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Test Statistic Calculator

Test Statistic Calculator

Select your data type and input the necessary parameters. The tool will readily calculate the test statistics for it.

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To Calculate:

$$ \frac{\overline{x} - μ_0}{\frac{σ}{\sqrt{n}}} $$

$$ \frac{\overline{x} - \overline{y}}{\sqrt{\frac{σ^2_x}{n_1} + \frac{σ^2_y}{n_2}}} $$

$$ \frac{\stackrel{\text{^}}{p} - \ p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $$

$$ \frac{\stackrel{\text{^}}{p_1} - \stackrel{\text{^}}{p_2}}{\sqrt{\stackrel{\text{^}}{p}(1-\stackrel{\text{^}}{p})(\frac{1}{n_1} + \frac{1}{n_2})}} $$

Claimed Hypothesis Mean, μ0:

Sample Mean, x:

Standard Deviation, σ:

Sample Size, n:

Sample Size of the x values, n1:

Sample Size of the y values, n2:

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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):

df a = 0.1 0.05 0.025 0.01 0.005 0.001 0.0005
ta = 1.282 1.645 1.960 2.326 2.576 3.091 3.291
1 3.078 6.314 12.706 31.821 63.656 318.289 636.578
2 1.886 2.920 4.303 6.965 9.925 22.328 31.600
3 1.638 2.353 3.182 4.541 5.841 10.214 12.924
4 1.533 2.132 2.776 3.747 4.604 7.173 8.610
5 1.476 2.015 2.571 3.365 4.032 5.894 6.869
6 1.440 1.943 2.447 3.143 3.707 5.208 5.959
7 1.415 1.895 2.365 2.998 3.499 4.785 5.408
8 1.397 1.860 2.306 2.896 3.355 4.501 5.041
9 1.383 1.833 2.262 2.821 3.250 4.297 4.781
10 1.372 1.812 2.228 2.764 3.169 4.144 4.587
11 1.363 1.796 2.201 2.718 3.106 4.025 4.437
12 1.356 1.782 2.179 2.681 3.055 3.930 4.318
13 1.350 1.771 2.160 2.650 3.012 3.852 4.221
14 1.345 1.761 2.145 2.624 2.977 3.787 4.140
15 1.341 1.753 2.131 2.602 2.947 3.733 4.073
16 1.337 1.746 2.120 2.583 2.921 3.686 4.015
17 1.333 1.740 2.110 2.567 2.898 3.646 3.965
18 1.330 1.734 2.101 2.552 2.878 3.610 3.922
19 1.328 1.729 2.093 2.539 2.861 3.579 3.883
20 1.325 1.725 2.086 2.528 2.845 3.552 3.850
21 1.323 1.721 2.080 2.518 2.831 3.527 3.819
22 1.321 1.717 2.074 2.508 2.819 3.505 3.792
23 1.319 1.714 2.069 2.500 2.807 3.485 3.768
24 1.318 1.711 2.064 2.492 2.797 3.467 3.745
25 1.316 1.708 2.060 2.485 2.787 3.450 3.725
26 1.315 1.706 2.056 2.479 2.779 3.435 3.707
27 1.314 1.703 2.052 2.473 2.771 3.421 3.689
28 1.313 1.701 2.048 2.467 2.763 3.408 3.674
29 1.311 1.699 2.045 2.462 2.756 3.396 3.660
30 1.310 1.697 2.042 2.457 2.750 3.385 3.646
60 1.296 1.671 2.000 2.390 2.660 3.232 3.460
120 1.289 1.658 1.980 2.358 2.617 3.160 3.373
1000 1.282 1.646 1.962 2.330 2.581 3.098 3.300

 

Test Statistics Table (Two-Tail):

df a = 0.2 0.10 0.05 0.02 0.01 0.002 0.001
ta = 1.282 1.645 1.960 2.326 2.576 3.091 3.291
1 3.078 6.314 12.706 31.821 63.656 318.289 636.578
2 1.886 2.920 4.303 6.965 9.925 22.328 31.600
3 1.638 2.353 3.182 4.541 5.841 10.214 12.924
4 1.533 2.132 2.776 3.747 4.604 7.173 8.610
5 1.476 2.015 2.571 3.365 4.032 5.894 6.869
6 1.440 1.943 2.447 3.143 3.707 5.208 5.959
7 1.415 1.895 2.365 2.998 3.499 4.785 5.408
8 1.397 1.860 2.306 2.896 3.355 4.501 5.041
9 1.383 1.833 2.262 2.821 3.250 4.297 4.781
10 1.372 1.812 2.228 2.764 3.169 4.144 4.587
11 1.363 1.796 2.201 2.718 3.106 4.025 4.437
12 1.356 1.782 2.179 2.681 3.055 3.930 4.318
13 1.350 1.771 2.160 2.650 3.012 3.852 4.221
14 1.345 1.761 2.145 2.624 2.977 3.787 4.140
15 1.341 1.753 2.131 2.602 2.947 3.733 4.073
16 1.337 1.746 2.120 2.583 2.921 3.686 4.015
17 1.333 1.740 2.110 2.567 2.898 3.646 3.965
18 1.330 1.734 2.101 2.552 2.878 3.610 3.922
19 1.328 1.729 2.093 2.539 2.861 3.579 3.883
20 1.325 1.725 2.086 2.528 2.845 3.552 3.850
21 1.323 1.721 2.080 2.518 2.831 3.527 3.819
22 1.321 1.717 2.074 2.508 2.819 3.505 3.792
23 1.319 1.714 2.069 2.500 2.807 3.485 3.768
24 1.318 1.711 2.064 2.492 2.797 3.467 3.745
25 1.316 1.708 2.060 2.485 2.787 3.450 3.725
26 1.315 1.706 2.056 2.479 2.779 3.435 3.707
27 1.314 1.703 2.052 2.473 2.771 3.421 3.689
28 1.313 1.701 2.048 2.467 2.763 3.408 3.674
29 1.311 1.699 2.045 2.462 2.756 3.396 3.660
30 1.310 1.697 2.042 2.457 2.750 3.385 3.646
60 1.296 1.671 2.000 2.390 2.660 3.232 3.460
120 1.289 1.658 1.980 2.358 2.617 3.160 3.373
8 1.282 1.645 1.960 2.326 2.576 3.091 3.291

 

FAQs

What is the Difference Between T-score and Z-score?

When finding Z-score, we assume that population standard deviation is given but while finding the T-score, we need to estimate the population standard deviation on our own. It is not wrong to say that both T-score and Z-score are used to make comparisons. 

How Can I Find a Test Statistic or T-statistic?

You can easily use a test statistic formula calculator or follow the below-mentioned steps:

  • Find the population and sample mean.
  • Take the square root of the variance to compute the sample standard deviation.
  • Now put the values of sample, population, and standard deviation in the following formula: (x̄ – μ) / (s / √n) and n is the sample size.

Who is the Father of Student’s T-distribution?

Gosset was a talented statistician who proposed the theory of student’s t-distribution in the year 1908.

References:

From the source of Wikipedia: Common test statistics

From the source of Khan Academy: two-sample t test, Hypotheses, conclusions about the difference of means 

From the source of Lumen Learning: Random Variables, Properties