# Excels T Distribution Function: How and Why you Use This Tool

 By: Stephen L. Nelson, CPA
 If you're working with a small sample (less than about 30 or 40) in Microsoft Excel, you can use the Student's t-test instead of the z-value or z-score to find the probability with which a value falls below a certain number or to test how far an individual observation is from the mean. To doso, you use the TINV function.Using the Excel TDIST FunctionYou can use the TDIST function to make inferences about the value of a population mean.For example, if you randomly select 20 people from a factory floor, ask them to try a new production method, and then find that they can produce 17.25 units an hour with a sample standard deviation of 3.3, you can find the probability that the population mean takes the value of 16 or less. To do so, you use Excel's TDIST function. The function uses the following syntax:=TDIST(x, degrees of freedom, tails)For this example, the function takes the following form:=TDIST (16,19,1)Depending on your level of significance, you accept or reject the hypothesis.The hypothesis in this example is one-tailed; that is, you're interested in finding probabilities of values less than 16. If instead you need to find the probabilities of values both above and below x, your hypothesis is two-tailed.Using the Excel TINV FunctionIf you know the probability and want to find the t-value, use the TINV function. This function has the following syntax:=TINV (probability, degrees of freedom)If this is based on a one-tailed t distribution, multiply the probability by 2.Using the Excel TTEST FunctionTo find the probability associated with a Student's t-test, use the TTEST function. The t-test is most frequently used to test for a difference between two means. The TTEST function uses the following syntax:=TTEST (data set 1,data set 2,tails,type)where type equals 1 for paired, 2 for two samples with equal variance, or 3 for 2 samples with unequal variance.
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