Use our free T-Test Calculator to quickly determine the t-statistic, degrees of freedom (df), and p-value for your hypothesis testing. Ideal for comparing the means of two independent groups, this tool simplifies complex statistical analysis. Understand the significance of your data with ease.
Formula:
The t-test is a statistical method used to determine if there is a significant difference between the means of two groups. Our calculator primarily uses the formula for an independent two-sample Welch's t-test (assuming unequal variances), which is robust and widely applicable.
Welch's t-test Statistic (t):
t = (X̄1 - X̄2) / √((s12 / n1) + (s22 / n2))
Degrees of Freedom (df) for Welch's t-test:
df ≈ ( (s12/n1 + s22/n2)2 ) / ( ((s12/n1)2 / (n1-1)) + ((s22/n2)2 / (n2-1)) )
Where:
- X̄1: Mean of Sample 1
- X̄2: Mean of Sample 2
- s12: Variance of Sample 1 (square of standard deviation s1)
- s22: Variance of Sample 2 (square of standard deviation s2)
- n1: Sample Size of Sample 1
- n2: Sample Size of Sample 2
The p-value is then derived from the calculated t-statistic and degrees of freedom using a t-distribution table or statistical software, indicating the probability of observing such data if the null hypothesis were true.