Critical Value Calculator - T & Z Critical Value calculator
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  • t value
  • z value
  • chi-square value
  • f value
  • r value

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.

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Critical Value Calculator

Critical t value calculator enables you to calculate the 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, the difference between t and z critical value, and how to calculate the critical value of t and z without using a 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 the test statistic is greater than the critical value, statistical significance can be declared as well as the null hypothesis can be rejected.

Critical value tests can be:


Left-tailed test: Q (α)


left tailed test graph

 


Right-tailed test: Q (1 - α)


Right tailed test graph

 


Two-tailed test: Q (α/2)] ∪ Q (1 - α/2)


two tailed test graph

 


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 an area under the standard normal distribution. The 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

A 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 the 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 the size of the sample is 5 and the 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 the 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 at the intersection of the mentioned row and column.
In this case, the t critical value is 2.132.

 

T Critical Value Example

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 the two-tailed test.

z Critical Value Example
 

T-Distribution Table (One Tail)


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

Download Table Preview Loader
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

 

 


T-Distribution Table (Two Tail)


The t table for two-tail probability is given below.

Download Table Preview Loader
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

 

 


Z table (right-tailed)


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

Download Table Preview Loader
Z0.000.010.020.030.040.050.060.070.080.09
0.00.00000.00400.00800.01200.01600.01990.02390.02790.03190.0359
0.10.03980.04380.04780.05170.05570.05960.06360.06750.07140.0753
0.20.07930.08320.08710.09100.09480.09870.10260.10640.11030.1141
0.30.11790.12170.12550.12930.13310.13680.14060.14430.14800.1517
0.40.15540.15910.16280.16640.17000.17360.17720.18080.18440.1879
0.50.19150.19500.19850.20190.20540.20880.21230.21570.21900.2224
0.60.22570.22910.23240.23570.23890.24220.24540.24860.25170.2549
0.70.25800.26110.26420.26730.27040.27340.27640.27940.28230.2852
0.80.28810.29100.29390.29670.29950.30230.30510.30780.31060.3133
0.90.31590.31860.32120.32380.32640.32890.33150.33400.33650.3389
1.00.34130.34380.34610.34850.35080.35310.35540.35770.35990.3621
1.10.36430.36650.36860.37080.37290.37490.37700.37900.38100.3830
1.20.38490.38690.38880.39070.39250.39440.39620.39800.39970.4015
1.30.40320.40490.40660.40820.40990.41150.41310.41470.41620.4177
1.40.41920.42070.42220.42360.42510.42650.42790.42920.43060.4319
1.50.43320.43450.43570.43700.43820.43940.44060.44180.44290.4441
1.60.44520.44630.44740.44840.44950.45050.45150.45250.45350.4545
1.70.45540.45640.45730.45820.45910.45990.46080.46160.46250.4633
1.80.46410.46490.46560.46640.46710.46780.46860.46930.46990.4706
1.90.47130.47190.47260.47320.47380.47440.47500.47560.47610.4767
2.00.47720.47780.47830.47880.47930.47980.48030.48080.48120.4817
2.10.48210.48260.48300.48340.48380.48420.48460.48500.48540.4857
2.20.48610.48640.48680.48710.48750.48780.48810.48840.48870.4890
2.30.48930.48960.48980.49010.49040.49060.49090.49110.49130.4916
2.40.49180.49200.49220.49250.49270.49290.49310.49320.49340.4936
2.50.49380.49400.49410.49430.49450.49460.49480.49490.49510.4952
2.60.49530.49550.49560.49570.49590.49600.49610.49620.49630.4964
2.70.49650.49660.49670.49680.49690.49700.49710.49720.49730.4974
2.80.49740.49750.49760.49770.49770.49780.49790.49790.49800.4981
2.90.49810.49820.49820.49830.49840.49840.49850.49850.49860.4986
3.00.49870.49870.49870.49880.49880.49890.49890.49890.49900.4990
3.10.49900.49910.49910.49910.49920.49920.49920.49920.49930.4993
3.20.49930.49930.49940.49940.49940.49940.49940.49950.49950.4995
3.30.49950.49950.49950.49960.49960.49960.49960.49960.49960.4997
3.40.49970.49970.49970.49970.49970.49970.49970.49970.49970.4998
3.50.49980.49980.49980.49980.49980.49980.49980.49980.49980.4998
3.60.49980.49980.49990.49990.49990.49990.49990.49990.49990.4999
3.70.49990.49990.49990.49990.49990.49990.49990.49990.49990.4999
3.80.49990.49990.49990.49990.49990.49990.49990.49990.49990.4999

 

 


Z table (left-tailed)


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

Download Table Preview Loader
Z 0.000.010.020.030.040.050.060.070.080.09
0.00.50000.50400.50800.01200.01600.01990.52390.02790.03190.0359
0.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.5753
0.20.57930.58320.58710.59100.59480.59870.60640.10640.61030.6141
0.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.6517
0.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.6879
0.50.69150.69500.69850.70190.70540.70880.71230.71570.71900.7224
0.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.7549
0.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852
0.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.8133
0.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389
1.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.8621
1.10.86430.86650.86860.87080.87290.87490.87700.87900.88100.8830
1.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.9015
1.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.9177
1.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319
1.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.9441
1.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.9545
1.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.9633
1.80.96410.96490.96560.96640.96710.96780.96860.96930.96990.9706
1.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.9767
2.00.97720.97780.97830.97880.97930.97980.98030.98080.98120.9817
2.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.9857
2.20.98610.98640.98680.98710.98750.98780.98810.98840.98870.9890
2.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.9916
2.40.99180.99200.99220.99250.99270.99290.99310.99320.99340.9936
2.50.99380.99400.99410.99430.99450.99460.99480.99490.99510.9952
2.60.99530.99550.99560.99570.99590.99600.99610.99620.99630.9964
2.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.9974
2.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.9981
2.90.99810.99820.99820.99830.99840.99840.99850.99850.99860.9986
3.00.99870.99870.99870.99880.99880.99890.99890.99890.99900.9990

 

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