T Critical Value Calculator (t Table Calculator) (2024)

Select the type of probability, enter the degree of freedom and significance level to calculate t value using our t value calculator.

Critical Value Calculator

T critical value calculator is an online statistical tool that calculates the t value for one-tailed and two-tailed probability. Moreover, the critical values calculator also shows the mapped t-value in the student t-distribution table for one sample and two samples.

What is the t value?

T value measures the size of the difference relative to the variation in sample data. It is basically the calculated difference represented in units of standard error.

  • If the t value is greater, there is evidence of a significant difference.
  • If the t-value is closer to 0, there are chances of no significant difference.

Right-Tailed T Critical Value

T Critical Value Calculator (t Table Calculator) (1)

Left-Tailed T Critical Value

T Critical Value Calculator (t Table Calculator) (2)

Two-Tailed T Critical Value

T Critical Value Calculator (t Table Calculator) (3)

T critical value formula

The formulas of t critical valuefor left, right, and two-tailed values are:

Name of TypeFormula of t critical value
Right-tailedQt,d(1 - α)
Left-tailedQt,d (α)
Two-tailed±Qt,d(1 - α/2)

How to find the critical value of t?

To calculate thet critical value manually (without using thet calculator), follow the example below.

Example:

Calculate the critical t value (one tail and two tails) for a significance level of 5% and 30 degrees of freedom.

Solution:

Step 1: Identify the values.

Significance level = 5% = 5/100 = 0.05

Degree of freedom = 30

Step 2: Look for the significance level in the top row of the t distribution table below (one tail) and degree of freedom (df) on the left side of the table. Get the corresponding value from a table.

T critical value (one-tailed) = 1.6978

Step 3: Repeat the above step but use the two-tailed t table below for two-tailed probability.

T critical value (two-tailed +/-) = 2.0428

Use our t table calculator above to quickly get t table values.

How to Calculate the T-Critical Value for a One-Tailed Distribution Table?

To calculate the T-critical value by one-tail t-distribution table, we have a proper significance level and degrees of freedom of the experimental data. Follow the below step to find its value.

  • First, take the one-tailed table, and the level of significance for one tail is written at the top of the table.

  • Choose the column from the table that contains the respective level of significance.

  • Then find the row for the degrees of freedom that match with your experimental data.

  • Finally, note the intersection value of the column and the rows from the table. That is the required T-critical value of your data or place is positive for the right-tailed test & negative for left left-tailed test.

To overcome this long process use our above T Critical Value calculator that provides answers in minor seconds.

T Distribution Table (One Tail)

The t table for one-tailed probability is given below.

DFA = 0.10.050.0250.010.0050.0010.0005
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

How to Calculate the T-Critical Value for a Two-Tailed Distribution Table?

Calculating the T-critical value for the two-tailed t-test by the t-distribution table, we required the value significance level and degrees of freedom of the given data to determine the value from a table. Follow the below step to find its value.

  • First, take the two-tailed table, and the level of significance is properly mentioned at the top of the table.

  • Choose the column from the t-distribution table that contains the significance level of your data.

  • Then find the row with respect to the degrees of freedom of your data in the selecting column of your level of significance.

  • Then the intersection value of the level of significance in the column and the degrees of freedom in the row is the required T-critical value of your data.

To verify the answer to your data, use the above T-Critical Value calculator.

T Distribution Table (Two Tail)

Here is the t table for two-tailed probability.

DFA = 0.20.100.050.020.010.0020.001
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
1.2821.6451.9602.3262.5763.0913.291

Frequently Asked Questions About T Critical Values

What is the Critical Value?

Critical value is found in the statistics for the analysis of the data of any experiment that helps us for the testing of the hypothesis and tells us whether the null hypothesis should be rejected or not.

What are the Different Types of Critical Value?

There are four different types of critical values depending on the distribution or test used for the analysis of data and also the sample size/ population size of data. These names and distribution are given below:

  • T-critical value (Student t-distribution used in T-test)
  • Z-critical value (Normal distribution used to find this value)
  • Chi-square value (Chi-squared distribution used to find this value)
  • F-critical value (F-distribution used for this value)

What is the difference between T-test & Z-test?

