#### RESULTS

Probabilities | P |
---|---|

one-tailed for —z | -- |

one-tailed for +z | -- |

two-tailed for ±z | -- |

area between ±z | -- |

## What is Critical Value

In literal terms, critical value is defined as any point present on a line which dissects the graph into two equal parts. The rejection or acceptance of null hypothesis depends on the region in which the value falls. The rejection region is defined as one of the two sections that are split by the critical value. If the test value is present in the rejection region, then the null hypothesis would not have any acceptance.

## Critical Value Formula

Two formulae can be used to determine the critical value. These are listed as follows.

**1.** `\( \mathrm{Critical Value = \dfrac{Margin of Error} {Standard Deviation}} \)`

**2.** `\( \mathrm {Critical Value = \dfrac{Margin of Error} {Standard Error of Sample}} \)`

Anyone of the two formulae listed above can be used to determine Critical Value depending on the known values.

## How to calculate critical value? - steps and process

Here are the steps you need to complete for calculating the critical value

### 1. Determination of Alpha

This is the first step which the user has to complete for finding out the critical value. To determine the value of Alpha level, the following formula will be used.

`\( \mathrm{Alpha Level} = 100% - \mathrm{Confidence Interval} \)`

Consider that the confidence interval is 80%. Thus, Alpha Level will be given as.

`\( \mathrm{Alpha Level} = 100 - 80 \)`

`\( \mathrm{Alpha Level} = 20% \)`

### 2. Converting the Alpha Percentage Value to Decimal

The second step involves converting the value of alpha to decimal. By default, it has the percentage unit. Hence, convert it to the decimal format. In step, the value of ( \(\alpha\) )alpha is \(20\%\). Thus, in terms of decimals, it would be \(0.2\)

`\( \alpha = 0.2 \)`

### 3. Divide the value of Alpha by 2

In this step, the value of alpha determined in step 2 would be divided by \(2\). In the above example, the value of alpha is `\(0.2\)`.

`\( \textbf{Thus}, \dfrac{\alpha} {2} = \dfrac{0.2}{2} \)`

`\( \dfrac{\alpha}{2} = 0.1 \)`

### 4. Subtract the result determined in step 3 from 1

The value of α /2 = 0.1. In this step, subtract this value from 1.

`\( \textbf{Thus}, 1 - \, 0.1 = 0.9 \)`

Converting this decimal value to a percentage. Thus, 0.9 would be 90%. The corresponding critical value will be for a confidence interval of 90%. It would be given as:

`\( \bold {Z = 1.645} \)`

Note: To calculate t critical value, f critical value, r critical value, z critical value and chi-square critical use our advance critical values calculator. It helps to calculate the value from the Z table very quickly in real-time.

## Common confidence levels and their critical values

The common confidence levels and the corresponding critical values in the form of a table are given below.

Confidence Level | Critical Value (Z-score) |

0.90 | 1.645 |

0.91 | 1.70 |

0.92 | 1.75 |

0.93 | 1.81 |

0.94 | 1.88 |

0.95 | 1.96 |

0.96 | 2.05 |

0.97 | 2.17 |

0.98 | 2.33 |

0.99 | 2.57 |

## Types of Critical Values

To get the null hypothesis, various methods are used to determine the required area. The common methods used include z tests, t scores and also chi tests. All these methods are used to determine null hypothesis. However, null hypothesis is the area between right and left tails. The right tail has positive values while the left tail has negative ones. This point is incorporated when the critical value has to be determined.

## Critical Value of Z

The standard normal model is used to determine the value of Z. The graphical display of normal distribution shows that the graph is divided into two main regions. The first one is called the Central Region and the other is the Tail Region.

- The central region includes the values of Standard Deviation. These values are derived from the mean.
- The tail values are on the edges of the graph. These values are determined after excluding the central region. To determine the tail values, the following formula is used.

`\( \mathrm {Tail Value = 1 \space - \space Central Value} \)`

## Assistance offered by this critical value calculator

This tool is actually very helpful for the determination of critical value. It cuts down the time needed to determine critical value. Other than that, it is very easy to use so users are able to calculate the correct results without any difficulties.

- To use the tool, enter the degrees of freedom (DF) and the value of Alpha (α). Consider that the value of DF is 12 and Alpha is 0.5. Once the values have been entered, click the calculate button to get the results.
- In accordance with these entered values, the following results would be generated.

- T Value is 0
- Upper Probability is 0.31
- T Value Right Tailed is 0.031