# Z_{0}, t_{0}, F_{0} & χ²_{0} Statistic Calculator

getcalc.com's statistic calculator & formulas to estimate Z_{0} for Z-test, t_{0} for student's *t-test*, F_{0} for F-test & (χ²)_{0} for χ² test of mean, proportion, difference between two *means* or proportions in statistics & *probability *experiments. use these statistic calculators to find the estimated value of Z_{0}, t_{0}, F_{0} & χ²_{0}.

## Z, t, F & χ² Statistic & Formulas

**Z, t, F & χ² Statistics** are the estimated values of characteristics of population parameter, often used in Z-Test, t-Test, F-Test & χ²-Test respectively to analyze the variations of sample data sets. In such tests, the samples observations drawn from the population is used to estimate the unknown values of the population.

**Z-Test Statistic**In statistics & probability, Z-statistic is inferential statistics function used to analyze variance of large samples to estimate the unknown value of population parameters. It's denoted by Z_{0} and used in Z-test for the test of hypothesis.

**Student's t-Test Statistic**

In statistics & probability, t-statistic is inferential statistics function used to analyze variance of very small samples to estimate the unknown value of population parameters. It's denoted by t_{0} and used in t-test for the test of hypothesis.

**F-Test Statistic**In statistics & probability, F-statistic is inferential statistics function used to analyze two or more sample *variances* to estimate the unknown value of population parameters. It's denoted by F_{0} and used in F-test for the test of hypothesis.

**Chi-squared Test Statistic**In statistics & probability, χ^{2}-statistic is inferential statistics function used to analyze the variances of not uniformly or normally distributed data sets to estimate the unknown value of population parameters. It's denoted by χ²_{0} and used in χ²_{0}-test for the test of hypothesis.

## Z-statistic (Z_{0}) for Z-Test Calculator

Generally, Z-statistic (Z_{0}) calculator is often related to the test of significance for large samples analysis. Z_{0} is an important part of Z-test to test the significance of large samples of *normal distribution*. By supplying corresponding input values to this Z-statistic calculator, users can estimate Z_{0} for single sample mean (x̄), single sample proportion (p), difference between two sample means (x̄_{1} - x̄_{2}) & difference between two sample proportions (p_{1} - p_{2}) in statistical surveys or experiments. The estimated Z_{0} for above test scenarios is further compared with critical values (Z_{e}) obtained from normal distribution table for the corresponding degrees of freedom to test if the null hypothesis (H_{0}) is accepted or rejected at a specified level of significance in one (left or right) tailed or two tailed Z-test.

### t-statistic (t_{0}) for One or Two Tailed t-Test Calculator

Generally, student's t-statistic (t_{0}) calculator is often related to the test of significance for very small samples analysis. t_{0} is an important part of t-test to test the significance of small samples. The test of analysis for t-distribution is similar to ANOVA test if the ANOVA test involves only two sample sets in the analysis. By supplying corresponding input values to this t-statistic calculator, users can estimate t_{0}) for single sample mean (x̄), difference between two sample means (x̄_{1} - x̄_{2}) & paired or related samples mean (x̄) in statistical surveys or experiments. The estimated t_{0} for above test scenarios is further compared with critical values (t_{e}) obtained from t-distribution table for the corresponding degrees of freedom ν to test if the null hypothesis (H_{0}) is accepted or rejected at a specified level of significance in one (left or right) tailed or two tailed t-test.

### F-statistic (F_{0}) for F-Test Calculator

Generally, Z-statistic (Z_{0}) calculator is often related to the test of significance for equality between two or more sample variances. F_{0} is an important part of F-test to test the significance of two or more sample variances. F-statistic or F-ratio is the integral part of one-way or two-way *anova* test to analyze three or more variances simultaneously. By supplying corresponding input values to this F-statistic calculator, users can estimate F_{0} for two or more samples in statistical surveys or experiments. The estimated F_{0} for analysis between two samples sets is further compared with critical values (F_{e}) obtained from *F-distribution table* for the corresponding degrees of freedom to test if the null hypothesis (H_{0}) is accepted or rejected in F-test, one-way ANOVA or two-way ANOVA experiments.

### Chi-squared Statistic (χ²_{0}) for χ²-Test Calculator

Generally, Chi-squared statistic (χ²_{0}) calculator is often related to the test of significance for samples which are not normally distributed in statistical experiments. χ²_{0} is an important part of χ²-test to test the significance between two abnormally distributed sample sets. By supplying corresponding input values to this chi-squared statistic calculator, users can estimate χ²_{0} for two or more sample sets in statistical surveys or experiments. The estimated χ²_{0} for analysis between two samples sets is further compared with critical values (χ²_{e}) obtained from χ²-distribution table for the corresponding degrees of freedom to test if the null hypothesis (H_{0}) is accepted or rejected in χ²-test.