Want to protect your cyber security and still get fast solutions? Ask a secure question today.Go Premium


using t test to compare sample mean to population mean

Posted on 2009-02-09
Medium Priority
Last Modified: 2012-08-13
I am new to statistics to please bear with me.

I am using a t test to compare a sample mean to a population mean (it's a question in a book). The t test gives a vaslue of 2.536. This gives a two tailed probability of
0.02 <p <0.05

and a one tailed probability of
0.1 < p< 0.025

The two tailed probability is double the one tailed probability. This doesnt make sense to me. Shouldn't it be the other way around.

Please can you clarify for me

Question by:andieje
LVL 27

Accepted Solution

aburr earned 800 total points
ID: 23592797
No it is just right. Each tail is similar to the other. If you have a 5% possibility to be in one tail you have a 5% probability to be in the other tail too. Total 10% probability

Assisted Solution

Obly earned 600 total points
ID: 23613278
Remember that p is the probability of obtaining a t of 2.536 or greater just by chance alone (i.e., not because your sample is actually different from the population).

If you're doing a one-tailed test, p is the probability of getting a result just in the one tail you're interested in. If you're only interested in really high scores, you care about the p of t >= 2.536, and if it's really low scores, it's p of t <= -2.536. Either way, in your case, p is between 0.01 and 0.025.

If you're doing a two-tailed test, p is the probability of getting EITHER t >= 2.536 OR t <= -2.536 just by chance alone. If your sample truly is random and there's nothing special about it, there's an equal chance of it being in the extreme of either tail. Thus the probability of it being in one tail OR the other is double the probability of it being in one particular tail.

Assisted Solution

jtm111 earned 600 total points
ID: 23632007
Maybe you're confused because you're thinking of the critical region, which is distinct from p.

First, define alpha as the risk of a type I error. This is something you decide. Say you will accept alpha = .05.

Next you decide if you want a 1 tailed or 2 tailed test. If it's one tailed, the entire .05 is in one side of the distribution. If it's two tailed, alpha is split in 2, with .025  on the left and .025 on the right. But alpha is still .05.

Thus you have an idea in your mind that a two tailed test has a smaller "p-value" but what's small is the size of the rejection region which is alpha/2. A two tailed test has a smaller critical rejection region on each side of the distribution.

The other commenters have it right when they're explaining why the p-value is larger for 2 tailed.

What I'm pointing out is why you are surprised by the fact that a 2-tailed p is larger. I think you're surprised because you're imaging the distribution with alpha/2 critical regions on each side of the curve, and you're thinking "smaller." But those are not p-values. Those are components of alpha.
Concerto Cloud for Software Providers & ISVs

Can Concerto Cloud Services help you focus on evolving your application offerings, while delivering the best cloud experience to your customers? From DevOps to revenue models and customer support, the answer is yes!

Learn how Concerto can help you.


Author Comment

ID: 23701288
hi, all of your answers were useful. The problem was simply that I had confused myself because of something I had read in a badly written book. I will split the points

Author Closing Comment

ID: 31544598

Author Comment

ID: 23751459
by the way jtm11, you were right in seeing how I had confused myself. Very intuitive

Featured Post

Industry Leaders: 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

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
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…

581 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