Student t Distribution Table

Bell shaped curves could be from a standard normal distribtion or a t-distribution.
The blue region represents two tails of the normal distribution. C.K.Taylor

This table below is a compilation of data from the Student t distribution. Anytime that a t-distribution is being used, a table such as this one can be consulted to perform calculations. This distribution is similar to the standard normal distribution, or bell curve, however the table is arranged differently than the table for the bell curve. The table below provides critical t-values for a particular area of one tail (listed along the top of the table) and degrees of freedom (listed along the side of the table).

Degrees of freedom range from 1 to 30, with the bottom row of "Large" referring to several thousand degrees of freedom.

Example of Using the Table

A brief example will illustrate the use of the table below.  Suppose that we have a simple random sample of size 11.  This means that we will consult the row with 11 - 1 = 10 degrees of freedom.  Along the top of the table we have various levels of significance.  Suppose that we have a level of significance of 1%.  This corresponds to 0.01.  This column in the row with 10 degrees of freedom gives us a critical value of 2.76377.

This means that in order to reject the null hypothesis, we need a t-statistic that exceeds this value of 2.76377.  Otherwise we will fail to reject the null hypothesis.

Table of Critical Values for t Distribution

 

t0.400.250.100.050.0250.010.0050.0005
10.3249201.0000003.0776846.31375212.7062031.8205263.65674636.6192
20.2886750.8164971.8856182.9199864.302656.964569.9248431.5991
30.2766710.7648921.6377442.3533633.182454.540705.8409112.9240
40.2707220.7406971.5332062.1318472.776453.746954.604098.6103
50.2671810.7266871.4758842.0150482.570583.364934.032146.8688
60.2648350.7175581.4397561.9431802.446913.142673.707435.9588
70.2631670.7111421.4149241.8945792.364622.997953.499485.4079
80.2619210.7063871.3968151.8595482.306002.896463.355395.0413
90.2609550.7027221.3830291.8331132.262162.821443.249844.7809
100.2601850.6998121.3721841.8124612.228142.763773.169274.5869
110.2595560.6974451.3634301.7958852.200992.718083.105814.4370
120.2590330.6954831.3562171.7822882.178812.681003.054544.3178
130.2585910.6938291.3501711.7709332.160372.650313.012284.2208
140.2582130.6924171.3450301.7613102.144792.624492.976844.1405
150.2578850.6911971.3406061.7530502.131452.602482.946714.0728
160.2575990.6901321.3367571.7458842.119912.583492.920784.0150
170.2573470.6891951.3333791.7396072.109822.566932.898233.9651
180.2571230.6883641.3303911.7340642.100922.552382.878443.9216
190.2569230.6876211.3277281.7291332.093022.539482.860933.8834
200.2567430.6869541.3253411.7247182.085962.527982.845343.8495
210.2565800.6863521.3231881.7207432.079612.517652.831363.8193
220.2564320.6858051.3212371.7171442.073872.508322.818763.7921
230.2562970.6853061.3194601.7138722.068662.499872.807343.7676
240.2561730.6848501.3178361.7108822.063902.492162.796943.7454
250.2560600.6844301.3163451.7081412.059542.485112.787443.7251
260.2559550.6840431.3149721.7056182.055532.478632.778713.7066
270.2558580.6836851.3137031.7032882.051832.472662.770683.6896
280.2557680.6833531.3125271.7011312.048412.467142.763263.6739
290.2556840.6830441.3114341.6991272.045232.462022.756393.6594
300.2556050.6827561.3104151.6972612.042272.457262.750003.6460
Large0.2533470.6744901.2815521.6448541.959962.326352.575833.2905
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Your Citation
Taylor, Courtney. "Student t Distribution Table." ThoughtCo, May. 9, 2016, thoughtco.com/student-t-distribution-table-3126265. Taylor, Courtney. (2016, May 9). Student t Distribution Table. Retrieved from https://www.thoughtco.com/student-t-distribution-table-3126265 Taylor, Courtney. "Student t Distribution Table." ThoughtCo. https://www.thoughtco.com/student-t-distribution-table-3126265 (accessed May 23, 2018).