Desmos Calculator T

T-Statistic Formula:

\[ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]

Mean 1:

Standard Deviation 1:

Sample Size 1:

Mean 2:

Standard Deviation 2:

Sample Size 2:

T-Statistic:

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1. What Is The T-Statistic?

The t-statistic is a measure used in hypothesis testing to determine if there is a significant difference between the means of two groups. It follows a t-distribution under the null hypothesis of no difference between group means.

2. How Does The Calculator Work?

The calculator uses the t-statistic formula:

\[ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]

Where:

\( \bar{x}_1 \) — Mean of group 1
\( \bar{x}_2 \) — Mean of group 2
\( s_1 \) — Standard deviation of group 1
\( s_2 \) — Standard deviation of group 2
\( n_1 \) — Sample size of group 1
\( n_2 \) — Sample size of group 2

Explanation: The formula calculates how many standard errors the difference between means is from zero, providing a standardized measure of the difference between groups.

3. Importance Of T-Statistic Calculation

Details: The t-statistic is crucial for determining statistical significance in comparing two sample means, particularly in research studies, A/B testing, and quality control applications.

4. Using The Calculator

Tips: Enter the means, standard deviations, and sample sizes for both groups. Standard deviations must be positive values, and sample sizes must be integers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this t-statistic formula?
A: Use this formula when comparing means from two independent groups with potentially unequal variances (Welch's t-test).

Q2: What is a typical range for t-statistic values?
A: There's no fixed range, but typically values beyond ±2.0 may indicate statistical significance, depending on degrees of freedom and chosen alpha level.

Q3: How do I interpret the t-statistic value?
A: Compare the calculated t-value to critical values from the t-distribution table based on your degrees of freedom and significance level to determine statistical significance.

Q4: What are the assumptions for this test?
A: The test assumes that both samples are randomly selected, observations are independent, and the sampling distribution of the difference between means is approximately normal.

Q5: Can this calculator handle one-sample t-tests?
A: No, this calculator is specifically designed for two-sample t-tests. For one-sample tests, a different formula would be required.