Confidence interval for difference between means

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SUMMARY

The discussion clarifies the construction of confidence intervals for the difference between means, specifically comparing two representations: (\bar{x1} - \bar{x2}) ± E and (\bar{x1} - \bar{x2}) - E < μ1 - μ2 < (\bar{x1} - \bar{x2}) + E. Both forms convey the same statistical concept, but the latter provides a more detailed explanation of the confidence interval's meaning. The concise form is commonly used in data tables, while the extended form is typically found in educational contexts.

PREREQUISITES
  • Understanding of basic statistics concepts, including means and confidence intervals.
  • Familiarity with statistical notation and symbols.
  • Knowledge of how to interpret confidence intervals in data analysis.
  • Experience with statistical software or tools for calculating confidence intervals.
NEXT STEPS
  • Research the calculation of confidence intervals using R or Python.
  • Learn about the implications of different confidence levels (e.g., 95% vs. 99%).
  • Explore the concept of margin of error in statistical analysis.
  • Study the application of confidence intervals in hypothesis testing.
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Statisticians, data analysts, students in statistics courses, and anyone involved in quantitative research who needs to understand confidence intervals for comparing means.

Deathfish
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My course notes and textbook express this differently:

To construct the confidence interval for diff. between means,

Course notes

(\bar{x1} - \bar{x2})\pmE

Textbook

(\bar{x1} - \bar{x2}) - E < \mu1 - \mu2 < (\bar{x1} - \bar{x2}) + E

why the difference?
 
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There's no difference in meaning. The second, longer form, shows in detail what it means to say that the difference is in a confidence interval. The first, using the ± symbol, is the way a confidence interval is typically expressed in a table of data or some such thing. It's concise and everyone knows that it means the second form. You're unlikely to see the second form except in an explanation of confidence intervals.
 
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