Designing Experiments with Orchids

Presented by Ian Parsons.

Designing Experiments with Orchids

Why experiment with orchids?

Designing Experiments with Orchids

Why experiment with orchids?

We may need to carry out experiments with orchids to estabish facts about optimum growing conditions.

Designing Experiments with Orchids

Why experiment with orchids?

We may need to carry out experiments with orchids to estabish facts about optimum growing conditions.

NutrientsCompostsGrowth SupplementsPotsOther factors

Designing Experiments with Orchids

Having established the reasons why experiments with orchids may be carried out, the factors affecting orchids in particular must now be considered.

Designing Experiments with Orchids

Having established the reasons why experiments with orchids may be carried out, the factors affecting orchids in particular must now be considered.

Orchids are relatively expensive, so small designs are appropriate.

Designing Experiments with Orchids

Having established the reasons why experiments with orchids may be carried out, the factors affecting orchids in particular must now be considered.

Orchids are relatively expensive, so small designs are appropriate.

Therefore use Non-Destructive testing.Quantitative Sampling.Relative Measurements.

Designing Experiments with Orchids Non Destructive Testing

Dry Weight and other mass measurements are the usual method employed in plant experiments, but not with orchids.

Quantitative Sampling is best for orchids. Counting the number of shoots, number of

leaves, number of flower spikes. Measuring the lengths of leaves and shoots. Relatives measures, where initial plant size

is measured, and subsequent sampling provides relative increases (or otherwise!).

Designing Experiments with Orchids

Statistics Initial steps

Design of experimental layout

Analysis of results

Repeatability (tell everything, hide nothing!)

Defined limits of experiments (know the boundaries)

Designing Experiments with Orchids

Statistics Initial steps

Design of experimental layout

Analysis of results

Repeatability (tell everything, hide nothing!)

Defined limits of experiments (know the boundaries)

Designing Experiments with OrchidsStatistics Initial steps

A Null Hypothesis, for example, that treatments have no measurable effects on the plants.

A Control treatment, an example is that of no treatment at all.

Replication, using as many different samples (plants) in an experiment as possible.

Randomization, to reduce the effects of external variables such as light, heat, humidity, draughts.

Designing Experiments with OrchidsStatistics Design of experimental layout

Latin Squares. A 4 x 4 Latin Square :-

A B C D

B C D A

C D A B

D A B C

A regular square,no letters repeatedin either rows or columns.

A D C B

D C B A

C B A D

B A D C

A randomized square,no letters repeatedin either rows or columns.

Designing Experiments with OrchidsStatistics Design of experimental layout

Graeco-Latin Squares. A 5 x 5 Greaco-Latin Square :-

Dβ E α A ε C γ B δ

A δ B γ C β E ε D α

B ε C δ D γ A α E β

C α D ε E δ B β A γ

E γ

A β B α D δ C ε

A randomised square, no Greek or LatinLetters repeated in either rowsor columns, and no combinations are repeated or absent.

Each Latin letter can representa level of one nutient.

Each Greek letter can representa level of one growth supplement

Designing Experiments with OrchidsCollecting Data

Measuring Shoot lengths.

One plant.

Initial Measurements. (A)

Subsequent Measurements. (B)

Relative increases. (C=B-A)

Example : Plant A γ (3 Shoots lengths in mm)

168

66

52

286

Shoot 1

Shoot 2

Shoot 3

Total

B

117

60

52

229

- A =

51

6

0

57

C (result)

Designing Experiments with OrchidsAnalysis of results

Designing Experiments with Orchids

Designing Experiments with Orchids

Designing Experiments with Orchids

Values in the data may be lost for several reasons. For example, a plant may die, or may be eaten by a pest.

Missing Values

In a case of loss, some value should be inserted in to the data table to replacethe missing values. It may not be wise to try to replace more that 2 values in a 5 X 5 design because for each missing value the total degrees of freedommust be reduced by one. This may leave only a few degrees of freedom forthe Error Mean Square, and 6 is the minimum acceptable. If there are more than 2losses in a 5 X 5 design then the experiment needs to be repeated.

There are two ways to estimate a value to replace one that has been lost.

The first is to use the overall mean from the remaining good values, and the second is to estimate a missing value from its component contributing parts.

Designing Experiments with Orchids

Using the overall mean may be sufficient as the Error Mean Square is computed from the square of deviations from the mean, by subtraction of the component Mean Squares from the Total Mean Squares.

This gives rise to a deviation of zero for the missing value(s) from the overall mean, hence its acceptability.

The second method is slightly more accurate in that it takes in to consideration the variability of each of the component contributions to the specific cell in the design for which the data is missing.

The next slide shows the formula.

Missing Values (continued...)

Designing Experiments with Orchids

The general form for this is :-

Missing Values (continued...)

yijkl=μ+ τ k+ λ l+ ρ i+ γ j+ ε ijklWhere i,j,k,l are each 1 to 5 in this example.

= the observation in the i th row, the j th column, and receiving the k th Latin treatment and the l th Greek treatment.

= The overall mean.

= the effect of the k th Latin treatment, = the effect of the l th Greek treatment.

= the effect of the i th row , = the effect of the j th column.

= random error.

yijkl

τ k λ lρ i γ j

ε ijkl

μτ k

Designing Experiments with Orchids

The Missing Values can be computed from adding to the overall mean the means of the remaining values in each row, column, Latin treatment, and Greek treatment corresponding to the position of the missing cell.

