How to Read a T Table
A t table has one more dimension than a z table — degrees of freedom — and one trap the z table never sets: its columns are one-tailed areas, so two-tailed work reads the α/2 column. Master those two facts and the table is yours.
The routine: (1) Compute df = n − 1 and find its row. (2) Decide one- or two-tailed; for two-tailed at level α, use the α/2 column (0.025 for a 0.05 test). (3) Read the cell: that is the critical t value your statistic must exceed, or the multiplier in a confidence interval.
A confidence interval, read properly
Sample of n = 16 (df = 15), x̄ = 52, s = 10, 95% confidence. The interval is x̄ ± t* × s/√n. Row 15 of the t distribution table, column 0.025 (because 95% two-sided leaves 0.025 in each tail): t* = 2.131. Standard error = 10/4 = 2.5, margin = 2.131 × 2.5 = 5.33, interval (46.67, 57.33). Compare the z shortcut (1.96): margin 4.90, interval (47.10, 56.90) — narrower, and dishonestly so, because with n = 16 the estimate s wobbles enough to matter. The t table's whole purpose is printed in that difference. As df climbs the rows — 2.042 at 30, 2.000 at 60, 1.980 at 120 — the t column melts into the z value 1.960, visible in the table's ∞ row.
A hypothesis test, read properly
One-tailed test at α = 0.05, df = 10, statistic t = 1.90. This time the column is 0.05 itself (one tail, no halving): critical value 1.812. The statistic exceeds it — significant at 0.05, one-tailed. Had the identical data been run two-tailed, the column would be 0.025, the critical value 2.228, and the verdict would flip. That sensitivity is exactly why the tail choice belongs to the design, not the results — a theme the p-value page develops for the z case. If your df is missing from a printed table, take the next smaller df row: its critical value is slightly larger, which is the conservative direction, and the convention examiners expect.
Bracketing a p-value from the table
Printed t tables also bound p-values, which is how results were reported for a century. A statistic of t = 2.50 at df = 10 falls between the 0.025 column (2.228) and the 0.01 column (2.764). Those columns are one-tailed areas; doubling for a two-tailed test, the p-value lies between 0.02 and 0.05 — and software confirms p ≈ 0.031, inside the bracket. Reporting "0.02 < p < 0.05" from a table is not a failure of precision; it is the table being used exactly as designed, and it forces the healthy habit of treating p as a range of evidence rather than a sacred point.
Related questions
Frequently asked questions
Why does the t table need degrees of freedom when the z table doesn't?
Because the t distribution's shape depends on how much data estimated σ. Small samples → heavy tails → a family of curves, one per df. The z table is the limiting member of that family (df = ∞), which is why it needs no row choice. See z table vs t table for the full comparison.
What if my test statistic falls between two columns?
Then the p-value falls between the two column levels, and you report it bracketed: "0.02 < p < 0.05". Printed tables bound p-values; software gives exact ones. Bracketing honestly is a complete answer in exam settings.
Also asked as: how to read t table · how to use a t table · how to read the t distribution table · t table reading.