SAMPLE SIZE FOR ASSESS THE LEAF BLAST SEVERITY IN EXPERIMENTS WITH IRRIGATED RICE

The aim of this study was to determine the sample size needed to assess the severity of leaf blast in rice in experiments with different fungicide treatments. The severity and the area under the disease progress curve data of three chemical disease control treatments carried out in Rio Grande do Sul, were used in the study. Analysis of variance was performed to verify whether the severity of the disease differed between treatments. The spread of disease was was also found to be different between treatments and assessments, using the variance/mean ratio and Morisita index. The spatial distribution of the disease among the treatments and during the evaluations is important for the choice of the equation used to calculate the sample size. The spatial distribution of the disease was not the same across the experiments, and it varied between treatments and evaluations. Thus, we decided to use a formula that was not associated with distributions to indicate the spatial distribution (negative binomial or Poisson) of the disease in the field. The sample size to estimate the average of rice leaf blast severity varied between treatments and evaluations. The area under the disease progress curve is necessary to be determined to reduce the number of samples needed. Thus, it is recommended to assess 293 sheets to estimate severity, and 63 to estimate AUDPC at 20% error.


INTRODUCTION
The leaf blast caused by the fungus Pyricularia grisea (Cooke) Sacc.(=Pyricularia oryzae Cavara) is a disease commonly found in irrigated rice.The characteristic symptoms of the disease on the leaves are elliptical lesions with a gray center and reddish brown edges, with the reproductive structures (conidia) of the pathogen in the necrotic center (BEDENDO, 1997).The disease occurs in all rice-producing areas and results in yield losses that can reach 100% (FILIPPI et al., 2007).Owing to the high potential for damage caused by leaf blast on rice, research on fungicide efficiency is critical for proper disease management, as well as to find an alternative way to chemical control, which is one of the main methods to control rice leaf disease (CELMER et al., 2007;SANTOS et al., 2008).
In agricultural experiments, the quality of the results obtained depends on experimental precision.Therefore, the experimental error corresponding to the variation between repetitions of the same treatment must be minimized so that the effect of the treatments is reliably estimated (CATAPATTI et al., 2008).Experimental precision can be improved by the proper sizing of the number of repetitions and choice of experimental design (STORCK et al., 2006;CATAPATTI et al., 2008).However, many variables must be obtained by sampling experimental plots (KRAUSE et al., 2013), since the entire population cannot be sampled due to the excessive demand for labor, time, and financial resources.Sampling within the plot also generates a new variance within the plot, and this should be minimized by an appropriate sample size (CARGNELUTTI FILHO et al., 2009).
Sample size is influenced by the variability of the data, which is affected by genetic and environmental factors (MARTIN et al., 2005;CARGNELUTTI FILHO et al., 2008),the application of treatments (TOEBE et al., 2011),and, in case of pests and diseases, by their spatial distribution in the field (LÚCIO et al., 2009;MICHEREFF et al., 2011).The distribution of the disease in the field influences the choice of methodology to calculate sample size.For randomly distributed diseases, the Poisson distribution is used for sample calculation, whereas in the case of aggregated distribution, the k parameter of the negative binomial distribution is the most informative (MICHEREFF et al., 2008;MICHEREFF et al., 2011).
Plant disease sampling has been widely studied, including the determination of sample size for the quantification of water-stain (Acidovorax avenae subsp.citrulli) in melon (SILVA et al., 2003), soft rot (Pectobacterium carotovorum subsp.Carotovorum Jones) in lettuce and Chinese cabbage (SILVA et al., 2008), leaf blight (Curvularia eragrostidis P. Henn.Meyer) in yam (MICHEREFF et al., 2008) and cercospora spot (Cercospora capsici) in chili (MICHEREFF et al., 2011).However, no published studies have estimated the sample size for the quantification of leaf blast of irrigated rice.
The purpose of this study was to determine the sample size, i.e., the number of leaves needed to assess the severity of leaf blast on irrigated rice, in experiments with different fungicide treatments.

