Version:

Last Modified: January 12, 2018

Performs a one-way analysis of variance (ANOVA) and determines whether the factor has a significant effect on the experimental outcome.

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an **error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

**Default: **No error

Acceptable probability that this node incorrectly rejects a true null hypothesis.

**significance level** is a threshold value used to judge whether a factor has a significant effect on the experimental outcome.

**Default: **0.05

Probability that a value sampled from the F distribution with *dofa* and *dofe* degrees of freedom is greater than *fa*, where *dofa*, *dofe*, and *fa* are elements in **summary**.

Algorithm for Calculating **significance**

This node calculates **significance** using the following equation:

$\mathbf{s}\mathbf{i}\mathbf{g}\mathbf{n}\mathbf{i}\mathbf{f}\mathbf{i}\mathbf{c}\mathbf{a}\mathbf{n}\mathbf{c}\mathbf{e}=\mathrm{Prob}\{{F}_{\mathrm{dofa},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{dofe}}>\mathrm{fa}\}$

where
*F*_{dofa, dofe} is the F distribution with *dofa* and *dofe* degrees of freedom.

A 2-by-5 matrix that displays the obtained values for analysis.

$\mathrm{summary}=\left[\begin{array}{cc}\mathrm{ssa}& \mathrm{dofa}\\ \mathrm{sse}& \mathrm{dofe}\end{array}\phantom{\rule{0ex}{0ex}}\text{\hspace{0.17em}}\phantom{\rule{0ex}{0ex}}\phantom{\square}\begin{array}{cc}\mathrm{msa}& \mathrm{fa}\\ \mathrm{mse}& \mathrm{0.0}\end{array}\begin{array}{c}\mathrm{F\; critical}\\ \mathrm{0.0}\end{array}\right]$

where

*ssa*and*sse*are the sums of squares associated with the factor and residual error, respectively*dofa*and*dofe*are the respective degrees of freedom*msa*and*mse*are the respective mean squares*fa*is the F value*F critical*is the F critical value that corresponds to**significance level**

Algorithm for Calculating Sums of Squares

This node calculates the sums of squares using the following equations:

$\mathrm{ssa}={\displaystyle \underset{i=0}{\overset{k-1}{\sum}}}{\displaystyle \underset{m=0}{\overset{{n}_{i}-1}{\sum}}{\left(\stackrel{\xaf}{{x}_{i\cdot}}-\stackrel{\xaf}{{x}_{\cdot \cdot}}\right)}^{2}}$

$\mathrm{sse}={\displaystyle \underset{i=0}{\overset{k-1}{\sum}}}{\displaystyle \underset{m=0}{\overset{{n}_{i}-1}{\sum}}{\left({x}_{im}-\stackrel{\xaf}{{x}_{i\cdot}}\right)}^{2}}$

where

*k*is the number of levels*i*is the index of each level, starting from 0*n*_{i}is the number of observational data at the*i*^{th}level*m*is the index of each observational data at a certain level, starting from 0-
$\stackrel{\xaf}{{x}_{i\cdot}}$ is the mean of all the observational data at the
*i*^{th}level - $\stackrel{\xaf}{{x}_{\cdot \cdot}}$ is the mean of all the observational data
*x*_{im}is the*m*^{th}observation data of the*i*^{th}level

Algorithm for Calculating Degrees of Freedom

This node calculates the degrees of freedom using the following equations:

$\mathrm{dofa}=k-1$

$\mathrm{dofe}=n-k$

where

*k*is the number of levels*n*is the number of all the observational data

Algorithm for Calculating Mean Squares

This node calculates the mean squares using the following equations:

$\mathrm{msa}=\frac{\mathrm{ssa}}{\mathrm{dofa}}$

$\mathrm{mse}=\frac{\mathrm{sse}}{\mathrm{dofe}}$

where

*ssa*is a measure of variation attributed to the factor*dofa*is the degree of freedom of*ssa**sse*is a measure of variation attributed to random fluctuation*dofe*is the degree of freedom of*sse*

Algorithm for Calculating the F Value

This node calculates the F value using the following equation:

$\mathrm{fa}=\frac{\mathrm{msa}}{\mathrm{mse}}$

where

*msa*is the mean square quantity of*ssa**mse*is the mean square quantity of*sse*

Algorithm for Calculating the F Critical Value

*F critical* is the value satisfying the following equation:

$\mathrm{Prob}\{{F}_{\mathrm{dofa},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{dofe}}\ge F\mathit{critical}\}=\mathbf{significance}\text{\hspace{0.17em}}\mathbf{level}$

where *F*_{dofa, dofe} is the F distribution with *dofa* and *dofe* degrees of freedom.

Boolean value that indicates whether the factor has a significant effect on the experimental outcome.

True | significance is equal to or less than significance level, which means the factor has a significant effect on the experimental outcome. |

False | significance is greater than significance level, which means the factor does not have a significant effect on the experimental outcome. |

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

Using age as a factor, this example demonstrates how to test whether age has a significant effect on the number of sit-ups a person can do.

The following table defines the levels of age.

Level 0 | 6 years old to 10 years old |

Level 1 | 11 years old to 15 years old |

Level 2 | 16 years old to 20 years old |

The following table lists the results of a random sampling of six people. The results are based on a series of observations of how many sit-ups people from different age groups can do.

Person 1 | 8 years old (Level 0) | 10 sit-ups |

Person 2 | 12 years old (Level 1) | 15 sit-ups |

Person 3 | 16 years old (Level 2) | 20 sit-ups |

Person 4 | 20 years old (Level 2) | 25 sit-ups |

Person 5 | 13 years old (Level 1) | 17 sit-ups |

Person 6 | 10 years old (Level 0) | 12 sit-ups |

The following table lists the inputs and outputs of this node.

levels |
3 | |

x |
[10, 15, 20, 25, 17, 12] | |

index |
[0, 1, 2, 2, 1, 0] | |

significance level |
0.05 | |

significance |
0.0367 | |

summary |
ssa |
133 |

sse |
16.5 | |

dofa |
2 | |

dofe |
3 | |

msa |
66.5 | |

mse |
5.5 | |

fa |
12.0909 | |

0.0 |
0 | |

F critical |
9.55209 | |

0.0 |
0 | |

significant? |
True |

Because **significant?** is True, you can conclude that based on the sampling data, age has a significant effect on the number of sit-ups a person can do.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application