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Statistics Calculators ▶ Test Statistic Calculator

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**Table of Content**

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

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

A particular statistical calculation that figures out the relationship among the sample and its population is known as the test statistics. Moreover, a studentâ€™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.

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

Test Statistic for One Population Mean = \(\frac{\overline{x} – Î¼_0}{\frac{Ïƒ}{\sqrt{n}}}\)

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

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

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})}}\)

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?

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

\(\overline{x}=66\)

\(n=16\)

\(Î¼=40\)

\(Ïƒ=4\)

\(\text{Test Statistic}=\frac{\overline{x} – Î¼_0}{\frac{Ïƒ}{\sqrt{n}}}\)

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

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

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

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

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.

df | a = 0.1 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 | 0.0005 |
---|---|---|---|---|---|---|---|

âˆž | t_{a} = 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 |

df | a = 0.2 | 0.10 | 0.05 | 0.02 | 0.01 | 0.002 | 0.001 |
---|---|---|---|---|---|---|---|

âˆž | t_{a} = 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 |

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.Â

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: (xÌ„ – Î¼) / (s / âˆšn) and n is the sample size.

Gosset was a talented statistician who proposed the theory of studentâ€™s t-distribution in the year 1908.

From the source of Wikipedia: Common test statistics

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

From the source of Lumen Learning: Random Variables, PropertiesÂ