What is Fisher's t-Test?
Fisher's t-test (also called Student's t-test) is a statistical hypothesis test used to determine if there's a significant difference between the means of two groups. Developed by William Sealy Gosset under "Student", it's widely used in research when comparing sample means from normally distributed populations with unknown variances. The test calculates a t-value that measures the difference between groups relative to data variability. It's particularly useful for small sample sizes (n < 30) and helps researchers determine if observed differences are statistically significant or due to random chance.
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Formula
t = (x̄₁ - x̄₂) / √((s₁²/n₁) + (s₂²/n₂))
Where:
x̄₁, x̄₂ = Sample means
s₁², s₂² = Sample variances
n₁, n₂ = Sample sizes
Where:
x̄₁, x̄₂ = Sample means
s₁², s₂² = Sample variances
n₁, n₂ = Sample sizes
Advantages & Disadvantages
Advantages:
- Simple implementation: Easy to calculate with basic statistical knowledge
- Small sample applicability: Works effectively with limited data points
- Versatile: Can be used for both paired and unpaired data
- Foundation for analysis: Serves as basis for more complex statistical methods
- Wide acceptance: Universally recognized in scientific research
Disadvantages:
- Normality assumption: Requires data to be normally distributed
- Variance sensitivity: Assumes equal variances between groups
- Sample size limitations: Less reliable with very large samples
- Outlier vulnerability: Sensitive to extreme values in data
- Limited scope: Only compares two groups at a time