The *t* table in **statistics** contains **critical t distribution values**. This article discusses the

*t*table, also referred to as the

**, and how to prepare it.**

*t*distribution table## Definition: *t* table

A *t* table is a reference statistical table that contains critical values of *t* distribution, also known as the *t* score or *t *value. The *t* value explains the **significance threshold** for specific **tests in statistics** and the upper or lower confines of **confidence intervals** for explicit estimates.^{3}

^{}The *t* table is used in statistics when the **sample size is small**, or when you don’t know the population’s **standard deviation**. You can also use the *t* table during a ** t-test**. A

*t*-test is a

**statistical test**used to liken the means of two sets or groups of data.

It is also used in **hypothesis testing.** You can also use the *t *table to test the difference between two means, if **two** **variable quantities** are significantly correlated, and to calculate the **confidence intervals** of **statistical means** or lapse/**regression coefficients**.

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## Using the *t* table

You can use a *t* table to determine a **critical value** of *t* to execute **statistical tests** or find a **confidence interval**.

### Step 1: One-tailed and two-tailed tests

Firstly, you must determine if you want to use a two or one-tailed test. Below are guidelines for determining when to use one-tailed and two-tailed tests.

Use a **one-tailed test** when you have a directional **alternative hypothesis**. A directional premise emphasizes that the population parameter (like mean or reversion constant) is more or a smaller amount than a specific value, like zero.^{2}

A directional alternative hypothesis features words like **greater than**, **less than**, **increases**, or **decreases**. So, a hypothesis that does not feature these words is usually non-directional.

Use a **two-tailed test** when the alternate premise is non-directional. This type of hypothesis states that the **mean** or **regression coefficient** (population parameter) is unequal to a certain value, like zero.^{1}

You can also use two-tailed t-tests when calculating a confidence interval. Many studies use two-tailed tests.

### Step 2: Calculating the degrees of freedom

Once you have decided to use a **two-tailed test**, the next step is calculating the **degrees of freedom**.

You can calculate the (**df**) degree of freedom from the general trial size (**n**).^{2} Also, the type of equation you need will depend on the test you decide to perform.

Test Type or Procedure |
df Equation |

One-sample t-test, confidence interval of a mean | |

Independent samples t-test |
is the trial or sample size of the 1st group, while is the trial or sample size of the 2nd group |

Dependent samples t-test | |

Linear regression, Pearson correlation, Spearman rank correlation, Confidence interval of a regression |

### Step 3: Choosing a significance level

Traditionally, the **level of significance**, denoted as, is **0.05**. However, in certain situations, you can decrease the **α** to reduce the chances of **Type I errors** or increase the** α** to decrease the risk of **Type II errors**.

So, you select the confidence interval depending on your selected confidence level. So, **α = 1 – confidence level**. The confidence interval is usually **0.95** since the most prevalent confidence interval is usually **0.05**.^{2}

It is worth noting that the **α** section is usually highlighted in the *t* table as it is the most prevalently applied significance level.

### Step 4: Finding the critical value

Now that you have all the data you require to apply the *t* table, you can find the **critical value**. Consider the following:^{3}

- Apply the first
*t*table when using a**two-tailed test**or finding a confidence interval. - Apply the second table when using a
**one-tailed test**. - The
**dfs**are**listed on the left side**of the table. Find the row with the df you found in the second step. You can round the number down to the nearest smallest if it is not listed. - You can find the
**level of significance**at the top of the*t*table. So, find the significance level you chose in step three. - You can determine the critical value of
*t*for your statistical test**where the row and the column intersect**or meet.

## FAQs

The t table **helps you determine** the **critical value of your sample** and compare it with your t value to determine whether to reject your null hypothesis.

The two types of t-tests are **one-tailed** and **two-tailed tests**.

Use a one-tailed test when you have a **directional alternative hypothesis**. In contrast, use a two-tailed test when the **alternate premise is non-directional**.

Firstly, you must **choose between one-tailed or two-tailed tests**, find the **degrees of freedom**, and **choose a significance level**. You can use this information to determine the *critical value of t *in the t table*.*^{1}

## Sources

^{1} Tutorialspoint. “Statistics – T-Distribution Table.” Accessed December 08, 2022. https://www.tutorialspoint.com/statistics/t_distribution_table.htm.

^{2} The Click Reader. “t Table: t Distribution Table with Usage Guide.” Accessed December 8, 2022. https://www.theclickreader.com/t-table-with-usage-guide/.

^{3} T Table. “T Table – T Distribution (Score, Chart).” Accessed December 8, 2022. https://t-tables.net/.