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The TINV(p, df) function returns the value x for which TDIST(x, df, 2) returns p. Therefore, TINV is evaluated by a search process that returns the appropriate value of x by evaluating TDIST for various candidate values of x until it finds a value of x for which TDIST(x, df, 2) is "acceptably close" to p.

Note 1 The distribution was found by W. S. Gossett, an employee of the Guinness brewery in Dublin, Ireland. He apparently wanted to remain anonymous and suggested that he be referred to as "student."

`TINV(p, df)`

data | mu0 | more data | ||||

12.01 | 12.1 | 12.01 | 12.01 | 12.01 | 12.01 | |

12.17 | 12.17 | 12.17 | 12.17 | 12.17 | ||

12.16 | 12.16 | 12.16 | 12.16 | 12.16 | ||

12.14 | 12.14 | 12.14 | 12.14 | 12.14 | ||

12.17 | 12.17 | 12.17 | 12.17 | 12.17 | ||

t-statistic | =(AVERAGE(A2:A6) - B2) / (STDEV(A2:A6) / SQRT(COUNT(A2:A6))) | =(AVERAGE(D2:G6) - B2) / (STDEV(D2:G6) / SQRT(COUNT(D2:G6))) | ||||

t-dist | =TDIST(B8,4,2) | =TDIST(D8,19,2) | ||||

tinv | =TINV(B9,4) | =TINV(D9,19) | ||||

=TINV(0.05,4) | =TINV(0.05,19) |

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If the sample size is n (and here n=5), under the null hypothesis, the t-statistic has a t distribution with n-1 degrees of freedom. The formula for the t-statistic is in cell B8, and its value is about 0.984. The value of TDIST in B9 shows that the probability under the null hypothesis of obtaining a t-statistic further from 0 in either direction (because this is a 2-tailed test) is about 0.381.

Note 2 This example comes from the following out-of-print text:

Bell, C.E., Quantitative Methods for Administration, Irwin, 1977.

TINV is called two times in cells B10 and B11. In cell B10, you verify the inverse relationship between TINV and TDIST by calling TINV with the value of TDIST (about 0.381) in cell B9. The result is the value of the t-statistic from B8. In B11, you ask, "How far from 0 would the t-statistic have to be so that the probability of a t-statistic that is even further from 0 was 0.05 under the null hypothesis?" The answer is about 2.78.The main criticism of this experiment is its small sample size. If instead you had the 20 observations in D2:G6, you would compute the t-statistic with 19 degrees of freedom in D8, cell D9 would reveal that (under the null hypothesis) a t-statistic value more extreme than that in D8 would occur with probability 0.045. Cell D10 again confirms the inverse relationship between TINV and TDIST. Cell D11 finds the cutoff value for the t-statistic, assuming that the appropriate probability of 0.05 of rejecting the null hypothesis when it is true. In this experiment, you must reject the null hypothesis at this significance level because the t-statistic value, 2.144, exceeds the cutoff value, 2.093.

- The accuracy of TDIST
- The design of the search process and the definition of "acceptably close"

Included in this set of inverse functions are BETAINV, CHIINV, FINV, GAMMAINV, and TINV. No modifications were made to the following functions that are called by these inverse functions: BETADIST, CHIDIST, FDIST, GAMMADIST, and TDIST.

Additionally, Excel 2003 and later versions of Excel refined the search process for NORMSINV. Excel 2003 and later versions of Excel also improved the accuracy of NORMSDIST (which is called by NORMSINV). These changes affect NORMINV and LOGINV (which call NORMSINV) and NORMDIST and LOGNORMDIST (which call NORMSDIST).

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Article ID: 828340 - Last Review: 09/19/2011 00:02:00 - Revision: 3.0

Microsoft Office Excel 2007

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