MATERIAL AND METHODS
All data used in this study are from three chemical control experiments of the blast in irrigated rice, one conducted in agricultural harvest 2009/2010 and two in agricultural harvest of 2010/2011.All field experiments were performed in an experimental area in the Santa Maria-RS, with an altitude of 95 m, latitude 29°43′43.2″S,and longitude 53°33′43.9″W.In the agricultural harvest of 2009/2010, sowing was carried out on 01/06/10, while in the agricultural harvest 2010/2011, it was carried out on 12/23/2010.Late sowing was conducted with the aim to enhance the severity of the blast, subjecting the rice plants to conditions favorable for the development of the disease.Seeding rate, fertilization, weed and pest control followed the technical recommendations for the culture (SOSBAI, 2007).
A randomized block design, with four repetitions, was used in all experiments.The experimental plots were 2 m wide and 5 m long.The treatments and cultivars of each experiment are described in detail in Table 1.Fungicides were applied with the aid of a precision backpack sprayer pressurized with carbon dioxide, consisting of a bar with four nozzles, spaced 0.5 m from each other.The spray tip used was type XR 110015, and spraying was calibrated to an application volume of 150 L ha -1 .In all experiments, two fungicide applications were performed, with the first being carried out during the phenological stage of anthesis (COUNCE et al., 2000) and the second 14 days thereafter.
The variables studied were the severity of rice blast and the area under the disease progress curve (AUDPC).Severity assessments of the disease were carried out 7, 14 and 21 days after fungicide application.For each replication (plot), 10 flag sheets were randomly assigned (for a total of 40 sheets per treatment), and a value corresponding to the percentage of leaf area with disease symptoms was assigned to each one.To assign blast severity values to leaves, a diagrammatic scale proposed by the International Research Institute of Rice (IRRI, 2002) was used.
Table 1.Year of performance, cultivars and doses of fungicides used in the three experiments.

