# T Distribution

This is a continuous distribution.

Also known as the **Students T Distribution**

This is probably the second most commonly used probability distribution function.

The normal convention for representing the T distribution is to use a lower case "t".

The T distribution is often used when you have a small sample size.

When the sample size is small and the standard deviation of the population is not known you need to use the T distribution as opposed to the normal distribution.

You can almost think of the normal distribution as a special case of the t distribution when sample sizes are large (over 50 etc)

### Examples

### Properties

Continuous

Symmetrical about t=0

right tail

has a family specified by the "degrees of freedom" value

one tail - one sides

two tails - two sided

### Assumptions

### Probability Distribution Graph

SS

### Cumulative Distribution Graph

SS

### Excel Functions

Returns**T.DIST(x, degrees_freedom, tails)** - (Replaces TDIST)

**T.DIST.2T(x, degrees_freedom)**

TDIST(t, dt, 2) - Two sided p value for t statistic where v is the degress of freedom.

**T.DIST.RT(x, degrees_freedom)**

TDIST(t, dt, 1)

**T.INV(probability, degrees_freedom)**

**T.INV.2T(probability, degrees_freedom)** - (Replaces TINV)

### Important

The function T.INV.RT does not exist.

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