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Critical Value Calculator


How does it
work?


To calculate T Critical Value

  • Enter significance level in the given input box.
  • Enter degrees of freedom in the given input box.
  • Hit the Calculate button to to find t critical value using t critical value calculator.

To calculate Z Critical Value

  • Click the z critical value tab.
  • Enter the significance level in the given input box.
  • Use the Calculate button to get the z critical value.
  • Use the Reset button to enter new values.






Results:







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.


 Table of Content




What is a critical value?


A 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:

Left-tailed test: Q (α)

Left Tailed Example

Right-tailed test: Q (1 - α)

Right Tailed Example

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

Two Tailed Example


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.



Critical value formula


Formula of z and t critical value can be expressed as:


Type of critical value t critical value formula z critical value formula
Left-tailed Qt,d (α) u(α)
Right-tailed Qt,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, and
α is the significance level.
Critical value of t calculator uses all these formulas to produce 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.


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 two tailed test.


T Critical Value Example


T-Distribution Table (One Tail)


The t table for one tail probability is given below.


DFA = 0.10.050.0250.010.0050.0010.0005
ta = 1.282 1.6451.9602.3262.5763.0913.291
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.


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 right-tailed test is given below.


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 left-tailed test is given below.


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

Criticalvaluecalculator.com is a free online service for students, researchers, and statisticians to find the critical values of t and z for right-tailed, left tailed, and two-tailed probability.

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