# Statistics calculators

## Test statistic calculator

# | Test name |
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1 | One Sample Z-TestCheck that the expected mean is correct, based on a sample average, when you know the standard deviation. |

2 | One Sample T-TestCheck that the expected mean is correct based on the sample average when you don't know the standard deviation |

3 | Two Sample Z-TestCompare the average of two groups, when you know the standard deviation. |

4 | Two Sample T-Test (Pooled variance)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be equal. |

5 | Two Sample T-Test (Welch's)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal. |

6 | Two Sample Mann-Whitney U TestCompare the value of two groups, when you can't assume normality distribution, the test is robust to outliers. |

7 | Paired T-TestCompare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal. |

8 | Paired Wilcoxon Sign Rank TestDetermine how a change has taken effect by considering each individual pair as an observation. The test uses a ranking methodn |

9 | One Way ANOVA TestCheck if the difference between the average (mean) of two or more groups (populations) is significant, using sample data. ANOVA is usually used when there are at least three groups, since for two groups you can use t tests. |

10 | Chi-Squared Test For Variance |

11 | F Test For Variances |

12 | Chi-Square Test For Goodness Of FitCheck if the statistical model fits the observations |

13 | Shapiro-Wilk TestCheck if the normal distribution model fits the observations |

Test | Assumptions | Required sample data |
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# | Test name | Check | Statistic | | IndIndependent observations | σYou know the population's standard deviation | σ_{1}=σ_{2}The standard deviations of both groups are equal | dYou know the expected difference between the means | μYou know the expected mean | xSample average | nSample size | sSample standard deviation | |
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1 | One Sample Z-TestCheck that the expected mean is correct, based on a sample average, when you know the standard deviation. | Mean | | ✔ | ✔ | ✔ | | | ✔ | ✔ | ✔ | | |

2 | One Sample T-TestCheck that the expected mean is correct based on the sample average when you don't know the standard deviation | Mean | | ✔ | ✔ | ✘ | | | ✔ | ✔ | ✔ | ✔ | |

3 | Two Sample Z-TestCompare the average of two groups, when you know the standard deviation. | Mean | | ✔ | ✔ | ✔ | | ✔ | | ✔ | ✔ | | |

4 | Two Sample T-Test (Pooled variance)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be equal. | Mean | | ✔ | ✔ | ✘ | ✔ | ✔ | | ✔ | ✔ | ✔ | |

5 | Two Sample T-Test (Welch's)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal. | Mean | | ✔ | ✔ | ✘ | ✘ | ✔ | | ✔ | ✔ | ✔ | |

6 | Two Sample Mann-Whitney U TestCompare the value of two groups, when you can't assume normality distribution, the test is robust to outliers. | Value | | | ✔ | | | ✔ | | | | | ✔ |

7 | Paired T-TestDetermine how a change has taken effect by considering each individual pair as an observation. The test uses T distribution | Mean | | ✔ | Paired | | | | | | | | ✔ |

8 | Paired Wilcoxon Sign Rank TestDetermine how a change has taken effect by considering each individual pair as an observation. The test uses a ranking methodn | Value | | | Paired | | | | | | | | ✔ |

9 | One Way ANOVA TestCheck if the difference between the average (mean) of two or more groups (populations) is significant, using sample data. ANOVA is usually used when there are at least three groups, since for two groups you can use t-tests. | Mean | | ✔ | ✔ | | | | | | | | ✔ |

10 | Chi-Squared Test For Variance | σ | | ✔ | ✔ | ✔ | | | | | ✔ | ✔ | |

11 | F Test For Variances | σ | | ✔ | ✔ | | | | | | ✔ | ✔ | |

12 | Chi-Squared Test For Goodness Of FitCheck if the statistical model fits the observations | Fit | | | ✔ | | | | | | | | ✔ |

13 | Shapiro-Wilk TestCheck if the normal distribution model fits the observations | Fit | | ✔ | ✔ | | | | | | | | ✔ |

** ✔- yes, ✘- no, empty - irrelevant

## Regression calculators

Bulk linear regression calculator for several dependent variables

## Sample size calculators

## Distribution calculators

## Measurements calculators

## Guide

### Statistical Tests