¹ Treatments.
The area under the disease progress curve (AUDPC) was subsequently calculated using the severity values obtained in the three assessments.The AUDPC for each treatment was calculated by the equation: where i is the number of days after the application of fungicides, Y is the percentage of leaf area affected by the blast at observation i, T i is the time of evaluation, and T i+1 is the evaluation time i+1.
Disease severity data (percentage of leaf area attacked by the pathogen) and AUDPC were subjected to the Shapiro-Wilk and Levene tests, to assess normality and homogeneity of errors, respectively.When these assumptions were violated, the variables were transformed using the Box-Cox methodology.In cases where assumptions continued to be violated even after transformation, the nonparametric Friedman test was used to detect differences between treatments (STORCK et al., 2006).The difference in severity was examined to assess whether the 40 leaves evaluated in each treatment should or should not be considered a specific sample.
Then, considering the 40 leaves evaluated in each treatment, the following statistics were calculated: minimum, maximum, mean, standard deviation, variance, and average coefficient of variation.To determine whether the 40 leaves should or should not be considered as a specific sample, a Levene test was again applied to verify the homogeneity of the variances, referring to the data for the severity of the blast in the following situations: between treatments in each experiment and between evaluations in each treatment.As for the AUDPC variable, the homogeneity of variances between treatments was verified.
The sample size (number of flag leaves) required to estimate the severity of AUDPC was determined for each treatment in each evaluation, using the following equation: where t α/2 is the critical value of the Student's t distribution (α = 0,05); is the sample variance; corresponds to the average severity of the disease in 40 leaves evaluated per treatment; and corresponds to the pre-established acceptable errors of 5%, 10%, 15%, 20, 25%, and 30%.
It is noteworthy that the theoretical distributions used in the two equations above are related to the nature of the study variables.The severity is proportional and follows a standard normal distribution when the sample is large (greater than 30); AUDPC is a continuous variable presenting a normal distribution (confirmed by the Shapiro-Wilk test), and it can be represented by the Student's t distribution.
All statistical analyses were performed at α = 5%, using the R software (R DEVELOPMENT CORE TEAM, 2012) and Microsoft Excel ® .
The high experimental error leads to an increased mean square of the experimental error, hindering the H 0 rejection of the hypothesis and raising possibility of Type II error (STORCK et al., 2006).Thus, the number of repetitions must be increased along with proper sizing of the sample size, which could contribute to reduced experimental error and thus obtain more precise conclusions (CARGNELUTTI FILHO et al., 2008;CARGNELUTTI FILHO et al.,2009;KRAUSE et al, 2013).
Variances of the data observed were heterogeneous between treatments, both for severity and AUDPC variable, in all experiments.The heterogeneity of variances of the data observed between assessments was observed in 79,41% of the treatments.The difference in blast's severity, disease progress (determined by AUDPC) between treatments, heterogeneity of variances of the data observed between treatments and evaluations showed that the 40 leaves evaluated in each treatment should be considered as an independent sample.Therefore, we chose to determine the sample size required to evaluate the severity of the blast and AUDPC for each treatment and assessment, separately.
The variability observed in field experiments is usually attributed to environmental factors, soil variability, or genetic factors (MARTIN et al., 2005;CARGNELUTTI FILHO et al., 2009;LÚCIO et al., 2009).However, in the case of diseases, factors such as the spread of the disease on the field must also be taken into consideration (MICHEREFF et al., 2011).
To obtain an optimal sample size, different conditions are desirable so that the recommendation is not so limited.In case of diseases, sampling practices should be considered among the different field conditions, since disease spread and, therefore, sample size may vary according to the year, sowing time, cultivation site, and time of evaluation (SILVA et al., 2008;MICHEREFF et al., 2008;MICHEREFF et al., 2011).
The interpretation of the values referring to the average coefficient of variation of blast severity and area under the disease progress curve variables (Table 2, 3 and 4) is indicative of the variation between the leaves evaluated and, thus, the sample size (STURMER et al., 2013).The larger the coefficient of variation, the greater the dispersion of the observations around the average, suggesting the need for a larger number of samples (number of flagged leaves) for more accurate estimation.Based on these values, the tendency of the sample size to be higher for the estimation of blast's severity in relation to AUDPC was observed.
From blast disease severity data, the distribution of the disease in each treatment and evaluation was determined.Variance/mean ratio and Morisita index values greater than 1 indicate an aggregated dispersion of the disease, whereas values less than or equal to 1 indicate a random dispersion (Table 2, 3 and 4).The type of distribution of the disease is associated with the statistics used to estimate the sample size.According to Campbell and Madden (1990), if the distribution of the disease is aggregated, the size of the sample is calculated by the equation , where k is a parameter associated with the negative binomial distribution, describing the aggregated arrangement of infected plants.According to the same authors, infected plants spread randomly in the field follow the Poisson distribution, which is characterized by .In this case, the equation used to calculate the sample size is .Finally, when the dispersion of the disease is not the same over time or between treatments, as in this study, the recommended formula to determine the sample size is , which many authors refer to as undetermined distribution.In our experiments, the dispersion of leaf blast was dependent on the treatment and the time of evaluation.The type of distribution of the disease was not the same throughout the experiment, indicating that the method used to calculate the sample size in this The sample size for the average estimation of blast's severity was different among treatments and evaluations.This behavior was expected, since the difference observed in the average severity of treatments and evaluations, as well as the heterogeneity of variances between treatments and evaluations in each treatment, leads to changes in the ratio between variance and variables average values.This ratio is indicative of disease spread in the field, which affects the sample size, and this relationship was included in the methodology used.Thus, three sample sizes per treatment (one evaluation) were estimated for this variable, with only the largest presented in Table 6.
In case of AUDPC, only one sample size was determined per treatment.It was observed that the tendency to reduce the number of flagged leaves evaluated when using the AUDPC variable in relation to severity variable.AUDPC is widely used in phytopathological studies, as it characterizes the interaction between the pathogen, the environment and the host, in addition to being used as a form of evaluation of control strategies (BERGAMIN FILHO, 1997).Table 6.Sample size, given as expressed as number of flagged leaves per plot, to estimate the average severity and area under the disease progress curve (AUDPC) of the blast in the three experiments analyzed.
For an acceptable error of 5%, the sample size required to estimate the average severity of blast is of 4696 flag leaves.As for AUDPC variable, the number of leaves that needs to be evaluated is 1014 (Table 6).The evaluation of this number of leaves becomes impractical, due to the amount of labor and time required.Therefore, it is recommended to use larger sample sizes with greater pre-established errors.Furthermore, the use of the variable AUDPC is recommended whenever possible, as a means of comparison between treatments.Therefore, for an error of 20% and confidence level of 95%, the evaluation of 63 flag leaves is necessary to estimate AUDPC, a more common form of quantification of the disease in works in the plant pathology field.If an experiment is formed of 4 repetitions, it is necessary to evaluate 16 leaves per plot.
The greater the precision required the more the leaves that should be evaluated.The accuracy of the estimate and, subsequently, the sample dimension should be left to the researcher, as the ideal sample size will depend on the minimum acceptable error in every situation (type of study) as well as the labor and resources available to each researcher (MICHEREFF et al., 2008;MICHEREFF et al., 2011;TOEBE et al., 2011;STÜRMER et al., 2013).