These result is then averaged to find the best estimate of the missing value.

In the final analysis, the Error Degrees of Freedom have to be reduced by one for each missing value.

This method is more accurate than just using the overall mean, but for large variance, a Bias may have to be subtracted from the Error Sum of Squares. This is beyond the scope of this presentation.

Missing Values (continued...)

Designing Experiments with Orchids

Basic Compost Mix :-

Equal parts(1) Fine Bark(2) Perlite(3) Sphagnum Moss (chopped)

Designing Experiments with Orchids25 small plants of Dendrobium kingianum.

Designing Experiments with Orchids

A potted and labeled plant.

Designing Experiments with Orchids

Plants ready for the bench.

Designing Experiments with Orchids

Plants in the greenhouse during an experiment.

Designing Experiments with OrchidsTreatments applied to the Greek and Latin components.

The Latin component of the design was 5 levels of nutrients where each levelwas as follows :-

A No nutrient.B 1.25 ml/litre, corresponding to half recommended strength.C 2.5 ml/litre, corresponding to recommended normal strength.D 5 ml/litre, double strength.E 10 ml/litre, quadruple strength.

The formulation of the nutrient mix is 1.8:1.2:2.1, with additional micro-elements :-% w/v

Nitrogen, in the form of soluble Nitrates 1.83Phosphorous pentoxide, soluble 1.19Potassium oxide 2.15Calcium oxide 1.72Copper chelated by EDTA 0.002Iron chelated by EDTA 0.040Manganese chelated by EDTA 0.010Zinc chelated by EDTA 0.0025(No Urea or Ammonia in this formulation)

This is similar to Growth Technology Orchid Focus Grow, but without supplements.

Designing Experiments with OrchidsTreatments applied to the Greek and Latin components.

The Greek component of the design was 5 levels of growth supplements where each levelwas as follows :-

α No supplement.β 3.75 ml/litre, corresponding to half recommended strength.γ 7.5 ml/litre, corresponding to recommended normal strength.δ 15 ml/litre, double strength.ε 30 ml/litre, quadruple strength.

The formulation of the supplement mix is :-

Humic Acid, in the form of soluble salts 53%Fulvic Acid, in the form of soluble salts 17%

This is diluted in steps to form a solution of 7.5 ml/litre For the recommended normal strength.This represents a solution of 0.0075% supplements per litre.

These supplements are part of Growth Technology Orchid Focus Grow and Bloom.

Designing Experiments with Orchids

Advantages and Disadvantages of Graeco-Latin Square Designs.

DisadvantagesRequires n2 combinations of treatments, in these examples, where n=5,

Each plant requires a different mix of nutrients and growth supplements.

Finding n2 similar plants may be a problem!

The design provides no analysis of interactions. As all combinations are represented in each in only one plant, there is no room for replication, and interactions must be analyzedUsing a Randomized Block design.

A small design as described here does not allow for a large number of missing values.

Enlarging a Graeco-Latin square requires stepping up to a 7 X 7 design, as Euler's Conjecture suggested that 4n+2 squares do not exist, so a 6 X 6is not possible.

Designing Experiments with Orchids

Advantages and Disadvantages of Graeco-Latin Square Designs.

AdvantagesThe design provides a good range of options for any form of treatments that

will be applied to the plants.

Recording results is not too onerous.

A simple analysis is provided for the design in the form of an Excel spreadsheet, with graphical displays of results, and this can be copied and reused.

Computation of up to 2 missing values is possible without the need to redesign.

Space required to carry out an experiment is not too large, even for anAmateur or hobby grower.

The costs of treatments is not too large for this design, and yet it copes withvariable conditions in a compact space.

The design is repeatable, so that another independent researcher can test the results.

Designing Experiments with Orchids

Several types of experiments offer themselves for examination. Some that need investigation are listed as follows :-

Further nutrient experiments e.g. the composition of the most successful nutrients.Composts, and their effects on quality of orchids.Types of pots, plastic, terra-cotta, clear, opaque, open mesh etc.Growth supplements, which to use for best results?Plant hormones, for growth, and for flower.Repeat experiments for different orchids.

More difficult, but possible in controlled conditions :-

Effects of light, temperature and humidity with combinations of the above.

Further Experiments

Designing Experiments with OrchidsNotes and references Graeco-Latin squares have been used in experimental design for over a century,and are experiencing a renaissance in communications theory and practice atat the present time.

The Swiss mathematician Euler (1707-1783) was fascinated by them, and did much work describing methods for their construction, and put forward the conjecture (1750) that 4n+2 (n=1 to infinity) Graeco-Latin squares did not exist. It was not until 1959 that Parker, Bose, and Shrikhande presented their paper showing Euler's conjecture to be false for all n ≥ 10. Thus, Graeco-Latin squares exist for all orders n ≥ 3 except n = 6.

Any number of papers can be found on the internet describing Graeco-Latin Squares,and their use in experiments design, along with the statistical analyses associated with them.

This presentation, and the spread sheet for the statistical analysis can be found on mywebsite as follows :-

Statistical Analysis - http://www.iantparsons.creators.co.uk/Experiments/Analysis.xlsMetric Rulers - http://www.iantparsons.creators.co.uk/Experiments/rulers_metric.pdfPresentation - http://www.iantparsons.creators.co.uk/Experiments/Presentation.odpPowerPoint - http://www.iantparsons.creators.co.uk/Experiments/Presentation.ppt