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Table of t-values

If a hypothesis is to be tested with the t test, the t value from the calculated test must be compared with the critical t value. The critical t-value can be read from the table below for a selected significance level alpha. Usually the significance level alpha is 0.05. If the calculated chi-squared value is smaller than the critical value, the null hypothesis can be retained.

Probability of error

=

Critical t-Value

=

Table t-value

Area two-tailed
df 00.50.60.70.80.90.950.980.990.9980.999
1 011.3761.9633.0786.31412.7131.8263.66318.31636.62
2 00.8161.0611.3861.8862.924.3036.9659.92522.32731.599
3 00.7650.9781.251.6382.3533.1824.5415.84110.21512.924
4 00.7410.9411.191.5332.1322.7763.7474.6047.1738.61
5 00.7270.921.1561.4762.0152.5713.3654.0325.8936.869
6 00.7180.9061.1341.441.9432.4473.1433.7075.2085.959
7 00.7110.8961.1191.4151.8952.3652.9983.4994.7855.408
8 00.7060.8891.1081.3971.862.3062.8963.3554.5015.041
9 00.7030.8831.11.3831.8332.2622.8213.254.2974.781
10 00.70.8791.0931.3721.8122.2282.7643.1694.1444.587
11 00.6970.8761.0881.3631.7962.2012.7183.1064.0254.437
12 00.6950.8731.0831.3561.7822.1792.6813.0553.934.318
13 00.6940.871.0791.351.7712.162.653.0123.8524.221
14 00.6920.8681.0761.3451.7612.1452.6242.9773.7874.14
15 00.6910.8661.0741.3411.7532.1312.6022.9473.7334.073
16 00.690.8651.0711.3371.7462.122.5832.9213.6864.015
17 00.6890.8631.0691.3331.742.112.5672.8983.6463.965
18 00.6880.8621.0671.331.7342.1012.5522.8783.613.922
19 00.6880.8611.0661.3281.7292.0932.5392.8613.5793.883
20 00.6870.861.0641.3251.7252.0862.5282.8453.5523.85
21 00.6860.8591.0631.3231.7212.082.5182.8313.5273.819
22 00.6860.8581.0611.3211.7172.0742.5082.8193.5053.792
23 00.6850.8581.061.3191.7142.0692.52.8073.4853.768
24 00.6850.8571.0591.3181.7112.0642.4922.7973.4673.745
25 00.6840.8561.0581.3161.7082.062.4852.7873.453.725
26 00.6840.8561.0581.3151.7062.0562.4792.7793.4353.707
27 00.6840.8551.0571.3141.7032.0522.4732.7713.4213.69
28 00.6830.8551.0561.3131.7012.0482.4672.7633.4083.674
29 00.6830.8541.0551.3111.6992.0452.4622.7563.3963.659
30 00.6830.8541.0551.311.6972.0422.4572.753.3853.646
40 00.6810.8511.051.3031.6842.0212.4232.7043.3073.551
60 00.6790.8481.0451.2961.67122.392.663.2323.46
80 00.6780.8461.0431.2921.6641.992.3742.6393.1953.416
100 00.6770.8451.0421.291.661.9842.3642.6263.1743.39
1000 00.6750.8421.0371.2821.6461.9622.332.5813.0983.3

Calculate t-value

The t-distribution results from a combination of a random variable X with chi-squared distribution and a random variable Y with standard normal distribution to

t-Distribution Formula

where Y and X are independent and n is the number of degrees of freedom

t-distribution table: The desired critical t-values ​​can be read from the above table of the t-distribution. In the case of a directional hypothesis, the area is read off at the 1-alpha point; in the case of a non-directional hypothesis, the area is read off at 1-alpha / 2.

This means that the critical t-value can be read from the t-test table above and can thus determine whether the null hypothesis is retained or rejected. This means that a hypothesis test can be calculated with the t-test table without statistical software.


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Cite DATAtab: DATAtab Team (2024). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net

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