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Test Statistic Calculator

Choose the method, enter the values into the test statistic calculator, and click on the “Calculate” button to calculate the statistical value for hypothesis evaluation

Select Format

Enter the data in row

Enter mean, SEM and n

Enter mean, SD and n

Group One

Group Two

Group 1

Mean (x̄)

SEM

Sample Size (n)

Group 2

Mean (x̄)

SEM

Sample Size (n)

Group 1

Mean (x̄)

Standard Deviation (SD)

Sample Size (n)

Group 2

Mean (x̄)

Standard Deviation (SD)

Sample Size (n)

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Test Statistic Calculator

This test statistic calculator helps determine the test value for hypothesis testing. The calculated value indicates whether there’s enough evidence to reject the null hypothesis. It works for:

One population mean
Two population means
Single population proportion
Two population proportions

Useful in research, experimentation, quality control, and data analysis.

What is a Test Statistic?

A test statistic is a number calculated from sample data that summarizes how much the observed data deviates from what we expect under the null hypothesis. It helps determine whether the observed differences are statistically significant.

How to Calculate Test Statistic

Gather data from the relevant population.
Compute the population's standard deviation.
Calculate the mean (μ) of the population.
Determine the appropriate z-value or sample size.
Apply the correct test statistic formula.

1. Test Statistic for One Population Mean

Formula:

x̄ - μ₀ σ / √n

x̄ = Sample mean
μ₀ = Hypothesized population mean
σ = Population standard deviation
n = Sample size

Example:

Test if the average height of adult males is 70 inches. Sample: n = 25, x̄ = 71, σ = 3.

t = (71 - 70) / (3 / √25) = 1 / 0.6 ≈ 1.67

2. Test Statistic Comparing Two Population Means

Formula:

t = (x̄ - ȳ) / √(σ₁²/n₁ + σ₂²/n₂)

ȳ = Mean of the second sample or population

Example:

School A: n₁ = 30, x̄₁ = 85, σ₁ = 5; School B: n₂ = 35, x̄₂ = 82, σ₂ = 6.

t = (85 - 82) / √(5²/30 + 6²/35) = 3 / √(0.833 + 1.029) = 3 / √1.862 ≈ 2.20

3. Test Statistic for a Single Population Proportion

Formula:

z = (P̂ - P₀) / √(P₀(1 - P₀)/n)

P̂ = Sample proportion
P₀ = Hypothesized population proportion
n = Sample size

Example:

Test if left-handed proportion = 10%. Sample: n = 100, 8 left-handed.

z = (0.08 - 0.10) / √(0.10 × 0.90 / 100) = -0.02 / √0.009 ≈ -0.67

4. Test Statistic for Two Population Proportions

Formula:

z = (P̂₁ - P̂₂) / √(P̂(1-P̂)(1/n₁ + 1/n₂))

P̂₁, P̂₂ = Sample proportions of groups 1 and 2
P̂ = Combined proportion of successes across both samples

Example:

City A: n₁ = 150, 30 smokers → P̂₁ = 0.20

City B: n₂ = 200, 50 smokers → P̂₂ = 0.25

P̂ = (30 + 50) / (150 + 200) ≈ 0.229

z = (0.20 - 0.25) / √(0.229 × 0.771 × (1/150 + 1/200))

z = -0.05 / √(0.176 × 0.011667) = -0.05 / √0.00205 ≈ -1.11

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