Proportion data from dose-response experiments are often overdispersed, characterised by a larger variance than assumed by the standard binomial model. Here, we present different models proposed in the literature that incorporate overdispersion. We also discuss how to select the best model to describe the data and present, using R software, specific code used to fit and interpret binomial, quasi-binomial, beta-binomial, and binomial-normal models, as well as to assess goodness-of-fit. We illustrate applications of these generalised linear models and generalised linear mixed models with a case study from a biological control experiment, where different isolates of Isaria fumosorosea (Hypocreales: Cordycipitaceae) were used to assess which ones presented higher resistance to UV-B radiation. We show how to test for differences between isolates and also how to statistically group isolates presenting a similar behaviour.

Metarhizium comprises a phylogenetically diverse genus of entomopathogenic fungi. In Brazil, Metarhizium anisopliae s.str. subclade Mani 2 is predominantly isolated from insects, while M. robertsii and M. brunneum mostly occur in the soil environment. Solar radiation and high temperatures are important abiotic factors that can be detrimental to fungal propagules. We hypothesized that among 12 Brazilian isolates of Metarhizium spp., M. anisopliae Mani 2 (n = 6), being adapted to abiotic conditions of the phylloplane, is more tolerant to UV light and high temperatures than M. robertsii (n = 3) and M. brunneum (n = 3). Inoculum of each isolate was exposed to UV-B for up to 8 h and viability evaluated 48 h later. After 8 h under UV-B, most of the isolates had germination rates below 5%. Discs of mycelia were incubated at different temperatures, and diameter of colonies were recorded for 12 days. Mycelia of M. robertsii isolates grew faster at 33 °C, while M. anisopliae and M. brunneum grew most at 25 °C. Dry conidia were incubated at 20, 25 or 40 °C for 12 days, and then viabilities were examined. At 40 °C, conidia of five M. anisopliae isolates were the most tolerant. In the three experiments, considerable intra- and inter-specific variability was detected. The results indicate that conclusions about tolerance to these abiotic factors should be made only at the isolate level.

In order to identify products acceptance and commercialization, researchers performed sensory evaluation. The responses to these studies are ordinal categorical variables, thus, they are normally based on a hedonic scale. Generally, in sensory experiments, each judge evaluate several products and the answers given by the same judge can be classed as repeated measures. In this paper, we propose an alternative statistical analysis to consider the natural ordering and repeated measures simultaneously using proportional odds mixed models. Such models were proposed to compare the taste acceptance of two varieties of tomato, Italian and Sweet Grape, after the osmotic dehydration process. The experiment was designed in the way that each judge, randomly selected and evaluated each variety once. The results showed that the Sweet Grape presented better acceptance than Italian variety. This model allowed the predictions and estimations probabilities to be calculated for each of the response categories according to each variety. Practical applications Tomate is a product highly perishable and new dehydration techniques are being developed and needs to have good accepted by consumers. In this paper, we proposed an alternative statistical model to compare the taste acceptance of two varieties of dehydrated tomato, Italian and Sweet Grape. The model presented can be used in different sensorial evaluations and can help researchers to analyze ordinal categorical data, focusing on how to identify and account for specific issues arising from experimental design (such as correlated observations). The results showed that the Italian tomato was 6.89 times more likely to be classified with lower scores at hedonic scale compared to Sweet Grape tomato regardless of sex. The Sweet Grape variety has a probability of 44% (32%; 57%) of receiving score 9 and for Italian variety this happens with a probability equal of 10% (5%; 19%). In addition, the results showed no significant correlation between responses from the same judge.

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