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T Critical Value: Easy Definition, Calculating

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Critical Values > T Critical Value

Not sure what I mean by a “critical value”? You might want to read this article first: What is a Critical Value?

What is a T Critical Value?

t-distribution

The t-distribution (black line) is taller than the normal (dotted line). Image: Columbia.edu

A T critical value is a “cut off point” on the t distribution. It’s almost identical to the Z critical value (which cuts off an area on the normal distribution); The only real difference is that the shape of the t distribution is a different shape than the normal distribution, which results in slightly different values for cut off points.

You’ll use your t value in a hypothesis test to compare against a calculated t score. This helps you to decide if you should support or reject a null hypothesis.

How to Find a T Critical Value

You’ve got several options for finding a T value with technology, including:


  • TI 83: See “How to Find t Critical Value on the TI 83.”
  • Excel: See Excel T Test; Excel will calculate the T critical value as part of the process.

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By hand

Step 1: Subtract one from your sample size. This is your df, or degrees of freedom. For example, if the sample size is 8, then your df is 8 – 1 = 7.

Step 2: Choose an alpha level. The alpha level is usually given to you in the question — the most common one is 5% (0.05).

Step 3: Choose either the one tailed T Distribution table or two tailed T Distribution table). This depends on if you’re running a one tailed test or two.

Step 4: Look up the df in the left hand side of the t-distribution table and the alpha level along the top row. Find the intersection of the row and column. For this example (7 df, α = .05,) the t crit value is 1.895.
t critical value


References

Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.
Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
Lindstrom, D. (2010). Schaum’s Easy Outline of Statistics, Second Edition (Schaum’s Easy Outlines) 2nd Edition. McGraw-Hill Education
Vogt, W.P. (2005). Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences. SAGE.

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Stephanie Glen. "T Critical Value: Easy Definition, Calculating" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/t-critical-value/
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