# Continuous Data

This section describes tests that apply to continuous random variables. Many important measurements fall into this category, such as times, dollar amounts, and chemical concentrations.

## Normal Distribution-Based Tests

We’ll start off by showing how to use some common
statistical tests that assume the underlying data is normally
distributed. Normal distributions occur frequently in nature, so this is
often a good assumption.^{[50]}

### Comparing means

Suppose that you designed an experiment to show that
some effect is true. You have collected some data and now want to know
if the data proves your hypothesis. One common question is to ask if
the mean of the experimental data is close to what the experimenter
expected; this is called the null hypothesis. Alternately, the
experimenter may calculate the probability that an alternative
hypothesis was true. Specifically, suppose that you have a set of
observations *x*_{1},
*x*_{2}, ...,
*x _{n}* with experimental mean

*μ*and want to know if the experimental mean is different from the null hypothesis mean

*μ*

_{0}. Furthermore, assume that the observations are normally distributed. To test the validity of the hypothesis, you can use a

*t*-test. In R, you would use the function

`t.test`

:## Default S3 method: t.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, paired = FALSE, var.equal = FALSE, conf.level = 0.95, ...)

Here is a description of the arguments to the `t.test`

function.

Argument | Description | Default |
---|---|---|

x | A numeric vector of data values. ... |

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