---
title: "Data formats for frequencies"
bibliography: "../inst/REFERENCES.bib"
csl: "../inst/apa-6th.csl"
output: 
  rmarkdown::html_vignette
description: >
  This vignette describes the various ways that frequencies can be entered in a data.frame.
vignette: >
  %\VignetteIndexEntry{Data formats for frequencies}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r, echo = FALSE, message = FALSE, results = 'hide', warning = FALSE}
cat("this is hidden; general initializations.\n")
library(ANOFA)
w<-anofa(Frequency ~ Intensity * Pitch, minimalExample)
dataRaw      <- toRaw(w)
dataWide     <- toWide(w)
dataCompiled <-toCompiled(w)
dataLong     <- toLong(w)
```

# Data formats for frequencies

Frequencies are actually not raw data: they are the counts of data belonging to 
a certain cell of your design. As such, they are _summary statistics_, a bit like
the mean is a summary statistic of data. In this vignette, we review various
ways that data can be coded in a data frame.

All along, we use a simple example, (ficticious) data of speakers classified
according to their ability to play high intensity sound (low ability, medium
ability, or high ability, three levels) and the pitch with which they play
these sound (soft or hard, two levels). This is therefore a design with 
two factors, noted in brief a $3 \times 2$ design. A total of 20 speakers
have been examined ($N=20$).

Before we begin, we load the package ``ANOFA``
(if is not present on your computer, first upload it to your computer from 
CRAN or from the source repository
``devtools::install_github("dcousin3/ANOFA")``): 

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
library(ANOFA)   
```

## First format: Raw data format

In this format, there is one line per _subject_ and one column for each 
possible category (one for low, one for medium, etc.). The column contains
a 1 (a checkmark if you wish) if the subject is classified in this category
and zero for the alternative categories. In a $3 \times 2$ design, there is 
therefore a total of $3+2 = 5$ columns.

The raw data are:

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
dataRaw
```

To provide raw data to ``anofa()``, the formula must be given as

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
w <- anofa( ~ cbind(Low,Medium,High) + cbind(Soft,Hard), dataRaw)
```

where ``cbind()`` is used to group the categories of a single factor.
The formula has no left-hand side (lhs) term because the categories are
signaled by the columns named on the left.

This format is actually the closest to how the data are recorded: if you 
are coding the data manually, you would have a score sheed and placing 
checkmarks were appropriate.

## Second format: Wide data format

In this format, instead of coding checkmarks under the relevant category (using
1s), only the applicable category is recorded. Hence, if ability to play
high intensity is 1 (and the others zero), this format only keep "High"
in the record. Consequently, for a design with two factors, there is only 
two columns, and as many lines as there are subjects:

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
dataWide
```

To use this format in ``anofa``, use

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
w <- anofa( ~ Intensity * Pitch, dataWide)
```

(you can verify that the results are identical, whatever the format by
checking ``summary(w)``).

## Third format: dataCompiled

This format is compiled, in the sense that the frequencies have been
count for each cell of the design. Hence, we no longer have access
to the raw data. In this format, there is $3*2 = 6$ lines, one for each
combination of the factor levels, and $2+1 = 3$ columns, two for the factor
levels and 1 for the count in that cell (aka the frequency). Thus,

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
dataCompiled
```

To use a compiled format in ``anofa``, use

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
w <- anofa(Frequency ~ Intensity * Pitch, dataCompiled )
```

where ``Frequency`` identifies in which column the counts are stored.

## Fourth format: dataLong

This format may be prefered for linear modelers (but it may rapidly becomes
_very_ long!). There is always the same three columns: One Id column, one
column to indicate a factor, and one column to indicate the observed level
of that factor for that subject. There are $20 \times 2 =40 $ lines in the
present example (number of subjects times number of factors.)

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
dataLong
```

To analyse such data format within ``anofa()``, use

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
w <- anofa( Level ~ Factor | Id, dataLong)
```

The vertical line symbol indicates that the observations are nested within
``Id`` (i.e., all the lines with the same Id are actually the same subject).

## Converting between formats

Once entered in an ``anofa()`` structure, it is possible to 
convert to any format using ``toRaw()``, ``toWide()``, ``toCompiled()``
and ``toLong()``. For example:

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
toCompiled(w)
```

The compiled format is probably the most compact format, but the 
raw format is the most explicite format (as we see all the subjects and
all the _checkmarks_ for each).

The only limitation is with regards to the raw format: It is not possible
to guess the name of the factors from the names of the columns. By default, 
``anofa()`` will use uppercase letters to identify the factors.

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
w <- anofa( ~ cbind(Low,Medium,High) + cbind(Soft,Hard), dataRaw)
toCompiled(w)
```

To overcome this limit, you can manually provide factor names with

```{r, message=FALSE, warning=FALSE, echo=TRUE, eval=TRUE}
w <- anofa( ~ cbind(Low,Medium,High) + cbind(Soft,Hard), dataRaw, 
            factors = c("Intensity","Pitch")
          )
toCompiled(w)
```

To know more about analyzing frequency data with ANOFA, refer to @lc23b or to
[What is an ANOFA?](https://dcousin3.github.io/ANOFA/articles/WhatIsANOFA.html).



# References





