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T-test Formula:
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The independent samples t-test compares the means of two independent groups to determine whether there is statistical evidence that the associated population means are significantly different. It's commonly used when comparing two sample means from normally distributed populations.
The calculator uses the t-test formula:
Where:
Explanation: The t-value represents how much the groups differ relative to the variation in the data. Larger absolute t-values indicate greater evidence against the null hypothesis.
Details: The t-test is fundamental in hypothesis testing, allowing researchers to determine if observed differences between groups are statistically significant or likely due to chance.
Tips: Enter the means, standard deviations, and sample sizes for both groups. All values must be valid (sample sizes > 0, standard deviations ≥ 0).
Q1: When should I use this t-test?
A: Use when comparing means from two independent groups with continuous, normally distributed data and when variances are not assumed equal.
Q2: What's a good t-value?
A: The significance depends on degrees of freedom and your alpha level. Typically, absolute t-values > 2 indicate potential significance for moderate sample sizes.
Q3: What if my sample sizes are unequal?
A: The formula accounts for unequal sample sizes and variances (Welch's t-test).
Q4: What are the assumptions of this test?
A: Independence of observations, approximately normal distribution, and homogeneity of variance (though this formula doesn't assume equal variances).
Q5: How do I get the p-value from the t-value?
A: You need degrees of freedom (approximated using Welch-Satterthwaite equation) and a t-distribution table or statistical software.