CONCLUSION
A variability of the sample size was observed in the evaluation of leaf blast, according to the treatments used and type of evaluations carried out over time.The sample size required to estimate the average area under the blast progress curve is smaller than that to assess severity.For an acceptable error of 20%, the sample size per plot required to estimate the average severity of the blast is 293 flag leaves and for the variable AUDPC, the number of flag leaves to be evaluated is 63.

Table 2 .
Minimum and maximum values, mean, standard deviation (SD), variance, coefficient of variation (CV) variance, mean ratio (R), and Morisita index (I δ ) of blast's severity, and area under the disease progress curve, in experiment 1.* Randomness rejected at 5% probability of error.nsRandomness is not rejected.¹Treatmentsdescribedin details in Table1.-Values not calculated.

Table 2 .
Continuation.*Randomness rejected at 5% probability of error.ns Randomness is not rejected.¹Treatments described in details in Table 1.-Values not calculated.

Table 3 .
Minimum and maximum values, mean, standard deviation (SD), variance, coefficient of variation (CV) variance, mean ratio (R), and Morisita index (I δ ) of blast's severity, and area under the disease progress curve, in experiment 2.
* Randomness rejected at 5% probability of error.ns Randomness is not rejected.¹Treatments described in details in Table 1.-Values not calculated.

Table 4 .
Minimum and maximum values, mean, standard deviation (SD), variance, coefficient of variation (CV) variance, mean ratio (R), and Morisita index (I δ ) of blast's severity, and area under the disease progress curve, in experiment 3.*Randomness rejected at 5% probability of error.nsRandomness is not rejected.¹Treatmentsdescribedin details in Table1.-Values not calculated.

Table 5 .
Summary of the analysis of variance (ANOVA) of the three experiments for the area under the disease progress curve (AUDPC).
Significant effect by the F test at 5% error probability; : ns Not significant effect according to the F test at 5% error probability.¹Experimentsdescribed in details in Table1; ²SV = Sources of variation; DF = degrees of freedom; MS = Mean square; CVa = coefficient of variation of the amostral error; CVe = coefficient of variation of the experimental error; SW ( p-value) = pvalue of the Shapiro-Wilk normality test; Levene (p-value) = pvalue of the homogeneity test of Levene variances. *