t Critical Value Calculator


For t - Degrees of Freedom is Sample Size - 1

Critical Value of t (Right Tailed): 2.49
Critical Value of t (Two Tailed): ± 2.80

Tool Overview: t Critical Value Calculator

How To Find Critical Values of t

Planning a statistical experiment and trying to estimate what results you need to accept a hypothesis? In this case, where you need to find the critical values for the t-distribution for a given sample size? You've come to the right place. This critical values calculator is designed to accept your p-value (willingness to accept an incorrect hypothesis) and degrees of freedom. The degrees of freedom for a t-distribution can be derived from the sample size - just subtract one. (degrees of freedom = sample size - 1). You can use this as a critical value calculator with sample size.

Using the critical value calculators

This webpage provides a t critical value calculator with confidence level and sample size (subtract degrees of freedom). Simply enter the requested parameters (alpha level) into the calculator and hit calculate. The critical value represents an associated probability level of the result occurring on the cumulative probability distribution. It generates critical values for both a left tailed test and a two-tailed test (splitting the alpha between the left and right side of the distribution).

How To Conduct Hypothesis Testing

A hypothesis test reduces a statistical question down a single binary proposition. You are using the data points in your sample to assess which of two binary propositions is more likely. The default state is called the null hypothesis - in effect, "nothing to see here", there is no significant difference between your sample data points and sampling distribution for your test. It's just random noise. The other option is refered to the alternative hypothesis - which implies we reject the default state, that the trend in your data is unlikely to be random noise and should be taken seriously. Accepting the alternative hypothesis is dictated by the likelihood that those two samples were drawn from the same population (with the same parameters). We will take a sample, calculate a test statistic and compare it with the expected statistical distribution of that test statistic. When testing the mean of a distribution, you will be comparing the mean value with either the population standard deviation or the sample standard deviation (for large samples).

You're going to hear about another concept here - alpha. You see, we can test our tests - assess the likelhood of the test giving a false positive or a false negative. The alpha value of a given statistical test is the probability of rejecting the null hypothesis when, in fact, the null hypothesis is correct. Eg the probability of a false positive. This alpha is also referred to as the significance level of a test. While there are some common values for alpha (.05, 0.01), I encourage the analyst to carefully think about the cost vs. benefit of running tests at a given level of significance. The real world economics of testing should drive your choice of the correct significance level.

How to calculate critical values

This t score calculator replaces the use of a t distribution table ; it automates the lookup process and can generate a much broader range of values. In the traditional version, you use the t score table and alpha value to find the appropriate critical value for the test. Remember to adjust the alpha value to reflect the nature of the test - one sided or two sided.

critical value calculator with sample size

The degrees of freedom of the t distribution is the sample size - 1. So if you have the sample size, just subtract one and enter that value into the degrees of freedom box.

Other Versions of this T Score Calculator

This version of the t score calculator is used to generate the critical values of t - the cutoff values required to meet specific significance goals for a t test. If you are looking to convert a t statistic into a p value, you will want to use this p value calculator from t. We also have two other calculators you can use to directly compute the t-statistic from sample data: a single sample t test to compare a sample with a hypothesis and a two sample t-test for comparing two samples with each other.

When to Use Standard Normal (Z) vs. Student's T distribution

This t value calculator is good for situations where you're working with small sample sizes. Student's t distribution will converge on the standard normal distribution as the sample size increases. If you are working with a larger sample, you should consider using the version we set up to find critical values of a standard normal. The t distribution is generally perferred for using small samples to analyze the mean of a distribution (eg. use the t value vs. the z score).

About this Website

This t score calculator is part of a larger collection of tools we've assembled as a free replacement to paid statistical packages. The other tools on this site include a descriptive statistics tool, confidence interval generators (standard normal, proportions), linear regression tools, and other tools for probability and statistics. Many calculators allow you to save and recycle your data in similar calculations, saving you time and frustration. Bookmark us and come back when you need a good source of free statistics tools. This specific page replaces the need for a critical value calculator with sample size.

Other Tools: P Value From Z Score, P Value From T Score, Z critical value calculator, t critical value calculator

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