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# Critical Value Calculator

## How does T critical value calculator work?

• Enter Significance Level(α) In The Input Box.
• Put the Degrees Of Freedom In The Input Box.
• Hit The Calculate Button To Find T Critical Value.
• Use The Reset Button To calculate New Values.

## Other Calculators

Critical T value calculator enables to you to calculate critical value of z and t at one click. You don’t have to look into hundreds of values in t table or a z table because this z critical value calculator calculates critical values in real time.
Keep on reading if you are interested in critical value definition, difference between t and z critical value, and how to calculate critical value of t and z without using critical values calculator.

## What is a critical value?

critical value is a point on the t-distribution that is compared to the test statistic to determine whether to reject the null hypothesis in hypothesis testing. If the absolute value of test statistic is greater than the critical value, statistical significance can be declared as well as null hypothesis can be rejected.

Critical value tests can be:

## What is a t critical value?

T critical value is a point that cuts off the student t distribution. T value is used in a hypothesis test to compare against a calculated t score. The critical value of t helps to decide if a null hypothesis should be supported or rejected.

## What is a z critical value?

Z critical value is a point that cuts off area under the standard normal distribution. Critical value of z can tell what probability any particular variable will have.
Z and t critical values are almost identical.

## What is f critical value?

F critical value is a value at which the threshold probability α of type-I error (reject a true null hypothesis mistakenly).  The f statistics is the value that follows the f-distribution table.

Here are a few tests that help to calculate the f values.

• ANOVA
• Overall significance in regression analysis. k
• Compare two nested regression models.
• The equality of variances in two normally distributed populations.

All the above tests are right-tailed. F critical value calculator above will help you to calculate the f critical value with a single click.

## What is the chi-square value?

In certain hypothesis tests and confidence intervals, chi-square values are thresholds for statistical significance. The Chi-square distribution table is used to evaluate the chi-square critical values. It is rather tough to calculate the critical value by hand, so try a reference table or chi-square critical value calculator above.

The chi-square critical values are always positive and can be used in the following tests.

• Goodness-of-fit tests
• Homogeneity tests
• Tests for independence in contingency tables

Unlike the t & f critical value, Χ2 (chi-square) critical value needs to supply the degrees of freedom to get the result.

## Critical value formula

The formula of z and t critical value can be expressed as:

Type of critical valuet critical value formulaz critical value formula
Left-tailedQt,d (α)u(α)
Right-tailedQt,d(1 - α)u(1 - α)
Two-tailed±Qt,d(1 - α/2)±u(1 - α/2)

Where,

• Qt is the quantile function of t student distribution
• u is the quantile function of the normal distribution
• d refers to the degree of freedom
• α is the significance level

Critical value of t calculator uses all these formulas to produce the exact critical values needed to accept or reject a hypothesis.

## How to find critical values?

Calculating critical value is a tiring task because it involves looking for values into t distribution chart. The t distribution table (student t test distribution) consists of hundreds of values, so, it is convenient to use t table value calculator above for critical values.
However, if you want to find critical values without using t table calculator, follow the examples given below.

### How to find t critical value?

Example:

Find the t critical value if size of the sample is 5 and significance level is 0.05.

Solution:

Step 1:

Subtract 1 from the sample size to get the degree of freedom.
Degree of Freedom = N – 1 = 5 – 1
Degree of freedom = 4
α = 0.05

Step 2:

Depending on the test, choose one-tailed t distribution table or two-tailed t table below.

Step 3:

Look for the degree of freedom in the most left column. Also, look for the significance level α in the top row. Pick the value occurring on the intersection of mentioned row and column.
In this case, the t critical value is 2.132.

### How to find z critical value?

Example:

Find the z critical value if the significance level is 0.02.

Solution:

Step 1:

Divide the significance level α by 2
α/2 = 0.02/2
α/2 = 0.01

Step 2:

Subtract α/2 from 1.
1 - α/2 = 1 – 0.01
1 - α/2 = 0.99

Step 3:

Search the value 0.99 in the z table given below. Add the values of intersecting row (top) and column (most left) to get the z critical value.
2.3 + 0.03 = 2.33
Z critical value = ±2.33
for two-tailed test.

## T-Distribution Table (One Tail)

The t table for one tail probability is given below.

 DF A = 0.1 0.05 0.025 0.01 0.005 0.001 0.0005 ∞ 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 1000 1.282 1.646 1.962 2.33 2.581 3.098 3.3

## T-Distribution Table (Two Tail)

The t table for two tail probability is given below.

 DF A = 0.2 0.1 0.05 0.02 0.01 0.002 0.001 ∞ 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 ∞ 1.282 1.645 1.96 2.326 2.576 3.091 3.291

## Z table (right-tailed)

The normal distribution table for right-tailed test is given below.

 Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0 0.004 0.008 0.012 0.016 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.091 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.148 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.17 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.195 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.219 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.258 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.291 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.334 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.377 0.379 0.381 0.383 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.398 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.437 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.475 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.483 0.4834 0.4838 0.4842 0.4846 0.485 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.489 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.492 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.494 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.496 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.497 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.498 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.499 0.499 3.1 0.499 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993 3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995 3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997 3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998 3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 3.6 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 3.7 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 3.8 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999

## Z table (left-tailed)

The normal distribution table for left-tailed test is given below.

 Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5 0.504 0.508 0.012 0.016 0.0199 0.5239 0.0279 0.0319 0.0359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6064 0.1064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.695 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.719 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.758 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.791 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.834 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.937 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.983 0.9834 0.9838 0.9842 0.9846 0.985 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.989 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.997 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.998 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.999 0.999