Statistical Analysis for Plant Tissue Culture Data

STATISTICAL ANALYSIS FOR PLANT TISSUE CULTURE DATA

Source : Michael E. ComptonRobert N. Trigiano, Dennis J. Gray (1999) Plant Tissue Culture Concepts and Laboratory Exercises, Second Edition, CRC Press LLC, Pg. 61

Introduction

Statistics provide an objective, non biased way to evaluated experimental treatments.

Use probability that an event can occur to determine whether or not treatment effects are real.

Measures within and between experimental treatment => allow to select best treatment.

Discussed methodologies associated with:Scientific researchExperimental designsMethods of comparing treatment means

Methodologies associated with scientific research

The hypothesis is tested objectively and either accepted or rejected according to the result obtained.

The null hypothesis : all experiment treatments elicit in a similar response.

Rejection of null hypothesis -> imposed treatment vary in the response that they cause.


Steps in scientific research:1. Define precisely the problem to be solved.2. Formulate set of experimental objectives.3. Establish set of treatment.4. Select experimental materials ( eg. Cultural

vessels, culture medium, growth medium etc.) *selecting treatments and experimental materials based on knowledge of previous experiments.

5. Choose the experimental design along with the observational units, number of replicates per treatment and randomization scheme.


Observational unit Selection of explant type and source influence the

outcome. Most culture tissue, observational unit is the culture

vessel . When there is one explant per culture vessel :▪ Vessel : unit of replication▪ Explant : subsample

Number of replication for degree of replication affect precision of statistical test.

Precision increase as the number of replicates increase. However, plateau when increasing number of replicates

no longer improves precision.


Randomization Each replication assigned to a treatment. Important to make assignment in a manner such

that all have an equal chance of receiving a given treatment.

Schemes vary according to the experimental design employed.

After selecting the treatments and experimental design, one should determine the data to be collected.

Determine the data to be collected. Evaluate and explain treatments effects according to

experimental objectives


ANOVA(Analysis of variance) ANOVA summary tables with all the degree of freedom

(DF) and associated sources of variation (treatment, experimental error, etc.) along with graphs and tables that show the theoretical results constructed to evaluate the effectiveness of the proposed experiment.

Data must be statistically analysed and interpreted as planned before the experiment, according to the hypothesis , experimental conditions and previous facts.

Important to repeat the experiment to confirm results due to some degree of uncertainty regarding the conclusions from an experiments.

Experimental designs: completely randomized design

The completely randomized design Most popular because cell cultures are generally

grown in environmental chambers that accurately control light, temperature and humidity.

The numbers of treatments and replicates per treatment that can be tested are not limited.

Applied even there are missing data or unevenly spaced.

Most precise design because its maximize the degree of freedom (DF) for estimating error.

Reduce F-value to detect statistical difference among treatment.


Case study1 Identify tomato cultivars that displayed high

rates of shoot regeneration from pedicel explants.

Cultured in test tubes that contained 15ml of shoot regeneration medium.

24 tubes replicates per treatment, with the total of 264 experimental units.

Treatments assigned to the experimental units completely at random.

Experimental data ; number of explants with shoots and number of shoots per explant.


Case study1 ANOVA used o analyze the data to determine

the genotypes differed in their ability to produce shoots from pedicel explants.

Generate degree of freedom (DF), sum of squares (SS) and mean square values (MS) for treatment and experimental error to perform statistical test.

Treatment SS for measures the degree of variation associated with the treatment.

Experimental error SS measures variation associated with experimental units.


Case study1 In tomato study , the F-value for treatment (cultivitar)

calculated by dividing its MS (7.937) by the mean square error (MSE).


Case study1 Significance of the observed F-statistics was

determined using 10 and 253 DF. A significance of the observed F-statistics

indicates there are differences in shoot regeneration among treatment means, a mean separation procedure must be performed.

Mean separation procedure should be chosen prior to ANOVA to avoid personal bias in the test because each separation test uses a unique formula when calculating differences among means.


The CRD is most efficient when there is little variation among experimental units.

Efficiency and precision are reduced in situations where there is a high degree of variation is assigned with treatment effects.

Non treatment variation is assigned to experimental error.

In situations, where there is a high degree of outside error and the source can be identified, designs that employs blocking should be used.

