Sample size for estimation of the Pearson correlation coefficient in cherry tomato tests

portuguesO objetivo deste trabalho foi determinar o tamanho de amostra necessario para estimar o coeficiente de correlacao de Pearson entre variaveis do tomate cereja. Foram instalados dois ensaios de uniformidade em ambiente protegido na primavera/verao de 2014. As variaveis observadas em cada planta foram comprimento medio de fruto, largura media de fruto, peso medio de fruto, numero de cachos, numero de frutos por cacho, numero de frutos e peso total de frutos, sendo calculada a matriz de correlacao de Pearson entre elas. Foram planejados 68 tamanhos de amostra em uma estufa e 48 em outra, com tamanho inicial composto de 10 plantas e os demais obtidos acrescentando cinco plantas. Para cada tamanho de amostra planejado foram obtidas 3000 estimativas do coeficiente de correlacao de Pearson atraves de reamostragens “bootstrap” com reposicao. O tamanho de amostra de cada coeficiente de correlacao foi determinado quando o valor da amplitude do intervalo de confianca de 95% foi menor ou igual a 0,4. A obtencao das estimativas do coeficiente de correlacao de Pearson com elevada precisao e dificil para caracteres com relacao linear fraca e, consequentemente, maior e o tamanho amostra necessario para estima-los. As relacoes lineares envolvendo as variaveis relacionadas com o tamanho e o numero de frutos por planta tem menor precisao. Para estimar o coeficiente de correlacao entre variaveis produtivas do tomate cereja, com intervalo de confianca de 95% igual a 0,4, e necessario amostrar 275 plantas na estufa de 250m², e 200 plantas na estufa de 200m². Palavras-chave: Solanum lycopersicum var. cerasiforme; amostragem; reamostragem; ”bootstrap”. EnglishThe aim of this study was to determine the required sample size for estimation of the Pearson coefficient of correlation between cherry tomato variables. Two uniformity tests were set up in a protected environment in the spring/summer of 2014. The observed variables in each plant were mean fruit length, mean fruit width, mean fruit weight, number of bunches, number of fruits per bunch, number of fruits, and total weight of fruits, with calculation of the Pearson correlation matrix between them. Sixty eight sample sizes were planned for one greenhouse and 48 for another, with the initial sample size of 10 plants, and the others were obtained by adding five plants. For each planned sample size, 3000 estimates of the Pearson correlation coefficient were obtained through bootstrap re-samplings with replacement. The sample size for each correlation coefficient was determined when the 95% confidence interval amplitude value was less than or equal to 0.4. Obtaining estimates of the Pearson correlation coefficient with high precision is difficult for parameters with a weak linear relation. Accordingly, a larger sample size is necessary to estimate them. Linear relations involving variables dealing with size and number of fruits per plant have less precision. To estimate the coefficient of correlation between productivity variables of cherry tomato, with a confidence interval of 95% equal to 0.4, it is necessary to sample 275 plants in a 250m² greenhouse, and 200 plants in a 200m² greenhouse. Key words: Solanum lycopersicum var. cerasiforme; sampling; resampling; bootstrap.