# Table (Critical) Values for Z, t, F & χ² Test Calculator

getcalc.com's **Table (Critical) Values for Z, t, F & χ² Test calculator** is an online statistics & *probability *tool to check if the null hypothesis (H0) is accepted or rejected at a stated level of significance 99%, 98%, 97%, 96% 95%, etc or 0.01, 0.02, 0.03, 0.04, 0.05, etc in statistical experiments.

## Critical (Table) Values for Hypothesis (H_{0}) Test

**Critical Values** is often referred with test of hypothesis for Z-test for *normal distribution*, *t-test* for t-distribution, F-test for F-distribution & χ²-test for χ²-distribution to analyze if the results of statistics & probability experiments is statistically significant. Generally, the critical values are the values obtained from the normal distribution, single or two tailed t-distribution, F-distribution & χ^{2} table based on the values degrees of freedom (df) and the level of confidence 99%, 98%, 97%, 96% 95%, etc or 0.01, 0.02, 0.03, 0.04, 0.05, etc. These table values Z_{e}, t_{e}, F_{e} & χ²_{e} obtained from the corresponding distribution tables at stated level of significance are compared with the calculated values of Z-statistic (Z_{0}), t-statistic (t_{0}), F-statistic (F_{0}) & χ²-statistic (χ²_{0}) to check if the null hypothesis is accepted or rejected in Z-test, single or two tailed t-test, F-test & χ²-test respectively.

## Critical Value (Z_{e}) for Z-Test calculator

Generally, critical (table) value of (Z_{e}) calculator is often related to the test of significance for large samples analysis. Z_{e} is an important part of Z-test to test the significance of large samples of normal distribution. By supplying corresponding input values to this normal distribution critical values calculator, users can estimate Z_{e} 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}) to check if the results of statistical surveys or experiments statistically significant. The critical value Z_{e} obtained from the normal distribution table for the corresponding degrees of freedom at a stated level of confidence (99%, 98%, 97%, 96% 95%, etc or 0.01, 0.02, 0.03, 0.04, 0.05, etc) is further compared with the estimated value of Z-statistic (Z_{0}) 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.

### Critical Value (t_{e}) for Student's t-Test Calculator

Generally, table (critical) value (t_{e}) for student's t-test calculator is often related to the test of significance for very sample analysis. t_{e} is an important part of t-test to check if the results of statistical experiment is statistically significant. By supplying corresponding input values to this critical value for t-test calculator, users can estimate t_{e}) for single independent sample mean (x̄), difference between two sample means (x̄_{1} - x̄_{2}) & paired or related sample means (x̄) in statistical surveys or experiments. The critical value t_{e} obtained from the one or two tailed t-distribution table for the corresponding degrees of freedom at a stated level of confidence (99%, 98%, 97%, 96% 95%, etc or 0.01, 0.02, 0.03, 0.04, 0.05, etc) is further compared with t-statistic (t_{0}) estimated 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.

### Critical Value (F_{e}) for F-Test Calculator

Generally, the table (critical) value (F_{e}) for F-test calculator is often related to the test of significance to analyze the quality between two or more sample *variances*. F_{0} is an important part of F-test to test the significance for two or more sample variances. By supplying corresponding input values to this critical value for F-test calculator, users can estimate F_{e} for two or more samples in statistical surveys or experiments. The obtained F_{e} from *F-distribution table* for the corresponding degrees of freedom at a stated level of confidence 99%, 98%, 97%, 96% 95%, etc or 0.01, 0.02, 0.03, 0.04, 0.05, etc to test if the null hypothesis (H_{0}) is accepted or rejected in F-test, one-way *anova* or two-way ANOVA experiments.

### Critical Value (χ²_{e}) for χ²-Test Calculator

Generally, table (critical) value (χ²_{e}) for Chi-squared calculator is often related to the test of significance for samples which are not normally distributed in statistical experiments. χ²_{e} is an important part of χ²-test to test the significance between two abnormally distributed sample sets. By supplying the corresponding input values to this chi-squared table value calculator, users can find χ²_{e} for two or more sample sets in statistical surveys or experiments. The critical value χ²_{e} obtained from χ²-distribution table for the corresponding degrees of freedom at a stated level of confidence (99%, 98%, 97%, 96% 95%, etc or 0.01, 0.02, 0.03, 0.04, 0.05, etc) is further compared with the estimated value of χ^{2} statistic (χ²_{0}) to test if the null hypothesis (H_{0}) is accepted or rejected in χ²-test.