Experimental designs :Single factor CRD with subsampling

Culture several explants in a single culture vessel. The response of each explant is measured, resulting

in multiple measurements for each vessel (subsampling).

More efficient when there is a wide range in response among explants.

Statistical precision unit when there is a wide range in response among explants.

Improved by making several measurement per culture vessel, thus reducing variation among replicates of the same treatment.

Subsampling ma be used to study variability among explant, which may be useful in future experiment.


Case study 2 Examined the ability of watermelon cotyledon explant

to produce adventitious shoots illustrates the use of subsampling.

Objective to identify genotypes with high level adventitious shoot organogenesis.

Cotyledons from seedlings of 11 cultivars were cultured in a total of 66 dishes and 330 explants.

Explants from each cultivars assigned to petri dish at random , making sure that only explant from one cultivars cultured together.

The number of explants with adventitious shoots and the number of shoots per explants were recorded.


Case study 2 ANOVA for CRD experiments with subsampling differs

from a CRD with one observational unit per experimental unit in that SS are generated for treatment, experimental error and subsampling error.


Case study 2 A special error term is used for calculating the treatment

F-value and measures variation among experimental units. Subsampling SS represents variation caused by culturing

multiple explants within the same experimental units and not used in computing treatment differences.

Improves statistical precision by removing variation among explants from the experimental error.

In this example, significance among treatment s detected by dividing the treatment with MS by the new MSE, resulting in a significance F-value = 6.83 and indicates that the cultivars displayed varying levels of shoot regeneration.

Statistical test be conducted on the treatment.


Case study 2 When conducting mean separation tests in subsampling

experiments, the special MSE must be used to calculate values for statistical test.

Failure specify the correct error term may result in the grouping of means that should be separated and/or separation of similar means.

subsampling experiments promote efficient use of space and material and measures variability among observational units.

Design not efficient when there is little variation among explants or when there is a high degree of variability from some other identifiable source.

Reduces the DF for experimental error, which means that a higher F-value is required to detect significant differences among treatments.

Little variation among explants, a CRD without subsampling should be used.

If variation from an identifiable outside source exists, a RCBD with subsampling should be used.

Experimental designs :Randomized complete block design (RCBD)

CRD is only efficient when experimental units are homogenous. This is because unrecognized variation, regardless of source, is lumped into the experimental error term.

Heterogeneity among experimental units results in a high MSE and reduces statistical precision.

In experiment with high heterogeneity, it is best to group experimental units into homogeneous units or block.

Grouping experimental units into uniform blocks provides a better estimates of treatment effects ad improves statistical precision.


In RCBDs, treatment are grouped into blocks that contain at least one replicate from each treatment. Experimental units are randomized within blocks, each employing a separate randomized scheme. This minimizes variability within a block while maximizing variability among blocks.

Each block should be as uniform as possible. The number of treatments should be limited

because variability within each block increases as the number of treatment increase.


Based on Case study 1 Arrange into 24 blocks , each containing one test

tubes with a single pedicel explant rom each cultivars from each cultivars.

The ANOVA for a RCBD differs from that of a CRD in that block SS is calculated in addition to treatment and experimental error SS.

Block SS identifies variation controlled by blocking. Treatment SS represent variability related to the

imposed treatment. Experimental error SS measures variability among

experimental units.


Based on case study 1 Blocking improves statistical precision by

removing variability controlled by blocking from the experimental error.

F-value for cultivars (5.99) was obtained by dividing the cultivar MS (7.937) by the MSE (1.326) and significance determined using 10 and 230 DF.

A means separation procedure must be performed to determine which treatment means differ.


Based on case study 1


Based on case study 1 RCBD useful when some variation is caused by

something there than the imposed treatment. If little diffefence among blocks occurs , a RCBD will

not inprove statistical precisio and a CRD should be used.

If there is much variation among explants , a RCBD with subsampling should be used

Experimental designs :Split –plot design

This design used when two treatment factors are superimposed on each other.

One treatment is assigned to main plots that contain all levels of the second factor.

Main plot treatments assigned to subplots are randomized within each main plot.

Each subplot is randomized differently. It identifies experiment error associated

with each treatment factor.

Experimental designs :Split –plot design

Treatments with large experimental error rates assigned to main plots and those with reduced experimental error to subplots.

Dividing experimental error into main plots and subplots improves statistical precision.

