1 / 16

REVIEW t-Distribution

REVIEW t-Distribution. REVIEW. If tails = 1, TDIST (a,df,1) is calculated to determine P(t>a). Excel does not work on negative a. If tails = 2, TDIST (a,df,2) is calculated to determine P(|t| > a) = P(t > a or t < -a).

marinel
Télécharger la présentation

REVIEW t-Distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. REVIEW t-Distribution

  2. REVIEW • If tails = 1, TDIST (a,df,1) is calculated to determine P(t>a). • Excel does not work on negative a. • If tails = 2, TDIST (a,df,2) is calculated to determine P(|t| > a) = P(t > a or t < -a). • If test is two-tail, TINV(,df) returns that value a, such that P(|t| > a) = P(t < -a or t > a) = . • If test is one-tail, TINV(2*,df) returns that value a, such that P(t > a).

  3. 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.

  4. t-distribution for various degree of freedoms

  5. 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

  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. Example: TINV(0.05, 30) = 2.0423

  7. Right Tail Probability One Tail Probabilities from a to  P(t>a) a

  8. RIGHT TAIL PROBABILITIESOne Tail P(t>a) = area between a and ∞ • Probability to the RIGHT of a EXCEL: =TDIST(a,df,1) P(t100>0.56) = TDIST(0.56,100,1) = 0.2884

  9. RIGHT TAIL PROBABILITIESOne Tail negative value P(t>a) P(t<a) a

  10. RIGHT TAIL PROBABILITIESOne Tail negative 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,f,1) gives the area to the right of a negative value of a. P(t100>-0.56) = 1-TDIST(0.56,100,1) = 0.7116

  11. Left Tail Probability One Tail Probabilities from - to a P(t>a) P(t<a) a

  12. LEFT TAIL PROBABILITIESOne Tail P(t>a) = area between -∞ and a • Probability to the LEFT of a EXCEL: =1-TDIST(t,df,1) P(t100<0.56) = 1-TDIST(0.56,100,1) = 1-0.2884 = 0.7116

  13. PROBABILITIESTwo Tails EXCEL: =TDIST(a,df,2)

  14. PROBABILITIESTwo Tails • TDIST(a,df,2) gives twice the area to the right of a positive value of t. P(t>|a|) = P(t<-a) + P(t>a) = area between –a and -∞ and area between a and ∞ EXCEL: =TDIST(a,df,2) P(t100>0.56) = TDIST(0.56,100,2) = 0.5767

  15. 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 or t > a) = probability EXCEL: =TINV(P,df) t0.05,100 = TINV(0.05,100) = 1.984

  16. 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 2 EXCEL: =TINV(2*P,df) t0.05,100 = TINV(2*0.05,100) = 1.66

More Related