The robustness of F-test to non-normality has been studied from the 1930s through to the present day. However, this extensive body of research has yielded contradictory results, there being evidence both for and against its robustness. This study provides a systematic examination of F-test robustness to violations of normality in terms of Type I error, considering a wide variety of distributions commonly found in the health and social sciences. We conducted a Monte Carlo simulation study involving a design with three groups and several known and unknown distributions. The manipulated variables were: Equal and unequal group sample sizes; group sample size and total sample size; coefficient of sample size variation; shape of the distribution and equal or unequal shapes of the group distributions; and pairing of group size with the degree of contamination in the distribution. The results showed that in terms of Type I error the F-test was robust in 100% of the cases studied, independently of the manipulated conditions.

Parametric statistics are based on the assumption of normality. Recent findings suggest that Type I error and power can be adversely affected when data are non-normal. This paper aims to assess the distributional shape of real data by examining the values of the third and fourth central moments as a measurement of skewness and kurtosis in small samples. The analysis concerned 693 distributions with a sample size ranging from 10 to 30. Measures of cognitive ability and of other psychological variables were included. The results showed that skewness ranged between −2.49 and 2.33. The values of kurtosis ranged between −1.92 and 7.41. Considering skewness and kurtosis together the results indicated that only 5.5% of distributions were close to expected values under normality. Although extreme contamination does not seem to be very frequent, the findings are consistent with previous research suggesting that normality is not the rule with real data.

Statistical analysis is crucial for research and the choice of analytical technique should take into account the specific distribution of data. Although the data obtained from health, educational, and social sciences research are often not normally distributed, there are very few studies detailing which distributions are most likely to represent data in these disciplines. The aim of this systematic review was to determine the frequency of appearance of the most common non-normal distributions in the health, educational, and social sciences. The search was carried out in the Web of Science (WOS) database, from which we retrieved the abstracts of papers published between 2010 and 2015. The selection was made on the basis of the title and the abstract, and was performed independently by two reviewers. The inter-rater reliability for article selection was high (Cohen’s kappa = 0.84), and agreement regarding the type of distribution reached 96.5%. A total of 262 abstracts were included in the final review. The distribution of the response variable was reported in 231 of these abstracts, while in the remaining 31 it was merely stated that the distribution was non-normal. In terms of their frequency of appearance, the most-common non-normal distributions can be ranked in descending order as follows: gamma, negative binomial, multinomial, binomial, lognormal, and exponential. In addition to identifying the distributions most commonly used in empirical studies these results will help researchers to decide which distributions should be included in simulation studies examining statistical procedures.

Test anxiety has detrimental effects on the academic performance of many university students. Moreover, female students usually report higher levels of test anxiety than do their male peers. The present study examined gender differences in test, trait, and math anxiety among university students, as well as differences in their academic achievement. Participants were 168 students from the University of Barcelona, all of whom completed measures of test anxiety, math anxiety, and trait anxiety. They were also asked about their expected level of anxiety when faced with four specific test situations: multiple-choice, open-question, oral presentation, and an exam involving calculations. At the end of the course in which they were enrolled, students were assessed through a multiple-choice and an open-question exam. Compared with their male counterparts, female students reported higher levels of test, math, and trait anxiety, as well as greater expected anxiety in three of the four test situations considered. However, females did not show lower academic achievement than male students in either the open-question or the multiple-choice exams. These results are discussed in terms of gender differences in socialization patterns and coping styles

This study examines whether math anxiety and negative attitudes toward mathematics have an effect on university students" academic achievement in a methodological course forming part of their degree. A total of 193 students were presented with a math anxiety test and some questions about their enjoyment, self-confidence and motivation regarding mathematics, and their responses were assessed in relation to the grades they had obtained during continuous assessment on a course entitled"Research Design". Results showed that low performance on the course was related to math anxiety and negative attitudes toward mathematics. We suggest that these factors may affect students" performance and should therefore be taken into account in attempts to improve students" learning processes in methodological courses of this kind