Weed control is very important for crop management. Weed density counts or weed control efficacy has been traditionally quantified by manual weed density counts, and it is time-consuming and labor-intensive process. To overcome these challenges, photographic data taken by a digital camera can be used for quantifying weed densities instead of manual assessments. In recent years, many researchers have used image analysis techniques in agricultural research. For instance, Peña et al. (2015) detected weed plants with visible-light and multispectral cameras to obtain highly accurate results of weed detection [1]. Mahlein (2016) introduced RGB, spectral, thermal, fluorescence, and 3D sensors to detect color difference in cell, leaf, plant, plot, field, and ecosystem conditions [2].

Soil fumigants are an important part of the weed control program for strawberries in California. However, regular use of Methyl bromide (MB), the widely used soil fumigant for soil disinfestation in strawberry, has been discontinued in many countries in 2005 due to its ozone-depleting effect [3]. Steam and allyl-isothiocyanate (AITC) are being evaluated as alternatives to MB. Both methods are effective on weed control and do not deplete the ozone layer [4] [5].

RGB imaging is a simple method for quantifying a combination of red (R), green (G), and blue (B) colors. Most people have access to digital camera sensors in mobile phones or tablet PCs, and there are abundant image analysis programs available to analyze RGB data for plant recognition, identification, classification, and leaf area. Despite the technological advances, RGB data are often difficult to interpret due to lack of appropriate statistical methods for comparison. Downie et al. (2015) noted that limitations for image analysis still exist in statistical processes [6].

Some researchers have applied statistical hypothesis testing to RGB data. Woebbecke et al. (1995) tested and compared various color indices using t-tests to distinguish between a green plant from a nonplant background [7]. Golzarian et al. (2012) used the non-parametric Kruskal-Wallis and Friedman tests, which are alternatives to parametric ANOVA tests, to compare various color indices [8]. They used 240 digital images of wheat, ryegrass, brome grass, and wild oat, and they found that the 2G-R-B index (known as the excessive green index or EGI) is computationally simple and effective when the contrast between the background and the target is high. Longchamps et al. (2012) used the non-parametric Friedman test to compare the weed coverage in three different areas of ground by randomly selecting 110 images per plot [9].

In this article, RGB data were obtained from non-treated (control), steam, and AITC treatments. According to the previous studies, a traditional multiple comparison test, the Dunnett-Tukey-Kramer (DTK) test, and two alternative statistical methods, a bootstrap method and the Poisson model, were evaluated via simulation studies to compare their statistical power. The Poisson model can be applied to the case when the number of green spots is very low, and it was indicated in the current study. The two alternative statistical methods were preferred because they were more sensitive (i.e., higher statistical power). After confirming their advantage in the simulation studies, these two alternative statistical methods were applied to provide statistical evidence for effect of steam and AITC on weed control.

For the DTK test discussed in the previous section, an estimated proportion of green area (e.g., 0.2206) is treated as a single data point. In other words, the DTK test ignores individual pixel values for each green color obtained from the image analysis program, and it treats the entire data as a sample of size three per treatment. In this section, in order to utilize detail information contained in the RGB data, a bootstrap method and a Poisson model are considered for pairwise comparisons. The bootstrap method estimates and compares the proportion of green area, and a Poisson model estimates and compares the expected count of a small green spot in the case of a rare occurrence of weed. In a later section, the operating characteristics of the bootstrap method and the Poisson model (e.g., Type I error rate and statistical power) are compared to the operating characteristics of the DTK test by simulation studies.

The non-numeric values (RGB codes) have been transformed to the proportion of green area which is a numeric value between zero and one. The general structure of the data per treatment group is demonstrated in Table 1. In the table, let R_i, G_i, and B_i denote the decimal code of red, green, and blue in the i^th row. Let W_i denote the weight of the i^th row such that ∑ i = 1 n W i = 1. For example, in a previous section, W₄₂ = 19151/3422208 = 0.0056 was calculated. According to the RGB decimal code, Z_i = 1 if G_i > R_i and G_i > B_i and Z_i = 0 otherwise. Then the proportion of green area in the microplot is estimated by the weighted sum S = ∑ i = 1 n W i Z i.

