# T Table: Understand the probabilities with various distribution degrees

## What is T-Table?

T-Score table Calculator involves the inclusion of critical values, also known as percentiles, for proper calculation of t-distribution series. The table houses a column headed as df or degrees of freedom that adds value to each row in the table. The column part of the t-table score calculator is labelled as “Percent”, “Two-Sided”, and “One-Sided”. The percent here is the distribution function which is calculated from 100X the cumulative of the said distribution function.

## Uses of T-Distribution Table

T-table is generally used in testing of several hypotheses. This helps is figuring out the fact that you need to accept/reject the null hypothesis.

T-Distribution or T-Value table is the type of probability distribution that is continuous with random values at the real line. The major properties of the t-statistic calculator include.

1. The t-distribution statistic is continuous due to which the probability for acquiring any single or specific outcome is zero.
2. It is similar to normal curves with bell shape.
3. The value is efficiently determined by 1 parameter which is “df” or “Degrees of Freedom”. For example, 1 sample has df= n-1, which is zero and here n is the sample size.
4. The t-score table is symmetric with regards to 0.
5. T-distribution efficiently “converges” towards the standard type of normal distribution given the fact that df here converges towards infinity.

## What does each entry in the T-Table mean ?

The entries in the t-distribution table are corresponding percentile for the t-distribution. The one-sided entry is used to describe the significance for the level for one-sided upper aligned critical value. The Two-sided entry gives a significance level for two-sided value.

## How should one use T-value calculator with t-table?

When described in general terms, the two-tailed case with critical value corresponds to 2 point towards the left & right for the distribution center. This houses the sum property of cumulative under curve for left tail and area under curve in right tail equals the given level of significance α.

## T-Distribution Table (One Tail and Two-Tails)

### T-Distribution Table (One Tail)

ta = 1.2821.6451.9602.3262.5763.0913.291
13.0786.31412.70631.82163.656318.289636.578
21.8862.9204.3036.9659.92522.32831.600
31.6382.3533.1824.5415.84110.21412.924
41.5332.1322.7763.7474.6047.1738.610
51.4762.0152.5713.3654.0325.8946.869
61.4401.9432.4473.1433.7075.2085.959
71.4151.8952.3652.9983.4994.7855.408
81.3971.8602.3062.8963.3554.5015.041
91.3831.8332.2622.8213.2504.2974.781
101.3721.8122.2282.7643.1694.1444.587
111.3631.7962.2012.7183.1064.0254.437
121.3561.7822.1792.6813.0553.9304.318
131.3501.7712.1602.6503.0123.8524.221
141.3451.7612.1452.6242.9773.7874.140
151.3411.7532.1312.6022.9473.7334.073
161.3371.7462.1202.5832.9213.6864.015
171.3331.7402.1102.5672.8983.6463.965
181.3301.7342.1012.5522.8783.6103.922
191.3281.7292.0932.5392.8613.5793.883
201.3251.7252.0862.5282.8453.5523.850
211.3231.7212.0802.5182.8313.5273.819
221.3211.7172.0742.5082.8193.5053.792
231.3191.7142.0692.5002.8073.4853.768
241.3181.7112.0642.4922.7973.4673.745
251.3161.7082.0602.4852.7873.4503.725
261.3151.7062.0562.4792.7793.4353.707
271.3141.7032.0522.4732.7713.4213.689
281.3131.7012.0482.4672.7633.4083.674
291.3111.6992.0452.4622.7563.3963.660
301.3101.6972.0422.4572.7503.3853.646
601.2961.6712.0002.3902.6603.2323.460
1201.2891.6581.9802.3582.6173.1603.373
10001.2821.6461.9622.3302.5813.0983.300

### Two Tails T Distribution Table

 ∞ ta = 1.282 1.645 1.96 2.326 2.576 3.091 3.291 1 3.078 6.314 12.706 31.821 63.656 318.289 636.578 2 1.886 2.92 4.303 6.965 9.925 22.328 31.6 3 1.638 2.353 3.182 4.541 5.841 10.214 12.924 4 1.533 2.132 2.776 3.747 4.604 7.173 8.61 5 1.476 2.015 2.571 3.365 4.032 5.894 6.869 6 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 1.397 1.86 2.306 2.896 3.355 4.501 5.041 9 1.383 1.833 2.262 2.821 3.25 4.297 4.781 10 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 1.356 1.782 2.179 2.681 3.055 3.93 4.318 13 1.350 1.771 2.16 2.65 3.012 3.852 4.221 14 1.345 1.761 2.145 2.624 2.977 3.787 4.14 15 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 1.337 1.746 2.12 2.583 2.921 3.686 4.015 17 1.333 1.74 2.11 2.567 2.898 3.646 3.965 18 1.330 1.734 2.101 2.552 2.878 3.61 3.922 19 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 1.325 1.725 2.086 2.528 2.845 3.552 3.85 21 1.323 1.721 2.08 2.518 2.831 3.527 3.819 22 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 1.319 1.714 2.069 2.5 2.807 3.485 3.768 24 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 1.316 1.708 2.06 2.485 2.787 3.45 3.725 26 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 1.314 1.703 2.052 2.473 2.771 3.421 3.689 28 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 1.311 1.699 2.045 2.462 2.756 3.396 3.66 30 1.310 1.697 2.042 2.457 2.75 3.385 3.646 60 1.296 1.671 2 2.39 2.66 3.232 3.46 120 1.289 1.658 1.98 2.358 2.617 3.16 3.373 8 1.282 1.645 1.96 2.326 2.576 3.091 3.291

## Z-score and T-score: When should one use the T-score?

As per general thumb rule with regards to the use of t-score, it can be used when the sample is:

• Below a size 30.
• Has unknown standard deviation for the population.
Technically, the z-scores act as a converter for individual scores to the standard form. This conversion allows one to easily compare the different set of data. It is basically based on the knowledge of standard deviation for the population and its mean value.
On the other hand, t-scores also act as the individual score converter into the standard form. However, the t-scores can easily be used when the students doesn’t know the standard deviation in the population.

## How should one use the T-value calculator with t-table?

When described in general terms, the two-tailed case with critical value corresponds to 2 points towards the left & right for the distribution centre. This houses the sum property of cumulative under the curve for left tail and area under the curve in right tail equals the given level of significance α.