The normal distribution (bell curve or Gaussian distribution) is a distribution that happens commonly in many circumstances. Real-life data rarely, if ever, follow a perfect normal distribution. Many tests are useful to test normality and more particularly skewness and kurtosis tests assess the comparability of a given distribution from a normal distribution. These tests are widely used in statistics, business, and epidemiological data including blood pressure, heights, IQ scores and measurement errors. This report provides a review assessing the essential methods employed for testing normality and highlighting the importance of skewness and Kurtosis in statistics. Moreover, it gives some examples of the importance of normality in epidemiological health studies analysis.

Doubly truncated data appear in a number of applications, including astronomy and survival analysis. In this paper we review the existing methods to compute the nonparametric maximum likelihood estimator (NPMLE) under double truncation, which has no explicit form and must be approximated numerically. We introduce the bootstrap as a suitable method to estimate the finite sample distribution of the NPMLE under double truncation. The performance of the bootstrap is investigated in a simulation study. The nonstandard case in which the right- and left-truncation times determine each other is covered. As an illustration, nonparametric estimation and inference on the birth process and the age at diagnosis for childhood cancer in North Portugal is considered.

Background: Lung function is an important predictor of health and a marker of physical functioning at older ages. This study aimed to quantify the years of lung function lost according to disadvantaged socioeconomic conditions across the life-course. Methods: This multicohort study used harmonised individual-level data from six European cohorts with information on life-course socioeconomic disadvantage and lung function assessed by forced expiratory volume in 1 s (FEV ₁ ) and forced vital capacity (FVC). 70 496 participants (51% female) aged 18–93 years were included. Socioeconomic disadvantage was measured in early life (low paternal occupational position), early adulthood (low educational level) and adulthood (low occupational position). Risk factors for poor lung function ( e.g. smoking, obesity, sedentary behaviour, cardiovascular and respiratory diseases) were included as potential mediators. The years of lung function lost due to socioeconomic disadvantage were computed at each life stage. Results: Socioeconomic disadvantage during the life-course was associated with a lower FEV ₁ . By the age of 45 years, individuals experiencing disadvantaged socioeconomic conditions had lost 4–5 years of healthy lung function versus their more advantaged counterparts (low educational level −4.36 (95% CI −7.33–−2.37) for males and −5.14 (−10.32–−2.71) for females; low occupational position −5.62 (−7.98–−4.90) for males and −4.32 (−13.31–−2.27) for females), after accounting for the risk factors for lung function. By the ages of 65 years and 85 years, the years of lung function lost due to socioeconomic disadvantage decreased by 2–4 years, depending on the socioeconomic indicator. Sensitivity analysis using FVC yielded similar results to those using FEV ₁ . Conclusion: Life-course socioeconomic disadvantage is associated with lower lung function and predicts a significant number of years of lung function loss in adulthood and at older ages.

(1) Background: In an ageing society, social relationships may benefit cognitive performance with an impact on the health of older people. This study aims to estimate the effect of different social support sources on the risk of cognitive impairment in a sample of older Portuguese people. (2) Methods: From the Portuguese EpiPorto cohort study, we followed a sample of participants with 60 to 85 years (N = 656) between 2009 and 2015 (4.63 mean years of follow-up). The participants’ perception of social support from family, friends and significant others was evaluated. Cox’s regression models were used to investigate the association between this and sociodemographic variables. (3) Results: It was found that social support from friends reduces the risk of cognitive impairment. Men, participants aged 60 to 64 and those not married have a lower risk of cognitive impairment after adjusting for other variables. Participants between 80 and 85 years old (p = 0.021), those with less than four years of education (p < 0.001), and those with cognitive impairment (p = 0.007) have perception of less social support from friends. (4) Conclusions: A social support network from friends reduces the risk of cognitive impairment for older people.