In order to calculate the test statistics for one population mean, compare two means, a single population proportion, and two population proportions the test statistic calculator is used. It has the ability to summarize your data into a single number.
“The measurement that evaluates the strength of evidence by refuting the hypothesis is known as test statistics”.
It helps to determine the population hypothesis and helps us to summarize the data. Therefore it is also known as the significance hypothesis.
The test statistic formula calculator is used to evaluate the strength of evidence from the sample. However, the formula varies with the size of the population and the sample, and with these, you can evaluate how far your observed data is from the null hypothesis.
For one population mean the test statistics formula is as follows:
$$ \frac{\overline{x} - μ_0}{\frac{σ}{\sqrt{n}}} $$
Where:
The formula to evaluate the independent samples are given below:
$$ \frac{\overline{x} - \overline{y}}{\sqrt{\frac{σ^2_x}{n_1} + \frac{σ^2_y}{n_2}}} $$
Where:
$$ \frac{\stackrel{\text{^}}{p} - \ p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $$
Where:
$$ \frac{\stackrel{\text{^}}{p_1} - \stackrel{\text{^}}{p_2}}{\sqrt{\stackrel{\text{^}}{p}(1-\stackrel{\text{^}}{p})(\frac{1}{n_1} + \frac{1}{n_2})}} $$
Where:
In this type of statistics, the quantitative measures assess the strength of evidence against the hypothesis. So look at the below example which indicates how the value of test statistic calculator summarizes your data into a single number.
Suppose a cricket series was held against Pakistan and Sri Lanka in Colombo in which Baber Azam makes an average score of about 78 in five matches. As you know the average batting for a player is 40. In this case, the deviation in scoring is 4, what are the performance stats of Baber Azam?
Given Data:
$$ \frac{\overline{x} - μ_0}{\frac{σ}{\sqrt{n}}} $$
$$ \text{Test Statistic}=\frac{78 – 40}{\frac{4}{\sqrt{5}}} $$
$$ \text{Test Statistic}=\frac{38}{\frac{4}{2.236}} $$
$$ \text{Test Statistic}=\frac{26}{1.79} $$
$$ \text{Test Statistic}= 14.53 $$
Suppose there is a 3% and it means that the performance for 5 matches is considerably better than average.
The test value calculator transforms the data analysis by simplifying the hypothesis testing. Attach to the guide below to utilize the test statistics calculator.
Input:
Output:
Our standardized test statistic calculator will give you the following results.
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 |
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 |
240 | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 | 3.091 | 3.291 |
A negative test statistics value indicates that it occurs on the left side of the mean. All left values are negative and all right values are positive. A negative test is just like a standard normal that has a zero mean.
If the test statistics value is equal to zero it means that sample results are equal to the null hypothesis.
From the source Wikipedia: Test statistic, Example.
From the source Khan Academy: Significance tests (hypothesis testing),
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