In this section, three hypothesis testing methods, the bootstrap method, the Poisson model (with LRT), and the DTK test, are evaluated. Various scenarios were considered under H₀ and under H₁. In a case of H₀, the probability of rejecting H₀ (type I error rate) should be close to α = 0.05. In a case of H₁, the probability of rejecting H₀ (statistical power) should be high. The Bonferroni’s correction was used with the bootstrap method, and it was not for the Poisson approach because H₁ of the LRT negates H₀: θ₀ = θ₁ = θ₂ (i.e., at least one pairwise difference is nonzero).

From the actual data described in a previous section, μ₀₁, μ₀₂, and μ₁₂ were estimated as 1.57, 263.7, and 168.3, respectively, using the bootstrap method. When Group 0 (control) was compared to Group 1 (Dominus), the estimated proportion of green area was 1.6 times greater. When Group 0 was compared to Group 2 (steam), it was 264 times greater. When Group 1 was compared to Group 2, it was 168 times greater. The resulting bootstrap CIs were (1.13, 2.29), (137.6, 726.0), and (90.4, 451.2), respectively. At significance level α = 0.05, all three pairwise groups were significantly different. This conclusion is different than the conclusion from the aforementioned DTK test. In particular, steam is substantially more effective than both control and Dominus, and Dominus is slightly more effective compared to control. Using the Poisson model with LRT, the resulting p-value was nearly zero, and the respective CIs for μ_jk were (1.17, 1.97), (7.78, 29.18), and (5.07, 19.43) which are different than the CIs using the bootstrap method. Recall that θ_j is interpreted as the proportion of green area in the bootstrap method, and it is interpreted as the expected count of green spots in the Poisson model.

Fig 4 graphically presents the resulting CIs from the DTK method (left), the bootstrap method (middle), and the Poisson model (right). To avoid the extremely large magnitude of the CIs in the figure, the resulting CIs for μ_jk were log-transformed, so the null value became zero after the log-transformation in the bootstrap method and the Poisson model.

In the data collection, there was an additional experimental group, a combination of steam and Dominus (referred to as Group 3). In three microplots of Group 3 (steam + Dominus), the observed green areas were 0.0004, 0.0006, and 0.0004. In the three microplots of Group 2 (steam only), recall that the observed green areas were 0.0008, 0.0003, and 0.0007. Since these are very low proportions (i.e., W_i is close to zero for Z_i = 1), the Poisson model would be more appropriate to compare these two experimental groups. μ₂₃ was estimated as 0.82 with a 95% CI (0.41, 1.67). As shown in S1 Fig, the effect of steam was nearly 100% effective by itself, so it would make sense that Dominus would not improve upon the effect of steam. It appears that the estimated μ₂₃ is accurate under the Poisson model.

All supporting information including data and R code are available in S1 Fig, S1, S2 and S3 Files, and S1 Code.

Woebbecke et al. (1995) reported that the 2G-R-B index (known as the excessive green index or EGI) or the modified hue was sensitive for separation of plants and soil [7], so the similar idea was applied for separation of weeds and soil in this study. Although they used a modified version of the EGI, Golzarian et al. (2012) reported that the EGI is computationally simple and effective when the contrast between the target (weed) and the background (soil) is high [8]. Among various indices for defining “green,” the simple definition “G > R and G > B” was used in this study, and the effect of steam was statistically significant based on the bootstrap approach and the Poisson approach. These approaches also detected the small effect of Dominus based on three microplots per group. These results reflect that an appropriate statistical method can leverage the sensitivity of simple color indices. Our supplementary experiment showed that even smart phones are highly reliable for estimating the proportion of green area with an intraclass correlation of 0.9 when three randomly chosen smartphones were tested [19] [20] [21]. (The data of supplementary experiment are available in S4 File.) Therefore, the simple color indices, together with the statistical methods demonstrated in this article, can be an alternative strategy for examining the effects of weed control and other similar types of comparative analysis, particularly when a large sample size is not available. Most of the aforementioned studies focused on the technical advantages of various color indices with a less of an emphasis on statistical methodology to detect the effect of a treatment.