The split plot design is most efficient when treatment factors have different experimental error between main plots and subplots.

Factorial experiments

All possible combinations of two or more factors are examined simultaneously.

Allow to examined treatment interdependencies and are more powerful than multiple single factor experiments.

Any of the aforementioned treatment randomization schemes can be used for factorial treatment designs.


Case study 3 Examining the effects of BA and IBA on

tobacco callus growth. Treatment ere three levels (0,1,10 μM) of BA

and IBA arranged in 3x3 complete factorial. Pieces of tobacco callus (1cm3) transferred to

test tubes that contained 15ml of test medium. There were six replicates test tubes per

treatment that were randomized in a CRD. Callus height , diameter, and dry weight

recorded after 1 month after culture initiation.


Case study 3


Case study 3 SS are generated for each treatment, treatment

interaction and for experimental error. F-value for BA, IBA and their interaction were obtained

by dividing the MS for each by the MSE. Significance for the main effects (BA and IBA) was

determined using 2 and 98 DF, whereas significance for the BA by IBA interaction was tested at 4 and 98 DF.

ANOVA indicted that callus growth in the form of dry weight was influenced by BA by IBA simultaneously.

Indicate BA affected callus dry weight differently at each level of IBA and IBA affected callus dry weigh differently at each BA concentration.


Case study 3


Case study 3 Interactions means for this type data are

represented in a line graph with treatment differences estimates using SE.

When treatment interactions are significant, the influence of each treatment separately should not be discussed.


Factorial experiments can become prohibitive with relatively few factors.

For example; The above 3x3 factorial experiment had 9

treatments. If a third factor with three levels was added the

number of treatment combinations would increase to 27.

Add to that 10 replicates and there would be 270 observational units.

Interpretation of higher order interactions may be difficult in any factorial experiment.

Methods for comparing treatment means

Once a significance F-test with a small P-value is obtained, scientist must elucidate specific differences among treatments.

This is not a problem when there are only two treatments because treatments means are simply presented in a table with the associated F-test significance level.

When there are more than two treatment, a post- ANOVA analysis is necessary.

The easiest way to compare treatment means is to rank the in ascending or descending order and pick the best treatments.

Methods for comparing treatment means

The problem with this method is that natural variation that occurs within a treatment is not considered.

There are many mean separation procedures that account for within treatment variation.

These are standard error of the mean (SE), multiple comparison and multiple range tests and regression analysis.

Methods for comparing treatment means : Standard error of the mean

SE is obtained by dividing the sample standard deviation by the square root of the number observations for that treatment.

The size of SE depends on the magnitude f the data.

When using SE for mean separation purposes, treatment means are ranked along with their respective SE and the difference between paired values calculated.

Methods for comparing treatment means : Standard error of the mean

Treatments are declared different if the collective values for the paired treatments do not overlap.

Using SE provides an indication of variability within treatments and allows the reader to make comparisons.

One disadvantages of using SE for mean separation purposes is that t is considered conservative and may only detect differences between means ranked far apart.

Methods for comparing treatment means : Multiple comparison and multiple range tests

Only be used when treatments are unrelated e.g different growth regulators, genotypes etc.

Multiple comparison test use the same critical value to compare adjacent and non adjacent

means. Eg: Bonferoni, Fisher’s least significant difference (LSD), Scheffe’s,

Tukey’s Honestly Significant Difference test (Tukey’s HSD) and Waller-Duncan K-ratio T-test (T-test)

Multiple range test Employ different critical values to compare adjacent and non

adjacent. Protects against commiting type 1 error (instance where treatment are declared different that truly same).

Duncan’s New Multiple Range Test (DNMRT), Ryan Eionot Gabriel Welsh Multple F-test (REGWF) , Ryan Einot Gabriel Welsh Multiple Range Test (REGWQ) and Student Newman Kuels (SNK).

Methods for comparing treatment means : Multiple comparison and multiple range tests

Best used only after obtaining a significant ANOVA.

Most mean separation procedures may be used in situations when a significant ANOVA has not been obtained if specific comparisons were planned prior to data analysis.

High probability to create type 1 error, especially when comparing non adjacents means.

Most recommended mean separation procedures for unrelated treatments; DNMRT, REGWQ, SNK and Tukey’s HSD and Waller-Duncan.

