t-table

Percent Confidence Limit

d.f.

80

90

95

99

99.9

1

3.078

6.314

12.706

63.656

636.578

2

1.886

2.920

4.303

9.925

31.600

3

1.638

2.353

3.182

5.841

12.924

4

1.533

2.132

2.776

4.604

8.610

5

1.476

2.015

2.571

4.032

6.869

6

1.440

1.943

2.447

3.707

5.959

7

1.415

1.895

2.365

3.499

5.408

8

1.397

1.860

2.306

3.355

5.041

9

1.383

1.833

2.262

3.250

4.781

10

1.372

1.812

2.228

3.169

4.587

20

1.325

1.725

2.086

2.845

3.850

50

1.299

1.676

2.009

2.678

3.496

100

1.290

1.660

1.984

2.626

3.390

1000

1.282

1.646

1.962

2.581

3.300

10000

1.282

1.645

1.960

2.576

3.291

• With a set of N measurements, for which you have computed a mean value, the d.f. will be N-1.
• With two sets of data having N1 and N2 measurements respectively, and two mean values, and a pooled standard deviation, the d.f. are N1+N2-2.
• With a set of N (x,y) data points lying in a straight line, for which you have computed a slope and an intercept, d.f.=N-2.
• The t-value tells you how many standard deviations of distance are required between two values before they can be declared "significantly different" at the given confidence level. If the sample standard deviation is computed only from the N data on hand, use the appropriate d.f. and confidence level to find t. If the value of the standard deviation is computed from a long historical record of many analyses, then it is said that "s approaches sigma" and you use the t-value at the bottom of the table, usually labeled as "infinite" d.f. (In the table above it is labeled 10,000 d.f. from an actual Excel calculation using the TINV() function.)