Statistics Reference

T-Table for α = 0.10 (t Critical Values)

Student's t critical values at the lenient 0.10 level for every degree of freedom from 1 to 100 (plus the large-sample tail). The one-tail column serves 10% directional tests; the two-tail column serves 10% non-directional tests and 90% confidence intervals.

How to Read This Table

Rows are degrees of freedom — every integer from 1 to 100, then 120, 150, 200, 500, and 1000, finer than the stepped rows of the main table. The one-tail column puts all of α = 0.10 in a single tail (directional tests); the two-tail column splits it across both tails (non-directional tests and confidence intervals). The distribution is symmetric, so lower-tail tests use the negative of the printed value.

90% confidence interval from a sample of 16 (df = 15):

  1. Row df = 15, two-tail column: 1.753.
  2. Interval: sample mean ± 1.753 standard errors.
  3. The one-tail column's 1.341 would instead serve a directional test at 10%.

Common uses of this level:

  • 90% confidence intervals for a mean (two-tail column)
  • Screening-level directional t-tests at α = 0.10 (one-tail column)
  • Sample-size sketches where a wider interval is acceptable

t Critical Values, α = 0.10, df 1–1000

Student's t critical values at significance level 0.1 for degrees of freedom 1 to 1000
dfOne-tail α = 0.1Two-tail α = 0.1
13.0786.314
21.8862.920
31.6382.353
41.5332.132
51.4762.015
61.4401.943
71.4151.895
81.3971.860
91.3831.833
101.3721.812
111.3631.796
121.3561.782
131.3501.771
141.3451.761
151.3411.753
161.3371.746
171.3331.740
181.3301.734
191.3281.729
201.3251.725
211.3231.721
221.3211.717
231.3191.714
241.3181.711
251.3161.708
261.3151.706
271.3141.703
281.3131.701
291.3111.699
301.3101.697
311.3091.696
321.3091.694
331.3081.692
341.3071.691
351.3061.690
361.3061.688
371.3051.687
381.3041.686
391.3041.685
401.3031.684
411.3031.683
421.3021.682
431.3021.681
441.3011.680
451.3011.679
461.3001.679
471.3001.678
481.2991.677
491.2991.677
501.2991.676
511.2981.675
521.2981.675
531.2981.674
541.2971.674
551.2971.673
561.2971.673
571.2971.672
581.2961.672
591.2961.671
601.2961.671
611.2961.670
621.2951.670
631.2951.669
641.2951.669
651.2951.669
661.2951.668
671.2941.668
681.2941.668
691.2941.667
701.2941.667
711.2941.667
721.2931.666
731.2931.666
741.2931.666
751.2931.665
761.2931.665
771.2931.665
781.2921.665
791.2921.664
801.2921.664
811.2921.664
821.2921.664
831.2921.663
841.2921.663
851.2921.663
861.2911.663
871.2911.663
881.2911.662
891.2911.662
901.2911.662
911.2911.662
921.2911.662
931.2911.661
941.2911.661
951.2911.661
961.2901.661
971.2901.661
981.2901.661
991.2901.660
1001.2901.660
1201.2891.658
1501.2871.655
2001.2861.653
5001.2831.648
10001.2821.646

Other Significance Levels

The t-table overview carries the classic multi-column grid, degrees-of-freedom rules, and the z-convergence walkthrough. The other levels each have a dedicated page:

Frequently Asked Questions

When is the α = 0.10 t-table appropriate?

For 90% confidence intervals - common in engineering tolerance work and early-stage research - and for screening tests where missing a real effect costs more than a false alarm. Results at this level invite confirmation at a stricter one rather than final conclusions.

Why does this page show both a one-tail and a two-tail column?

Because 'α = 0.10' means different cutoffs depending on the test's direction. A directional test puts all 10% in one tail (smaller critical value); a non-directional test splits it 5%/5% (larger value). At df = 15 they read 1.341 and 1.753 - using the wrong column doubles or halves your intended false-alarm rate.

How do these values relate to the z-table?

As degrees of freedom grow, both columns converge to the z critical values: the one-tail column approaches 1.282 and the two-tail column 1.645. By df = 1000 the table reads within 0.002 of those limits - the visible reason 'use z for large samples' works as a shortcut.

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