Hypothesis test for the difference of the difference of means?

  • Context: Undergrad 
  • Thread starter Thread starter CaptainP
  • Start date Start date
  • Tags Tags
    Difference Means Test
Click For Summary

Discussion Overview

The discussion centers around the statistical testing of the hypothesis that the difference between two means (μ2 - μ1) is equal to the difference between another pair of means (μ3 - μ2) using three independent samples. The context involves understanding how to approach this specific hypothesis test, which is distinct from standard tests for differences of means.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant seeks guidance on how to test the hypothesis that μ2 - μ1 = μ3 - μ2, noting familiarity with testing for differences of means but uncertainty about testing for differences of differences.
  • Another participant suggests that ANOVA may be applicable, referencing its use for analyzing variance among multiple samples.
  • A subsequent reply clarifies that ANOVA tests whether all means are equal (μ1 = μ2 = μ3), which does not directly address the specific hypothesis of interest regarding the differences between pairs of means.
  • One participant acknowledges a misunderstanding of the original question in their response.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the appropriate method for testing the hypothesis regarding the differences of means, with differing interpretations of the applicability of ANOVA.

Contextual Notes

The discussion highlights the need for clarity in statistical testing methods, particularly when dealing with hypotheses involving differences of differences, and the limitations of ANOVA in this context.

CaptainP
Messages
11
Reaction score
0
Hello all,

Consider 3 different samples. Each sample is independent.

1: 23, 25, 21, 22, 21, 22, 20, 23, 19, 22, 19, 21
2: 28, 27, 27, 29, 26, 29, 27, 30, 28, 27, 26, 29
3: 23, 20, 25, 21, 22, 23, 21, 20, 19, 20, 22, 21

I am being asked to test whether μ2 - μ1 = μ3 - μ2 with 99% confidence. How am I meant to perform this test? I know how to test for the difference of means, that's quite simple, but how does one test for the difference of differences?
 
Physics news on Phys.org
ANOVA tests whether the means of all samples are the same, so in this case an ANOVA test would test whether μ1 = μ2 = μ3. I need something rather different, testing whether the differences between specific pairs are equal.
 
Sorry I misread the post.
 

Similar threads

The length of the line in the MCNP cell card MCNP
  • · Replies 2 ·
Replies
2
Views
2K
How is Alpha Particle Energy Defined in MCNP6?
  • · Replies 0 ·
Replies
0
Views
2K
MHB Does the entrance test score determine the final exam score?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Difference between relative risk and odds ratio
  • · Replies 7 ·
Replies
7
Views
3K
MHB Performance of students - Hypothesis testing
  • · Replies 20 ·
Replies
20
Views
4K
High School How Can We Compare Two Means to Test the Effectiveness of Diet A on Weight Loss?
  • · Replies 20 ·
Replies
20
Views
3K
Why Are MCNP Photons Getting Lost?
  • · Replies 13 ·
Replies
13
Views
4K
Determine the set of odd primes ## p ##?
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Two-sample t test vs. chi-squared test for homogeneity
  • · Replies 1 ·
Replies
1
Views
2K
Signal classification and processing for a gesture sensor module
  • · Replies 7 ·
Replies
7
Views
2K