manual-calculation

Tables give the critical values we compare our test statistic against.
They depend on:

• The significance level (α, often 0.05)
• The degrees of freedom (df)

t-table

• Rows = degrees of freedom (df)
• Columns = significance level (α)

Example:

• Independent-samples t-test with n₁ = 12, n₂ = 12
• df = 12 + 12 – 2 = 22
• At α = 0.05 (two-tailed) → critical t ≈ 2.07
• If $$|t| \geq 2.07$$ → significant

F-table

• Needs two df values:
  • df between (numerator)
  • df within (denominator)

Example:

• One-way ANOVA, 3 groups, N = 24
• df between = k – 1 = 2
• df within = N – k = 21
• At α = 0.05 → critical F ≈ 3.47
• If computed F ≥ 3.47 → significant

Student Tips

• Always compute df correctly.
• Use tables if no software is available.
• Most calculators or apps today give exact p-values — faster than tables.

📱 QR: Interactive critical value calculator (t and F tables online)

Visuals

Figure C.1 — Snippet of a t-table row (df = 22, α = 0.05 highlighted).
Figure C.2 — F-table grid with numerator df = 2, denominator df = 21 marked.

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