**π Part 1: Introduce**

**π Definition:**

The **CHISQ.INV** function in Microsoft Excel calculates the inverse of the left-tailed probability of the chi-squared distribution.

**π Purpose:**

This function is mainly used in statistical analysis, especially when conducting hypothesis testing of variance for two data sets. It can help determine critical values in the chi-squared distribution.

**π Syntax & Arguments:**

`=CHISQ.INV(probability, degrees_freedom) `

**π Explain the Arguments in the function:**

**probability:**This is the probability associated with the chi-squared distribution.**degrees_freedom:**This represents the degrees of freedom. It is typically the number of categories minus one.

**π Return value:**

The **CHISQ.INV** function will return a numeric value, the critical chi-squared value for the inputted probability and degrees of freedom.

**π Remarks:**

The probability should be between 0 and 1, and the degrees of freedom should be an integer greater than zero. If not, the function will return an error.

**π Part 2: Examples**

**βοΈ Example 1**

β’ **Purpose of example:**

Determine the critical value for evaluating sales performance variance across regions.

β’ **Data tables and formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Probability | Deg_freedom | Formula | Result |

2 | 0.05 | 3 | =CHISQ.INV(A2, B2) | 7.81 |

3 | 0.01 | 4 | =CHISQ.INV(A3, B3) | 13.28 |

4 | 0.10 | 2 | =CHISQ.INV(A4, B4) | 4.61 |

**Explanation:**

The values in column D are critical chi-square values for the given probabilities and degrees of freedom. For instance, for a degree of freedom of 3 and a probability of 0.05, the critical value is 7.81.

**βοΈ Example 2**

β’ **Purpose of example:**

Check the variance in product quality scores across batches.

β’ **Data tables and formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Probability | Deg_freedom | Formula | Result |

2 | 0.10 | 4 | =CHISQ.INV(A2, B2) | 9.49 |

3 | 0.05 | 5 | =CHISQ.INV(A3, B3) | 11.07 |

4 | 0.01 | 6 | =CHISQ.INV(A4, B4) | 16.81 |

**Explanation:**

Column D provides the critical values necessary for assessing quality score variance. For a probability of 0.05 and 5 degrees of freedom, the critical chi-square value is 11.07.

**βοΈ Example 3**

β’ **Purpose of example:**

We are assessing critical value for evaluating machinery performance variance over different quarters.

β’ **Data tables and formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Probability | Deg_freedom | Formula | Result |

2 | 0.10 | 3 | =CHISQ.INV(A2, B2) | 6.25 |

3 | 0.05 | 4 | =CHISQ.INV(A3, B3) | 9.49 |

4 | 0.01 | 2 | =CHISQ.INV(A4, B4) | 9.21 |

**Explanation:**

For machinery assessment, column D presents the critical chi-square values for given probabilities and degrees of freedom. For a 0.05 probability with 4 degrees of freedom, the critical value is 9.49.

**βοΈ Example 4**

β’ **Purpose of example:**

Evaluating differences in customer feedback scores among different product categories.

β’ **Data tables and formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Probability | Deg_freedom | Formula | Result |

2 | 0.10 | 5 | =CHISQ.INV(A2, B2) | 9.24 |

3 | 0.05 | 3 | =CHISQ.INV(A3, B3) | 7.81 |

4 | 0.01 | 4 | =CHISQ.INV(A4, B4) | 13.28 |

**Explanation:**

Column D provides the critical values to gauge the variance in feedback scores. For instance, with 4 degrees of freedom and a probability of 0.01, the critical chi-square value is 13.28.

**βοΈ Example 5**

β’ **Purpose of example:**

Checking the variance in employee performance scores across different departments.

β’ **Data tables and formulas:**

A | B | C | D | |
---|---|---|---|---|

1 | Probability | Deg_freedom | Formula | Result |

2 | 0.05 | 2 | =CHISQ.INV(A2, B2) | 5.99 |

3 | 0.10 | 4 | =CHISQ.INV(A3, B3) | 9.49 |

4 | 0.01 | 3 | =CHISQ.INV(A4, B4) | 11.34 |

**Explanation:**

The values in column D assist HR in understanding the critical chi-square values for the provided probabilities and degrees of freedom. For instance, a degree of freedom of 3 with a 0.01 possibility yields a crucial value of 11.34.

**π Part 3: Tips and tricks**

- π‘ Ensure the probability you input is between 0 and 1, or the function will return an error.
- π Always verify the degrees of freedom value. It should be an integer greater than zero.
- π Use the CHISQ.INV function alongside other statistical functions in Excel for a comprehensive analysis.
- π If you’re unsure about the degrees of freedom, remember it’s usually calculated as (number of categories – 1).
- π Familiarize yourself with chi-squared distribution tables to better understand and interpret the results from the CHISQ.INV function.

**Β **