Comparing Weight Gain in Rats: An Analysis of Diets A & B

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SUMMARY

The forum discussion centers on a statistical analysis comparing weight gain in male rats fed two different diets, A and B, with a focus on the application of an F-test and a t-test. The F-test was conducted to compare sample standard deviations, with a calculated F-value of 2.29 and a critical value of 3 at a 5% significance level, leading to the conclusion that the null hypothesis of equal variances cannot be rejected. Subsequently, a t-test was performed to compare the means, yielding a t-value of 3.49 and confirming the use of a 95% confidence interval. The discussion also touches on the appropriateness of using confidence intervals versus hypothesis testing and the considerations for determining sample size in such studies.

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  • Understanding of F-tests for variance comparison
  • Knowledge of t-tests for mean comparison
  • Familiarity with confidence intervals in statistical analysis
  • Basic principles of hypothesis testing
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  • Explore the interpretation of confidence intervals in practical research contexts
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  • #31
I like Serena said:
Yes...

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

Like that yeah?
 
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  • #32
Yes! :smile:

So how can you see from your interval whether it is significant or not?
 
  • #33
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?
 
  • #34
Yep! :smile:

When you use a CI in a test to compare the means of two samples, the criterion is whether the CI contains zero.
 
  • #35
Ah I see! :smile:

So it would be better to do a confidence interval instead of a t-test?
 
  • #36
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?
 
  • #37
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
 
  • #38
Maybe_Memorie said:
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.

Maybe_Memorie said:
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?
 

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