T Table - T Distribution (Score, Chart)

T Table contains the critical values of the T Distribution. The column contains all the T-Distribution probabilities denoted by "Alpha" or "p". The row contains all the degrees of freedom denoted by "df". Also, here you will get one and two tail T score tables or charts online.

T Table
cum. probt.50t.75t.80t.85t.90t.95t.975t.99t.995t.999t.9995
one-tail0.500.250.200.150.100.050.0250.010.0050.0010.0005
two-tails1.000.500.400.300.200.100.050.020.010.0020.001
df/p(α)
10.0001.0001.3761.9633.0786.31412.7131.8263.66318.31636.62
20.0000.8161.0611.3861.8862.9204.3036.9659.92522.32731.599
30.0000.7650.9781.2501.6382.3533.1824.5415.84110.21512.924
40.0000.7410.9411.1901.5332.1322.7763.7474.6047.1738.610
50.0000.7270.9201.1561.4762.0152.5713.3654.0325.8936.869
60.0000.7180.9061.1341.4401.9432.4473.1433.7075.2085.959
70.0000.7110.8961.1191.4151.8952.3652.9983.4994.7855.408
80.0000.7060.8891.1081.3971.8602.3062.8963.3554.5015.041
90.0000.7030.8831.1001.3831.8332.2622.8213.2504.2974.781
100.0000.7000.8791.0931.3721.8122.2282.7643.1694.1444.587
110.0000.6970.8761.0881.3631.7962.2012.7183.1064.0254.437
120.0000.6950.8731.0831.3561.7822.1792.6813.0553.9304.318
130.0000.6940.8701.0791.3501.7712.1602.6503.0123.8524.221
140.0000.6920.8681.0761.3451.7612.1452.6242.9773.7874.140
150.0000.6910.8661.0741.3411.7532.1312.6022.9473.7334.073
160.0000.6900.8651.0711.3371.7462.1202.5832.9213.6864.015
170.0000.6890.8631.0691.3331.7402.1102.5672.8983.6463.965
180.0000.6880.8621.0671.3301.7342.1012.5522.8783.6103.922
190.0000.6880.8611.0661.3281.7292.0932.5392.8613.5793.883
200.0000.6870.8601.0641.3251.7252.0862.5282.8453.5523.850
210.0000.6860.8591.0631.3231.7212.0802.5182.8313.5273.819
220.0000.6860.8581.0611.3211.7172.0742.5082.8193.5053.792
230.0000.6850.8581.0601.3191.7142.0692.5002.8073.4853.768
240.0000.6850.8571.0591.3181.7112.0642.4922.7973.4673.745
250.0000.6840.8561.0581.3161.7082.0602.4852.7873.4503.725
260.0000.6840.8561.0581.3151.7062.0562.4792.7793.4353.707
270.0000.6840.8551.0571.3141.7032.0522.4732.7713.4213.690
280.0000.6830.8551.0561.3131.7012.0482.4672.7633.4083.674
290.0000.6830.8541.0551.3111.6992.0452.4622.7563.3963.659
300.0000.6830.8541.0551.3101.6972.0422.4572.7503.3853.646
400.0000.6810.8511.0501.3031.6842.0212.4232.7043.3073.551
600.0000.6790.8481.0451.2961.6712.0002.3902.6603.2323.460
800.0000.6780.8461.0431.2921.6641.9902.3742.6393.1953.416
1000.0000.6770.8451.0421.2901.6601.9842.3642.6263.1743.390
10000.0000.6750.8421.0371.2821.6461.9622.3302.5813.0983.300
Z0.0000.6740.8421.0361.2821.6451.9602.3262.5763.0903.291
 0%50%60%70%80%90%95%98%99%99.8%99.9%
Confidence Level

Statistical Concept of T Table or T Distribution

Let's understand the concept of T distribution with an example. Suppose a sample space containing n observations from a normally distributed population. Then the Standard Normal Distribution:

Z = Standard Normal Distribution

This concept failed in real because we are mostly unaware of the value of population standard deviation (σ). It is a parameter for the standard deviation of the entire population. However, we don't know its value so we can't put it in the formula.

The best solution for the above problem will be to use the Sample Standard Deviation rather than using the Population SD.

Therefore, now the formula becomes:

T = T distribution Formula

Here "s" is the Sample Standard Deviation. The value of σ was constant and the value of s varies sample to sample. Hence, the Sample Standard Deviation will also vary sample to sample. Consequently, the whole quantity will have different values. Hence, we label this equation as T distribution.

The T distribution has (n - 1) degrees of freedom. In addition, when the degrees of freedom rise, the T distribution inclines towards the standard normal distribution.

Types of T Distribution Tables

In statistics, you will find two types of T table. The main difference between both the tables is in the number of ends of the distribution of sample statistic. The number of ends is known as tails.

Depending upon the number of tails, there are two types of T Distribution tables:

  1. One-tailed
  2. Two-tailed

The difference can be understood by seeing the graph below.

1. One-tailed T distribution
One-tailed T distribution table One-tailed t score table
2. Two-tailed T distribution
two-tailed T-table Two-tailed t chart

Uses of T Score Table

The most ideal case to use the T Score Table or implement the T distribution is when the sample size is small. Otherwise, the graph looks almost the same as normal. Hence, it's recommended to be used with a small sample space.

How to use the T Chart?

Till now, we have known about what is T table, its equation, types, and use. Now, let's learn how to calculate the score from the T chart. Here I have tried to explain the calculation process very easily. It's just two steps that you need to follow.

First Step

Find 'Degrees of Freedom'. The degrees of freedom can be easily estimated using the below formula.

DF = n - 1

Subtracting one from the sample size(n) ultimately gives you the degrees of freedom(DF).

So, if we take the n = 6, then the DF = 6 – 1 = 5.

Second Step

Now, you have the DF value. The next step is to locate it on the one-tailed or two-tailed charts. Usually, the left-hand side has degrees of freedom. After that, look for the alpha(α) value. The result is at the intersection of row and column of your DF and alpha value respectively.

Still, confused? Let's make it more simple with an example of a T-Distribution calculation. In this example, we will use a one-tailed T-table.

Example

Let's take,

Degree of freedom = 7
Alpha(α) Value = 0.025

Example

Look for the DF = 7 on the left-hand side of the table. Simultaneously, look for alpha(α) value = 0.025 on the top side of the table. You will find that 2.365 is the value present in between this row and column.

Finally, you can use the DF and alpha values to determine the probabilities for T-Distribution values from T table.