There are many statistical methods available for comparing two or more treatments such as ANOVA with Tukey’s range test, Dunnett-Tukey-Kramer (DTK) test, Kruskal-Wallis test, and Friedman test [22], [12] [23] [24] [25] [26]. If one of these statistical methods was considered, the RGB data would be treated as a sample of size three per treatment, and the hypothesis testing would suffer from low statistical power. For instance, the DTK test is a popular hypothesis testing method in agricultural studies to test for difference in means under the normality assumption with unequal variances [12]. With such a small sample size per group, it is difficult to check the normality assumption, and even if the assumption is true, there should be low statistical power for comparing treatment effects. To this end, two alternative statistical methods, bootstrap method and Poisson model, were considered for the RGB data. The simulation results demonstrated that the bootstrap method and the Poisson model provide higher statistical power while preserving the type I error rate at α = 0.05. In the applied example, the DTK only detected the difference between steam and control, but the bootstrap method and the Poisson model detected the difference among steam, Dominus, and control. In addition, unlike the non-parametric tests (e.g., Kruskal-Wallis and Friedman), the bootstrap method and the Poisson model can address the research objective with interpretable parameters. The bootstrap approach can estimate the relative proportion of weed area between two treatments, and the Poisson approach can estimate the relative average count of weed per given area between two treatments when the occurrence is rare. After determining the outperformance of these alternative methods when compared to the DTK test via the simulation studies, they were applied to the RGB data to compare the three treatment groups on weed control.

In the simulation study presented in this article, a number of assumptions were simplified, and more investigations are needed under weaker assumptions. In the weed control experiment presented in this article, all microplots were located close to each other (about one meter apart between two neighboring microplots), and they were completely randomized to one of the treatments. Because it was an outdoor experiment, there could be additional random error among the microplots due to environmental factors and other unknown factors. For instance, the weed species composition was not the same in all plots which may have contributed to variation. If these factors are significant, the Poisson model approach described in this manuscript can lead to an inflated Type I error rate in over-dispersed data. According to the simulation study, the Poisson approach outperforms the bootstrap approach in terms of both Type I error and power. In a case of severe over-dispersion, the Type I error rate should be controlled, and a quasi-Poisson model or a generalized linear mixed model may be considered alternatively. Comparing to these alternative approaches, the relative performance of the bootstrap approach remains unknown, and it is a potential topic for future research. In the simulation study, the Bonferroni’s correction was used for multiple comparisons, and an alternative correction method could be used. Benjamini and Hochberg (1995) discussed another procedure of multiple comparisons based on ranking p-values [27]. The choice of a correction method was not a main focus in this article, but it is an important topic in agricultural studies which involve many comparisons. The procedure of ranking p-values also controls the false discovery rate (i.e., Type I error rate), and it may be more powerful particularly when the number of comparisons is very large. Despite the fact that the estimated green proportions were generally lower in the Dominus group than in the control group, the observed variance was greater in the Dominus group. If it was the case for the count data (i.e., lower expected counts with higher variance), the data could not conform the mean-variance relationship of the Poisson model. In this case, the zero-inflated Negative-Binomial distribution would be a more flexible approach than the Poisson distribution, and this comparison was not made in the simulation study. Future research should focus on the impact of the simplified assumptions when the truth is more complex, and any negative consequences (e.g., an inflation of Type I error, a loss of statistical power) should be addressed by more sophisticated statistical methods than the methods discussed in this article.

The bootstrap method and the Poisson model (particularly for rare green spots of weed occurrence) result in substantially higher statistical power than the DTK test. The bootstrap method and the Poisson model are more powerful than the DTK test because they utilize detail information (pixels) obtained from each microplot, whereas the DTK test treats an observed green proportion in a microplot as a single data point. Using the bootstrap method and the Poisson model, it was evident that weed control with steam is effective for at least 31 days, and weed control with steam is significantly more effective than weed control with Dominus. The powerful statistical methods described here are recommended particularly when the sample size is small. The combination of the RGB analysis and the statistical methods can be useful for various purposes such as interim evaluations (e.g., monitoring and quantifying color changes until a final harvest) and final evaluations in a large field (e.g., areas where it is practically impossible to count weeds).