard error0.25
t2.4

Step by step

  1. 1

    t is the estimate in standard errors

    0.6 / 0.25 = 2.4

  2. 2

    Rule of two

    |t| > 2 — significant at roughly the 5% level.

  3. 3

    Confidence interval shortcut

    0.6 ± 2 × 0.25

Coefficient 0.6, standard error 0.25. t-statistic? = 2.4

The theory behind it

Intuition

t is estimate divided by standard error: how many error-widths away from zero. Above about 2, the effect is unlikely to be noise.

Common pitfalls

  • ×Treating statistical significance as economic significance.
  • ×Comparing t-stats across models with different sample sizes without care.

In the interview

Deciding whether a driver in an exhibit is real.