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")):
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:
## Low Medium High Soft Hard
## 1 1 0 0 1 0
## 2 1 0 0 1 0
## 3 0 1 0 1 0
## 4 0 1 0 1 0
## 5 0 1 0 1 0
## 6 0 0 1 1 0
## 7 0 0 1 1 0
## 8 0 0 1 1 0
## 9 0 0 1 1 0
## 10 0 0 1 1 0
## 11 1 0 0 0 1
## 12 1 0 0 0 1
## 13 1 0 0 0 1
## 14 1 0 0 0 1
## 15 0 1 0 0 1
## 16 0 1 0 0 1
## 17 0 0 1 0 1
## 18 0 0 1 0 1
## 19 0 0 1 0 1
## 20 0 0 1 0 1To provide raw data to anofa(), the formula must be
given as
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.
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:
## Intensity Pitch
## 1 Low Soft
## 2 Low Soft
## 3 Medium Soft
## 4 Medium Soft
## 5 Medium Soft
## 6 High Soft
## 7 High Soft
## 8 High Soft
## 9 High Soft
## 10 High Soft
## 11 Low Hard
## 12 Low Hard
## 13 Low Hard
## 14 Low Hard
## 15 Medium Hard
## 16 Medium Hard
## 17 High Hard
## 18 High Hard
## 19 High Hard
## 20 High HardTo use this format in anofa, use
(you can verify that the results are identical, whatever the format
by checking summary(w)).
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,
## Intensity Pitch Frequency
## 1 Low Soft 2
## 2 Medium Soft 3
## 3 High Soft 5
## 4 Low Hard 4
## 5 Medium Hard 2
## 6 High Hard 4To use a compiled format in anofa, use
where Frequency identifies in which column the counts
are stored.
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 =40 $ lines in the present example (number of subjects times number of factors.)
## Id Factor Level
## 1 1 Intensity Low
## 2 1 Pitch Soft
## 3 2 Intensity Low
## 4 2 Pitch Soft
## 5 3 Intensity Medium
## 6 3 Pitch Soft
## 7 4 Intensity Medium
## 8 4 Pitch Soft
## 9 5 Intensity Medium
## 10 5 Pitch Soft
## 11 6 Intensity High
## 12 6 Pitch Soft
## 13 7 Intensity High
## 14 7 Pitch Soft
## 15 8 Intensity High
## 16 8 Pitch Soft
## 17 9 Intensity High
## 18 9 Pitch Soft
## 19 10 Intensity High
## 20 10 Pitch Soft
## 21 11 Intensity Low
## 22 11 Pitch Hard
## 23 12 Intensity Low
## 24 12 Pitch Hard
## 25 13 Intensity Low
## 26 13 Pitch Hard
## 27 14 Intensity Low
## 28 14 Pitch Hard
## 29 15 Intensity Medium
## 30 15 Pitch Hard
## 31 16 Intensity Medium
## 32 16 Pitch Hard
## 33 17 Intensity High
## 34 17 Pitch Hard
## 35 18 Intensity High
## 36 18 Pitch Hard
## 37 19 Intensity High
## 38 19 Pitch Hard
## 39 20 Intensity High
## 40 20 Pitch HardTo analyse such data format within anofa(), use
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).
Once entered in an anofa() structure, it is possible to
convert to any format using toRaw(), toWide(),
toCompiled() and toLong(). For example:
## Intensity Pitch Frequency
## 1 High Hard 4
## 2 Low Hard 4
## 3 Medium Hard 2
## 4 High Soft 5
## 5 Low Soft 2
## 6 Medium Soft 3The 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.
## A B Frequency
## 1 High Hard 4
## 2 Low Hard 4
## 3 Medium Hard 2
## 4 High Soft 5
## 5 Low Soft 2
## 6 Medium Soft 3To overcome this limit, you can manually provide factor names with
w <- anofa( ~ cbind(Low,Medium,High) + cbind(Soft,Hard), dataRaw,
factors = c("Intensity","Pitch")
)
toCompiled(w)## Intensity Pitch Frequency
## 1 High Hard 4
## 2 Low Hard 4
## 3 Medium Hard 2
## 4 High Soft 5
## 5 Low Soft 2
## 6 Medium Soft 3To know more about analyzing frequency data with ANOFA, refer to Laurencelle & Cousineau (2023) or to What is an ANOFA?.