# Test Statistic Calculator

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

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

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

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

## Table of Content

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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.

## What Is Test Statistics?

“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.

## Test Statistics Formula:

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.

### One Population Mean:

For one population mean the test statistics formula is as follows:

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

Where:

• Here, x̅ is the sample mean,
• μ0 is the population mean,
• σ is the standard deviation,
• n is the sample size.

### Comparing Two Means:

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:

• x and y are the means
• σx are the standard deviation of the x values
• σy are the standard deviation of the y values
• n1 is the sample size of the x
• n2 is the sample size of the y

### Single Population Portion:

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

Where:

• P is the sample proportion
• P0  is the claimed proportion
• n is the sample size

### Two Population Portions:

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

Where:

• P1 and  P2 are the populations
• n1 and n2 are the sample sizes

## How to Calculate Test Statistic?

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.

### Example:

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:

• x = 78
• n = 5
• μ = 40
• Deviation = 4

#### Solution:

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

$$\text{Test Statistic}=\frac{78 – 40}{\frac{4}{\sqrt{5}}}$$

$$\text{Test Statistic}=\frac{38}{\frac{4}{2.236}}$$

$$\text{Test Statistic}=\frac{26}{1.79}$$

$$\text{Test Statistic}= 14.53$$

Suppose there is a 3% and it means that the performance for 5 matches is considerably better than average.

## Working of Sample Test Statistic Calculator:

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:

• Choose the point that you want to calculate
• Put the values according to the chosen value
• Tap on “Calculate”

Output:

Our standardized test statistic calculator will give you the following results.

• Test statistics for sample and population mean
• Complete calculation in the steps given

## Test Statistics Table:

### One Tail Table:

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

### Two Tail Table:

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

## FAQs:

### What indicates the negative test statistics?

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.

### What are the applications of test statistics related to data sets?

• Product quality with the sample measurement
• Market research to analyze the survey data
• Strategies of investment and impact of market trends also analyzed
• Determination of significant change and physiological experiments

### What does a 0 test value mean?

If the test statistics value is equal to zero it means that sample results are equal to the null hypothesis.

## References:

From the source Wikipedia: Test statistic, Example.

From the source Khan Academy: Significance tests (hypothesis testing), ### Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.