F-test and t-test comparing weight gain on two rat diets

[Maybe_Memorie]

Yes...

So the interval would be close to zero in the plus and minus direction, something like
(-3, 3)

Like that yeah?

 

[I like Serena]

Yes!

So how can you see from your interval whether it is significant or not?

 

[Maybe_Memorie]

Because my interval has both boundaries greater than zero, we're 95% certain the difference is between these boundaries, so that means we're 95% certain the difference is greater than zero. This is significant and forces us to reject the null hypothesis?

 

[I like Serena]

Yep!

When you use a CI in a test to compare the means of two samples, the criterion is whether the CI contains zero.

 

[Maybe_Memorie]

Ah I see!

So it would be better to do a confidence interval instead of a t-test?

 

[I like Serena]

Ah, now we're getting into the murky stuff that is open questions and discussions.

Let me counter that by asking: what are the pro's and con's of a CI versus a t-test?
What's the difference anyhow between a t-test and this confidence interval?

And I'll ask one more question: can you do a 1-sided test with a confidence interval?

 

[Maybe_Memorie]

With a CI, we know that if the interval doesn't contain zero the means can't be the same. With a t-test we're relying on probabilities and approximations.

I would sat yes, because if you test Ha: u1>u2, and find a CI for u1-u2, and if this doesn't contain zero we're 95% certain Ha is true

 

[I like Serena]

With a CI, we know that if the interval doesn't contain zero the means can't be the same. With a t-test we're relying on probabilities and approximations.

Wow! Stop!
A CI does not give certainty!
Basically the CI is a t-test. It's just represented differently.
But the ultimate result (rejection or not) is the same.

I would sat yes, because if you test Ha: u1>u2, and find a CI for u1-u2, and if this doesn't contain zero we're 95% certain Ha is true

Hmm, suppose the CI is (-6, -1).
That does not contain 0.
Does that mean Ha is probably true?