t-test Calculator

A t-test Calculator is a statistical tool used to determine if there’s a significant difference between the means of two groups. It’s commonly used in hypothesis testing and helps researchers make inferences about population parameters based on sample data.

t-test Calculation Chart

t-test Formula

The formula for an independent samples t-test is:

t = (x̄₁ - x̄₂) / √[(s₁²/n₁) + (s₂²/n₂)]

Where:

• x̄₁ and x̄₂ are the means of the two groups
• s₁² and s₂² are the variances of the two groups
• n₁ and n₂ are the sample sizes

Using table data:

• x̄₁ = 70.6, x̄₂ = 73
• s₁² = 175 / (5-1) = 43.75, s₂² = 115 / (5-1) = 28.75
• n₁ = n₂ = 5

Now, we can calculate t:

t = (70.6 - 73) / √[(43.75/5) + (28.75/5)]
t = -2.4 / √14.5
t = -0.63

This t-value is then compared to critical values or used to calculate a p-value to determine statistical significance.

How Do You Calculate the t-test?

To calculate a t-test:

1. Collect data from two groups.
2. Calculate the mean and variance for each group.
3. Determine the degrees of freedom (df = n₁ + n₂ – 2).
4. Apply the t-test formula.
5. Compare the result to critical values or calculate the p-value.

Group A: 68, 75, 71, 63, 76; Group B: 72, 69, 78, 71, 75

Mean A = 70.6, Mean B = 73; Variance A = 43.75, Variance B = 28.75

df = 5 + 5 – 2 = 8

t = -0.63 (calculated earlier)

For α = 0.05 and df = 8, the critical value is ±2.306.

Since |-0.63| < 2.306, we fail to reject the null hypothesis, suggesting no significant difference between the groups at the 0.05 level.