Test Statistic Calculator

Our standardized test statistic calculator will calculate test statistics for one population mean, comparison of two populations, single population proportions and two population proportions.

How to Use This Test Statistic Calculator?

Stick to the guide below to utilize our best test value calculator!

Input:

• From the top drop-down, select the sample or population type
• After that, go by entering the required entities in their respective fields
• Tap the calculate button

Output:

• Test statistics for the sample or population

What is T-statistics and Student’s T-test?

A particular statistical calculation that figures out the relationship among the sample and its population is known as the test statistics. Moreover, a student’s t-test is used to evaluate hypotheses about the population mean. You can easily calculate the t-statistics on your own or by using a standard test statistic calculator.

What Is Test Statistics Formula?

Below we have four standard cases for which t value formulas differ.

One Population Mean:

Test Statistic for One Population Mean = \(\frac{\overline{x} – μ_0}{\frac{σ}{\sqrt{n}}}\)

Comparing Two Means:

Test Statistic Comparing Two Means = \(\frac{\overline{x} – \overline{y}}{\sqrt{\frac{σ^2_x}{n_1} + \frac{σ^2_y}{n_2}}}\)

Single Population Proportion:

Test Statistic for a Single Population Proportion = \(\frac{\stackrel{\text{^}}{p} – \ p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\)

Two Population Proportions:

Test Statistic for Two Population Proportions = \(\frac{\stackrel{\text{^}}{p_1}
-\stackrel{\text{^}}{p_2}}{\sqrt{\stackrel{\text{^}}{p}(1-\stackrel{\text{^}}{p})(\frac{1}{n_1} + \frac{1}{n_2})}}\)

Practical Example:

Let us make a supposition for a cricket series in which Jack has an average score of 66 or consecutive 16 matches. Now as you better know that an average batting average for a player is 40 (maximum). Keeping in view the deviation in scoring that is 4 in the case, what are the performance stats of Jack?

Solution:

You must consider here how to calculate test statistics. This is because it is the only way to help you in analysing Jack’s performance.

Data Given:

\(\overline{x}=66\)

\(n=16\)

\(μ=40\)

\(σ=4\)

Calculations:

\(\text{Test Statistic}=\frac{\overline{x} – μ_0}{\frac{σ}{\sqrt{n}}}\)

\(\text{Test Statistic}=\frac{66 – 40}{\frac{4}{\sqrt{16}}}\)

\(\text{Test Statistic}=\frac{26}{\frac{4}{4}}\)

\(\text{Test Statistic}=\frac{26}{1}\)

\(\text{Test Statistic}=26\)

Now as the computed value is 26 that could also be verified by this sample test statistic calculator, but what exactly does it mean? Let us explain!

Suppose the standard significance level is 5% and compare the results with it. Now if you look for the critical value for the normal threshold of 5%, it is 1.645. It means that the performance for 16 matches is considerably better than average.

Test Statistics Table (One Tail):

Test Statistics Table (Two-Tail):