1. EXCEL FUNCTION T Distribution

2. t-Distribution The student t distribution was first derived by William S. Gosset in 1908. t is used to represent random variable. t-distribution is very commonly used in statistical inference. Like normal distribution, t-distribution is symmetrical about 0. For larger degree of freedom, the t- distribution approaches standard normal distribution.

3. t-distribution for various degree of freedoms

4. EXCEL FUNCTION for t-Distribution Given t, to find cumulative probability TDIST(t, df, tails) t:Random variable, t can not be negative df:degree of freedoms Tails:1 for one tail, 2 for two tails TDIST returns the probability for random variable >t Example: TDIST(1.5,50,1) = 0.07

5. Negative t Value –Excel does not work for negative vales of t. –But the t-distribution is symmetric. Thus, TDIST(-a,df,1) gives the area to the left of a negative value of a. 1-TDIST(-a,df,1) gives the area to the right of a negative value of a. P(t 100 >-0.56) = 1-TDIST(0.56,100,1) = 0.7116

6. EXCEL FUNCTION for t-Distribution Given cumulative probability, to find random variable t for two-tail test TINV(p, df) p:probability df:degree of freedoms TINV is the reverse of TDIST. TINV returns the t-value of the t-distribution as a function of the probability and the degrees of freedom.

7. Given Two-Tail Probability to find t value TINV(p,df) returns the value a, such that P(|t| > a) = probability or P(t a) = probabilityEXCEL: =TINV(P,df) t 0.05,100 = TINV(0.05,100) = 1.984

8. Given One-Tail Probability to find t value If one-tail probability is given, to find the t value, you need to multiply the probability by 2EXCEL: =TINV(2*P,df) t 0.05,100 = TINV(2*0.05,100) = 1.66