t distribution table - Easy Guides - Wiki (2024)

FAQs

How to understand t-distribution table? ›

The t-distribution is used in statistics to estimate the significance of population parameters for small sample sizes or unknown variations. Like the normal distribution, it is bell-shaped and symmetric. Unlike normal distributions, it has heavier tails, which result in a greater chance for extreme values.

The Student t -distribution is the distribution of the t -statistic given by t=¯x−μs√n t = x ¯ − μ s n where ¯x is the sample mean, μ is the population mean, s is the sample standard deviation and n is the sample size.

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.

The t-distribution is used when data are approximately normally distributed, which means the data follow a bell shape but the population variance is unknown. The variance in a t-distribution is estimated based on the degrees of freedom of the data set (total number of observations minus 1).

If you draw a simple random sample of size n from a population that has an approximately a normal distribution with mean μ and unknown population standard deviation σ and calculate the t-score: t=¯¯¯x−μs√n t = x ¯ − μ s n is from its mean μ. For each sample size n, there is a different Student's t-distribution.

If the population standard deviation is known, use the z-distribution. If the population standard deviation is not known, use the t-distribution.

The t distribution describes the variability of the distances between sample means and the population mean when the population standard deviation is unknown and the data approximately follow the normal distribution.

It is calculated by subtracting the population mean (mean of the second sample) from the sample mean (mean of the first sample) that is [ x̄ – μ] which is then divided by the standard deviation of means. It is initially divided by the square root of n, the number of units in that sample [ s ÷ √(n)].

A t test is appropriate to use when you've collected a small, random sample from some statistical “population” and want to compare the mean from your sample to another value. The value for comparison could be a fixed value (e.g., 10) or the mean of a second sample.

Why do we use the t-distribution instead of the normal distribution? ›

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Use the t table to find t*-values (critical values) for a confidence interval involving t: Determine the confidence level you need (as a percentage). Determine the sample size (for example, n).

The t distribution table values are critical values of the t distribution. The column header are the t distribution probabilities (alpha). The row names are the degrees of freedom (df). Student t table gives the probability that the absolute t value with a given degrees of freedom lies above the tabulated value.

If a p-value reported from a t test is less than 0.05, then that result is said to be statistically significant. If a p-value is greater than 0.05, then the result is insignificant.

The number you see is the critical value (or the t-value) for your confidence interval. For example, if you want a t-value for a 90% confidence interval when you have 9 degrees of freedom, go to the bottom of the table, find the column for 90%, and intersect it with the row for df = 9.