Solved

Question About Two-Sample t-test and ANOVA F-test.

Posted on 2008-09-30
2
1,546 Views
Last Modified: 2010-11-15
If there are only 2 groups to be compared, the two-sided two sample t-test is equivalent to the ANOVA F-test? How can I prove this intuitively, and mathematically?

Thanks!
0
Comment
Question by:zxzwin
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
2 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 22617957
For two groups F = t².
0
 
LVL 3

Accepted Solution

by:
jtm111 earned 125 total points
ID: 22623654

ozo is right, but the author is asking for an intuitive explanation or basic pointers toward proof.

SS = sum of squared deviations, e.g., SUM(X - XBar)^2.
SS of random deviations is distributed Chi-square (scaled by (df)).
an F distribution is a ratio of scaled Chi-squares (by definition, see any math stat book)

Now take t^2

Numerator of t = [(M1 - M2) - (Xbar1 - Xbar2)]
Denominator of t = s = standard error of the difference.

Square the numerator? You get a Sum of Squared deviations (actually, a "sum" of one deviation)
Square the denominator? You get s^2 the variance which is a Sum of Squared deviations over (df).

You just found that t^2 is a ratio of chi-squares, i.e., because num and denom are sum of squares of random deviations.

which makes it exactly equal to an F statistic with (1 and df denominator) degrees of freedom.

This should be enough to get you to construct a proof.

0

Featured Post

Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

734 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question