What is Fisher's t-test?
Fisher's t-test (also called Student's t-test) is a statistical tool used to determine if there's a significant difference between the means of two groups. Researchers use it in various fields like medicine, psychology, and social sciences to validate hypotheses. It helps assess whether observed differences are genuine or due to random chance by calculating a t-value and corresponding p-value.
Calculator
Formula
t = (M₁ - M₂) / √(s₁²/n₁ + s₂²/n₂)
Where:
M = Mean of group
s² = Variance
n = Sample size
FAQs
What's the purpose of Fisher's t-test?
Fisher's t-test compares means of two independent groups to determine if they're statistically different. It's widely used in scientific research to validate experimental results and make data-driven decisions about population differences.
How to interpret t-test results?
Compare the p-value with your significance level (α), typically 0.05. If p-value < α, reject the null hypothesis, indicating significant difference. Higher t-values suggest greater difference between groups.
What's the difference between one-tailed and two-tailed tests?
One-tailed tests check for difference in one direction (greater/less than), while two-tailed tests check both directions. Choose based on whether you have directional prediction in your hypothesis.
What are the assumptions for t-test?
1. Continuous data 2. Normal distribution 3. Equal variances 4. Independent observations. Violations may require alternative tests like Welch's t-test or non-parametric tests.
Can I use this for small sample sizes?
Yes, Fisher's t-test works for small samples (n < 30). For very small samples (n < 15), ensure data is normally distributed. Consider non-parametric tests if normality assumption fails.
How is p-value calculated?
P-value is determined from t-distribution using calculated t-value and degrees of freedom. It represents probability of observing the results if null hypothesis is true.
What's the difference between t-test and z-test?
Z-test uses population standard deviation and is for large samples (n > 30). T-test uses sample standard deviation and is better for small samples. Both compare means between groups.
How to handle unequal variances?
Use Welch's t-test modification which doesn't assume equal variances. Our calculator automatically applies Welch's correction when variances are unequal between groups.
What's degrees of freedom in t-test?
Degrees of freedom (df) determine t-distribution shape. For independent t-test: df = n₁ + n₂ - 2. It affects critical values and p-value calculation accuracy.
Can I use this calculator for paired data?
No, this is for independent samples. Use paired t-test for related measurements (before/after treatment). Different formula accounts for paired observations correlation.