Compute the following metrics:

`MeanGermTime`

Mean germination time (\(\overline{T}\)) or Mean length of incubation time (Edmond and Drapala 1958; Czabator 1962; Mock and Eberhart 1972; Ellis and Roberts 1980; Labouriau 1983; Ranal and de Santana 2006) .

`VarGermTime`

Variance of germination time (\(s_{T}^{2}\)) (Labouriau 1983; Ranal and de Santana 2006) .

`SEGermTime`

Standard error of germination time (\(s_{\overline{T}}\)) (Labouriau 1983; Ranal and de Santana 2006) .

`CVGermTime`

Coefficient of variation of the germination time (\(CV_{T}\)) (Gomes 1960; Ranal and de Santana 2006) .

```
MeanGermTime(germ.counts, intervals, partial = TRUE)
VarGermTime(germ.counts, intervals, partial = TRUE)
SEGermTime(germ.counts, intervals, partial = TRUE)
CVGermTime(germ.counts, intervals, partial = TRUE)
```

- germ.counts
Germination counts at each time interval. Can be partial or cumulative as specified in the argument

`partial`

.- intervals
The time intervals.

- partial
logical. If

`TRUE`

,`germ.counts`

is considered as partial and if`FALSE`

, it is considered as cumulative. Default is`TRUE`

.

For `MeanGermTime`

, the mean germination time value in the same
unit of time as specified in the argument `intervals`

.

For `VarGermTime`

, the variance of germination time value as

\(\mathrm{time^{2}}\).

For `SEGermTime`

, the standard error of germination time in the same
unit of time specified in the argument `intervals`

.

For `CVGermTime`

, the value of coefficient of variation of the
germination time.

`MeanGermTime`

computes the mean germination time according to the
following formula
(Edmond and Drapala 1958; Czabator 1962; Smith and Millet 1964; Ellis and Roberts 1980; Labouriau 1983; Ranal and de Santana 2006)
.

\[\overline{T} = \frac{\sum_{i=1}^{k}N_{i}T_{i}}{\sum_{i=1}^{k}N_{i}}\]

Where, \(T_{i}\) is the time from the start of the experiment to the \(i\)th interval, \(N_{i}\) is the number of seeds germinated in the \(i\)th time interval (not the accumulated number, but the number corresponding to the \(i\)th interval), and \(k\) is the total number of time intervals.

It is the same as Sprouting Index (\(SI\)) or Emergence Index (\(EI\)) described by Smith and Millet (1964) and Mock and Eberhart (1972) as well as Germination Resistance (\(GR\)) described by Gordon (1969, 1971) .

It is the inverse of mean germination rate (\(\overline{V}\)).

\[\overline{T} = \frac{1}{\overline{V}}\]

It indicates the average length of time required for maximum germination of a seed lot. Lower the \(\overline{T}\), faster the sample has germinated and reflects seed vigor.

`VarGermTime`

computes the variance of germination time according to the
following formula
(Labouriau 1983; Ranal and de Santana 2006)
.

\[s_{T}^{2} = \frac{\sum_{i=1}^{k}N_{i}(T_{i}-\overline{T})^{2}}{\sum_{i=1}^{k}N_{i}-1}\]

Where, \(T_{i}\) is the time from the start of the experiment to the \(i\)th interval, \(N_{i}\) is the number of seeds germinated in the \(i\)th time interval (not the accumulated number, but the number corresponding to the \(i\)th interval), and \(k\) is the total number of time intervals.

`SEGermTime`

computes the standard error of germination time
(\(s_{\overline{T}}\)) according to the following formula
(Labouriau 1983; Ranal and de Santana 2006)
.

\[s_{\overline{T}} = \sqrt{\frac{s_{T}^{2}}{\sum_{i=1}^{k}N_{i}}}\]

Where, \(N_{i}\) is the number of seeds germinated in the \(i\)th time interval (not the accumulated number, but the number corresponding to the \(i\)th interval), and \(k\) is the total number of time intervals.

It signifies the accuracy of the calculation of the mean germination time.

`CVGermTime`

computes the coefficient of variation of germination time
(\(CV_{T}\)) according to the following formula
(Gomes 1960; Ranal and de Santana 2006)
.

\[CV_{T} = \frac{\sqrt{s_{T}^{2}}}{\overline{T}}\]

This indicates the uniformity of germination and permits comparisons irrespective of the magnitude of mean germination time (\(\overline{T}\)).

Czabator FJ (1962).
“Germination value: An index combining speed and completeness of pine seed germination.”
*Forest Science*, **8**(4), 386--396.

Edmond JB, Drapala WJ (1958).
“The effects of temperature, sand and soil, and acetone on germination of okra seed.”
*Proceedings of the American Society for Horticultural Science*, **71**, 428--434.

Ellis RH, Roberts EH (1980).
“Improved equations for the prediction of seed longevity.”
*Annals of Botany*, **45**(1), 13--30.

Gomes FP (1960).
*Curso De Estatistica Experimental*.
Escola Superior de Agricultura Luiz de Queiroz, Universidade de Sao Paulo.

Gordon AG (1969).
“Some observations on the germination energy tests for cereals.”
*Proceedings of the Association of Official Seed Analysts*, **59**, 58--72.

Gordon AG (1971).
“The germination resistance test - A new test for measuring germination quality of cereals.”
*Canadian Journal of Plant Science*, **51**(2), 181--183.

Labouriau LG (1983).
*A Germinacao Das Sementes*.
Organizacao dos Estados Americanos. Programa Regional de Desenvolvimento Cientifico e Tecnologico. Serie de Biologia. Monografia 24.

Mock JJ, Eberhart SA (1972).
“Cold tolerance in adapted maize populations.”
*Crop Science*, **12**(4), 466--469.

Ranal MA, de Santana DG (2006).
“How and why to measure the germination process?”
*Brazilian Journal of Botany*, **29**(1), 1--11.

Smith PG, Millet AH (1964).
“Germinating and sprouting responses of the tomato at low temperatures.”
*Proceedings of the American Society for Horticultural Science*, **84**, 480--484.

```
x <- c(0, 0, 0, 0, 4, 17, 10, 7, 1, 0, 1, 0, 0, 0)
y <- c(0, 0, 0, 0, 4, 21, 31, 38, 39, 39, 40, 40, 40, 40)
int <- 1:length(x)
# From partial germination counts
#----------------------------------------------------------------------------
MeanGermTime(germ.counts = x, intervals = int)
#> [1] 6.7
VarGermTime(germ.counts = x, intervals = int)
#> [1] 1.446154
SEGermTime(germ.counts = x, intervals = int)
#> [1] 0.1901416
CVGermTime(germ.counts = x, intervals = int)
#> [1] 0.1794868
# From cumulative germination counts
#----------------------------------------------------------------------------
MeanGermTime(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 6.7
VarGermTime(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 1.446154
SEGermTime(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 0.1901416
CVGermTime(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 0.1794868
```