Methods for comparing treatment means : Simple linear regression

Regression, or trend ,analysis used in experiment with quantitative treatments where the primary objective is to develop a model that quantifies the relationship between response variables and treatment levels.

Trend analysis is most appropriate when there are three or more evenly spaced, equally replicated treatments.

A forward step procedure is most often used to identify the best model.

The simplest model (linear) is tested first and more complicated models (quadratic and cubic) tested after rejection of lower order models.


Regression, or trend ,analysis used in experiment with quantitative treatments where the primary objective is to develop a model that quantifies the relationship between response variables and treatment levels.

Trend analysis is most appropriate when there are three or more evenly spaced, equally replicated treatments.

A forward step procedure is most often used to identify the best model.

The simplest model (linear) is tested first and more complicated models (quadratic and cubic) tested after rejection of lower order models.


Lack of fit (LOF), T and r-square (r2) values are used to determine the best model.

A significant T-value and non-significant LOF signify that the model accurately describes the relationship between treatment and response variables.

A significant LOF vale that the model does not fit the data and the other models should be tested.

The r2 value estimates variation described by the model. If a low r2 is obtained it may be advantageous to check

other models. The most appropriate model generally has significant T-

value, non significant LOF, a high r2. Extrapolation must be limited to within treatment

boundaries as the model equation may not accurately describe treatment effects beyond the tested parameters.


Case study 4 Regression analysis used to determine the effects

of sucrose on the growth of grape embryogenic cultures.

Embryogenic cells and somatic embryos (heart and globular stages) incubated on medium containing 60,90,120,150 or 180 g/l sucrose for 3 months.

Sbcultured monthly to fresh medium of the sme composition.

At the end of experiment, embryogenic cultures were dried in oven at 70oC for 72 h and dry weight determined.


Case study 4 ANOVA determined that the sucrose

concentration in the medium influenced the growth of grape embryogenic cultures.

Regression and LOF analyses indicated the growth of grape embryogenic cultures .

Regression and LOF analyses indicated that the data best fit the cubic model as indicted by a significant T- value and non significant LOF value value (-1774.06+57.92-0.4837x2+0.001x3)


Case study 4


Case study 4 Optimum growth obtained when embryogenic

culture incubated on medium with 9 to 120 g/l sucrose.[Fig.7.2]

The high 0.8815r2 obtained for this model indicates that much of the variation in the data was explained by the model.

The term high or low r2 are relative to the data analyzed.

High r2 values for biological data may range between 0.50 and 0.90, whereas a low r2 for non biological data may be 0.90.


Case study 4

Categorical data

Based on counts of individual that can be placed into groups.

This occurs when data consists of yes/no values (eg. Yes the explant responded or no the explant failed to respond) or when explant response is placed into a category (e.g. explants produced roots, shoots, somatic embryos or did not respond).

Categorical data are not continuous and not normally distributed and therefore, cannot be analyzed with the procedures mentioned above.

Chi-square or maximum likelihood are used to analyze categorical data.

Categorical data

Case study 5 Identifying the best dehydration treatment for maize

somatic embryos. Somatic embryo reared on a medium without ABA

(M1) transferred to medium with 0.1M ABA (M2) for 2 weeks , or transferred to M2 for 2 weeks before transfer to medium with 60 g/o sucrose and no ABA (M3) prior to controlled relative humidity dehydration (CRHD) at 70% or 90% relative humidity for 2 weeks .

Embryo survival was determined 2 weeks after transfer to germination medium by the ability of somatic embryo to produce chlorophyll, roots, coleoptiles or leaves.

Control embryos obtained from each of the above media were transferred directly to germination medium without CRHD .

Categorical data

Case study 5 surviving embryos were assigned a 1 ,

whereas those that failed to survived were assigned 0 (no response).

According to ANOVA , culture medium and dehydration treatment simultaneously influenced the ability of maize somatic embryos to survive dehydration as determined by the significant treatment by medium interaction contrast.

The ability of maize somatic embryos to survive dehydration depended on the pretreatment medium and RH level used during CRHD.

Categorical dataCase study 5 SE was used to compare treatment means . Categorical data can be transformed using arc sine prior

to ANOVA and converted back to the original scale for demonstration in tables or graphs.

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Statistical Analysis for Plant Tissue Culture Data

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