Desmos T Test Calculator

T Test Formula:

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

Mean 1 (x̄₁):

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Standard Deviation 1 (s₁):

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Sample Size 1 (n₁):

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Mean 2 (x̄₂):

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Standard Deviation 2 (s₂):

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Sample Size 2 (n₂):

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T Statistic:

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1. What is the T Test?

The T Test is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. It calculates a t-statistic that measures the size of the difference relative to the variation in the sample data.

2. How Does the Calculator Work?

The calculator uses the T Test 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 sample 1
\( \bar{x}_2 \) — Mean of sample 2
\( s_1 \) — Standard deviation of sample 1
\( s_2 \) — Standard deviation of sample 2
\( n_1 \) — Size of sample 1
\( n_2 \) — Size of sample 2

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

3. Importance of T Test

Details: T Tests are fundamental in research for comparing group means, testing hypotheses, and determining if observed differences are statistically significant or due to random chance.

4. Using the Calculator

Tips: Enter the means, standard deviations, and sample sizes for both groups. All values must be valid (standard deviations > 0, sample sizes ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a T Test?
A: Use a T Test when comparing the means of two independent groups with continuous data and when the assumptions of normality and equal variances are met.

Q2: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests check for a difference in one direction only, while two-tailed tests check for any difference in either direction.

Q3: What is a significant t-value?
A: Significance depends on degrees of freedom and chosen alpha level (typically 0.05). Generally, |t| > 2 indicates potential significance.

Q4: What are the assumptions of the T Test?
A: Assumptions include normality of data, independence of observations, and homogeneity of variances (though Welch's correction can handle unequal variances).

Q5: Can I use T Test for paired data?
A: For paired or matched data, use a paired T Test which has a different formula accounting for the correlation between measurements.