T-test & Z-test, both are parametric statistical tests that are used to measure the interval scale and find the different critical values according to the size of the sample by using t-distribution and normal distribution. T-test is applied if the sample size is smaller than n<30 while Z-test is applied if the sample size is larger than n>30.

Can a T-Critical Value be Negative?

Yes, the t-critical value is negative if the left-tailed test is conducted to find its value and the value is placed along the left side of the mean in the graphical distribution. i.e., if the critical value is -1.5 then is placed to the left side of the mean while if it’s positive “1.5” then placed to the right of the mean.

T Critical Value Calculator (t Table Calculator) (2024)

FAQs

How do you find the T critical value on a TI 84? ›

The t-critical value is under the “stat” button. Press “2nd+vars” to get the stat apps and then look for “invT(”. The input format is: “invT(p-value, degrees_of_freedom)”. Example would be invT(0.05, 6) for 5% confidence level and 6 degrees of freedom.

What is the critical t-value calculator? ›

The t critical value calculator calculates the critical value for the t statistic, choose the Student's t distribution and enter the degrees of freedom (n - 1).

How to determine critical value? ›

Determine the critical value by finding the value of the known distribution of the test statistic such that the probability of making a Type I error — which is denoted (greek letter "alpha") and is called the "significance level of the test" — is small (typically 0.01, 0.05, or 0.10).

What is the t-critical value at a .05 level of significance? ›

The most commonly used significance level is α = 0.05. For a two-sided test, we compute 1 - α/2, or 1 - 0.05/2 = 0.975 when α = 0.05. If the absolute value of the test statistic is greater than the critical value (0.975), then we reject the null hypothesis.

How to find the critical value of a function? ›

To find any critical numbers of a function, simply take its derivative, set it equal to zero, and solve for x. Any x values that make the derivative zero are critical numbers. Moreover, any x values that make the derivative undefined are also critical numbers.

How to find the critical value of t in Excel? ›

You can use the T. INV() function to find the critical value of t for one-tailed tests in Excel, and you can use the T. INV. 2T() function for two-tailed tests.

What is the critical value for a 95 confidence interval? ›

The critical value for a 95% confidence interval is 1.96, where (1-0.95)/2 = 0.025.

How do you solve for the t-value? ›

The t-score formula is: t = x ― − μ S n , where x ― is the sample mean, μ is the population mean, S is the standard deviation of the sample, and n is the sample size.

Is the t-value always positive? ›

Therefore t can be negative. Depending on the degree-of-freedom, t = -14 is very likely to correspond with a decision to reject the null hypothesis of equality of the two means for the alternative hypothesis.

What is the Z value for critical value? ›

Critical value (z*) for a given confidence level. If we want to be 95% confident, we need to build a confidence interval that extends about 2 standard errors above and below our estimate. More precisely, it's actually 1.96 standard errors. This is called a critical value (z*).

What is a critical value in calculus? ›

The critical values of a function are the values of the function at the critical points. For example, if (c, f(c)) is a critical point of y = f(x) then f(c) is called the critical value of the function corresponding to the critical point (c, f(c)).

What is the 95% critical value for T? ›

Student's T Critical Values
Conf. Level50%95%
One Tail0.2500.025
20.8164.303
30.7653.182
40.7412.776
36 more rows

How do you find the T crit in Excel? ›

You can use the T. INV() function to find the critical value of t for one-tailed tests in Excel, and you can use the T. INV. 2T() function for two-tailed tests.

How to calculate t statistic? ›

To calculate t-statistic:
  1. Determine the sample mean ( x̄ , x bar), which is the arithmetic mean of your data set.
  2. Find the population mean ( μ , mu).
  3. Compute the sample standard deviation ( s ) by taking the square root of the variance. ...
  4. Calculate the t-statistic as (x̄ - μ) / (s / √n) , where n denotes the sample size.
Jul 29, 2024

What are the critical values for a two-tailed t-test when a 0.02 and n=19? ›

Final Answer

The critical value for a two-tailed t-test when α = 0.02 and n = 19 is 2.878.

References

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