discordance.delta {AmpliconDuo} | R Documentation |

## Measure Of Discordance Between Two Amplicon Data Sets

### Description

Calculates delta (`\Delta`

) and delta prime (`\Delta'`

), the fraction of amplicon frequencies and amplicons, respectively, with a false discovery rate below a certain threshold `\theta`

as a measure of discordance between two amplicon data sets A and B.

### Usage

```
discordance.delta(x, names = NULL, theta = 0.05, corrected = TRUE,
printToTex = FALSE, directory = NULL, file.name = NULL)
```

### Arguments

`x` |
A list of amplicon duo data frames as returned by the |

`names` |
Optional. Vector or list of characters specifying the sample/amplicon pair names. By default
names are taken from the element names of |

`theta` |
Optional. Numeric, threshold for the false discovery rate. Default value is 0.05. |

`corrected` |
Optional. Logical, indicates whether the p-value from Fisher's exact test (FALSE) or the
adjusted p-value (TRUE), here called q, is used for calculation of |

`printToTex` |
Optional. Logical, if |

`directory` |
Optional. If |

`file.name` |
Optional. If |

### Details

Calculates `\Delta`

and `\Delta'`

, the fraction of frequencies of amplicons and amplicons, respectively, with false discovery rate below a certain threshold `\theta`

as a measure of discordance between two amplicon data sets A and B with occurence `r_{(iAS)}`

of amplicon *i* in amplicon set A of sample S (the ampliconduo data frame).
`\Delta`

and `\Delta'`

are defined as follows:

```
\Delta_{S\theta} = \frac{\sum_{i=1}^{n_S}(r_{iAS}+r_{iBS})\delta(q_{iS}<\theta)}{\sum_{i=1}^{n_S}(r_{iAS}+r_{iBS})}\\
```

```
\Delta'_{S\theta} = \frac{\sum_{i=1}^{n_S}\delta(q_{iS}<\theta)}{n_S},\\
```

```
\mathrm{with\;} \delta(q_{iS}<\theta) =
\left\{
\begin{array}{cc}
1 & \mathrm{\;for\;} q_{iS} < \theta\\
0 & \mathrm{\;for\;} q_{iS} \ge \theta
\end{array}
\right.
```

for number `n_S`

of amplicons detected in sample/ampliconduo S. `\Delta_{S\theta}`

and `\Delta'_{S\theta}`

are located between 0 (no discordance, i.e. no statistically significant deviations between experimental branches) and 1 (complete discordance).

`x`

is the return value of a `ampliconduo`

call.

### Value

Data frame with three columns. The first column contains the sample/amplicon pair names. Second and third column
harbor the corresponding `\Delta`

and `\Delta'`

values, respectively.

### Author(s)

Anja Lange & Daniel Hoffmann

### See Also

`ampliconduo`

, generates the expected data format for `x`

`xtable`

, used to convert the returned data frame into a `Latex`

table.

### Examples

```
## load example ampliconduo data frame
data(amplicons)
## calculate the discordance between amplicon data sets of an ampliconduo data frame
dd.a <- discordance.delta(amplicons)
dd.b <- discordance.delta(amplicons, theta = 0.1)
```

*AmpliconDuo*version 1.1.1 Index]