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.

Introduction: One-way repeated measures ANOVA requires sphericity. Research indicates that violation of this assumption has an important impact on Type I error. Although more advanced alternative procedures exist, most classical texts recommend the use of adjustedF-tests, which are frequently employed because they are intuitive, easy to apply, and available in most statistical software. AdjustedF-tests differ in the procedure used to estimate the corrective factorε, the most common being the Greenhouse-Geisser (F-GG) and Huynh-Feldt (F-HF) adjustments. Although numerous studies have analyzed the robustness of these procedures, the results are inconsistent, thus highlighting the need for further research.Methods: The aim of this simulation study was to analyze the performance of theF-statistic,F-GG, andF-HFin terms of Type I error and power in one-way designs with normal data under a variety of conditions that may be encountered in real research practice. Values ofεwere fixed according to the Greenhouse–Geisser procedure (ε̂). We manipulated the number of repeated measures (3, 4, and 6) and sample size (from 10 to 300), withε̂values ranging from the lower to its upper limit.Results: Overall, the results showed that theF-statistic becomes more liberal as sphericity violation increases, whereas bothF-HFandF-GGcontrol Type I error; of the two,F-GGis more conservative, especially with large values ofε̂and small samples.Discussion: If different statistical conclusions follow from application of the two tests, we recommend usingF-GGforε̂values below 0.60, andF-HFforε̂values equal to or above 0.60.

The aim was to analyse the psychometric properties of the 10-item version of the Connor-Davidson Resilience Scale (CD-RISC 10©) in breast cancer patients. A sample of 169 Spanish women who had undergone surgery for breast cancer completed the CD-RISC 10©, along with questionnaires assessing life satisfaction, emotional intelligence, self-esteem, and positive and negative affect. Confirmatory Factor Analysis supported a single-factor structure with adequate fit indices. Reliability was analysed by calculating McDonald's omega coefficient, which yielded a value of .83. Validity evidence based on relationships with other variables was provided by positive and significant correlations between scores on the CD-RISC 10© and scores on emotional intelligence (clarity and repair), life satisfaction, self-esteem and positive affect, and by a negative and significant correlation with negative affect. The majority of these correlations were above |.50|. The CD-RISC 10© has satisfactory psychometric properties and is a suitable tool for measuring resilience in patients with cancer. The instrument is quick and easy to apply and may be used in both clinical and research contexts.