Confidence Interval Difference Of Means Calculator

Confidence Interval Formula:

\[ CI = (Mean1 - Mean2) \pm t \times \sqrt{\frac{s1^2}{n1} + \frac{s2^2}{n2}} \]

Mean1 (value):

Mean2 (value):

t (value):

s1 (std dev):

n1 (count):

s2 (std dev):

n2 (count):

Confidence Interval:

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1. What is Confidence Interval for Difference of Means?

The confidence interval for the difference of means 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 used to determine if there is a statistically significant difference between two groups.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ CI = (Mean1 - Mean2) \pm t \times \sqrt{\frac{s1^2}{n1} + \frac{s2^2}{n2}} \]

Where:

\( Mean1 \) — Mean of first sample
\( Mean2 \) — Mean of second sample
\( t \) — t-value for desired confidence level
\( s1 \) — Standard deviation of first sample
\( n1 \) — Size of first sample
\( s2 \) — Standard deviation of second sample
\( n2 \) — Size of second sample

Explanation: The formula calculates the range within which the true difference between population means lies with a certain level of confidence.

3. Importance of Confidence Interval Calculation

Details: Confidence intervals provide more information than simple hypothesis tests by showing the precision of the estimate and the range of plausible values for the population parameter difference.

4. Using the Calculator

Tips: Enter the means, t-value, standard deviations, and sample sizes for both groups. Ensure all values are valid (sample sizes > 0, standard deviations ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: How do I determine the appropriate 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: What does it mean if the confidence interval includes zero?
A: If the confidence interval includes zero, it suggests there is no statistically significant difference between the two means at the chosen confidence level.

Q3: When should I use this method?
A: Use this method when you have two independent samples and want to estimate the difference between their population means with a confidence interval.

Q4: What are the assumptions for this calculation?
A: The main assumptions are that the samples are independent, approximately normally distributed, and have similar variances (though the formula uses separate variances).

Q5: How does this differ from a paired t-test confidence interval?
A: This calculator is for independent samples. For paired data, you would use a different formula that accounts for the correlation between paired measurements.