Confidence Interval Calculator Mean Difference

Confidence Interval Formula:

\[ CI = Diff \pm (t \times \sqrt{\frac{SD_1^2}{n_1} + \frac{SD_2^2}{n_2}}) \]

Mean Difference (Diff):

T-Value (t):

Standard Deviation 1 (SD1):

Sample Size 1 (n1):

Standard Deviation 2 (SD2):

Sample Size 2 (n2):

Confidence Interval:

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1. What Is The Confidence Interval For Mean Difference?

The confidence interval for mean difference provides a range of values that is likely to contain the true difference between two population means with a specified level of confidence. It's a fundamental statistical tool used in hypothesis testing and estimation.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ CI = Diff \pm (t \times \sqrt{\frac{SD_1^2}{n_1} + \frac{SD_2^2}{n_2}}) \]

Where:

\( Diff \) — Difference between sample means
\( t \) — T-value for the desired confidence level
\( SD_1 \) — Standard deviation of first sample
\( n_1 \) — Size of first sample
\( SD_2 \) — Standard deviation of second sample
\( n_2 \) — Size of second sample

Explanation: The formula calculates the range within which the true population mean difference is likely to fall, accounting for sample variability.

3. Importance Of Confidence Interval Calculation

Details: Confidence intervals provide more information than simple hypothesis tests by indicating both the magnitude and precision of an estimated effect. They are essential for making informed decisions in research, medicine, and data analysis.

4. Using The Calculator

Tips: Enter the mean difference, appropriate t-value for your confidence level and degrees of freedom, standard deviations for both samples, and sample sizes. All values must be valid (sample sizes > 0, standard deviations ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: How do I determine the correct t-value?
A: The t-value depends on your desired confidence level (typically 95%) and degrees of freedom, which can be calculated using the Welch-Satterthwaite equation.

Q2: When should I use this formula?
A: Use this formula when comparing means from two independent samples, especially when population variances are unknown and possibly unequal.

Q3: What does a 95% confidence interval mean?
A: It means that if we were to take many samples and build a confidence interval from each, approximately 95% of these intervals would contain the true population mean difference.

Q4: How does sample size affect the confidence interval?
A: Larger sample sizes result in narrower confidence intervals, indicating more precise estimates of the population mean difference.

Q5: Can I use this for paired samples?
A: No, this formula is for independent samples. For paired samples, use a different formula that accounts for the correlation between measurements.