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Root Length Density of Apple Trees

Keywords: exact zeros


The data concerns the underground root system of eight separate apple trees. Three different root stocks are considered (Mark, MM106 and M26) and two plant spacing (4x2 meters and 5x3 meters). For each plant, soil core sampling units taken have been classified as belonging to an inner or outer zone. The response variable is the density of fine roots, also called the root length density, which can have zeros as well as continuous positive values. There are 511 observations, of which 193 or 38% have a zero response.

The design is not a full factorial design: plants 1 and 2 are tested only with the Mark root stock and at a spacing of 5x3; plants 3 and 4 are tested only with Mark root stock at a spacing of 4x2; plants 5 and 6 are tested only with root stock MM106 at a spacing of 5x3; and plants 7 and 8 are tested only with M26 root stock at a spacing of 4x2. The Mark root stock is tested at both plant spacings but the MM106 only at 5x3 and M26 only at 4x2. So there are four unique treatment combinations: Mark stock at 5x3 and 4x2, MM106 at 5x3, and M26 at 4x2.

It is of interest to (1) compare effects of spacing within Mark rootstock, (2) compare root stocks within same spacing and (3) to look for any difference in RLD between inner and out zones.

Variable Description

Plant 1 to 8
Stock Root stock: Mark, MM106 or M26
Spacing Plant spacing: 5x3 or 4x2 meters
Zone Zone relative to the plant the soil core is taken from: Inner or Outer
RLD Root length density in cm/cm3


Data file (tab-delimited text)


de Silva, H. N., Hall, A. J., Tustin, D. S., and Gandar, P. W. (1999). Analysis of distribution of root length density of apple trees on different dwarfing rootstocks. Annals of Botany 83, 335-345.
Dunn, P. K., and Smyth, G. K. (2004). Series evaluation of Tweedie exponential dispersion model densities. (PDF)

The data were provided by Nihal de Silva, HortResearch, New Zealand.


The data requires special methods to deal with data which is continuous and positive except for exact zeros. No transformation to normality is likely to be successful for this data because of the large number of exact zeros,



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