An Approximation to the Distribution of the Sample Correlation Coefficient

Konishi, Sandnori

doi:10.2307/2335923

Cited by 1 publication

(1 citation statement)

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“…Having said that, however, each correlation is poorly estimated from just seven daily observations (such as when taken from 7‐day food intake records); therefore, it is possible that much of the variation in correlation is due to sampling rather than differences in the dietary behaviours of people. Moreover, sampling distribution of the correlation coefficient is complex, usually being described through approximations, such as Fisher (1922) and Konishi (1978).…”

Section: Introductionmentioning

confidence: 99%

Associations between fat, sugar and other macronutrient intakes in the National Diet and Nutrition Survey

Horgan

Whybrow

2012

Nutrition Bulletin

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Summary Observational studies show an inverse relationship between fat and sugar within diets, described as the ‘fat‐sugar seesaw’. It has been suggested however, that this is a consequence of expressing macronutrient intakes as percentages of energy intake rather than by the dietary choices made by individuals. To test this we examined the associations between macronutrient intakes in the diets of adults (n = 1724) participating in the UK National Diet and Nutrition Survey (NDNS) and within the same adults across different days of the week. Pearson's correlations were calculated between the macronutrient intakes from fat, total sugar, intrinsic sugars, non‐milk extrinsic sugars (NMES), non‐sugar carbohydrate, protein and alcohol. Energy intakes relative to estimated basal metabolic rate (BMR) were calculated to partially account for differences in energy requirements. Pearson's correlations also examined associations between the same macronutrients in foods from the Nutrient Databank (ND), used to analyse dietary intakes in the NDNS. Correlations between fat and sugar(s) were calculated in five ways: (i) percentage energy between individuals; (ii) amount (g) between individuals; (iii) amount (g) relative to BMR between individuals; (iv) within individuals over seven days; and (v) between food items in the ND. Negative correlations were obtained between mean daily percentage energy intakes of fat and, total sugars, NMES and intrinsic sugars (all P < 0.001). However, when mean daily macronutrient intakes were expressed in weight (g)/day, these were all positively correlated (all P < 0.001). Mean estimated correlations between macronutrient intakes (g/day) for each individual across the days of the week were also positive, indicating a lack of fat‐sugar seesaw effect. Within the ND, the correlation between fat and total sugar (g/100g of food) was weakly positive (P = 0.006). Only when examining the correlation between fat and sugar(s) between individuals in percentage terms (% energy) was the fat‐sugar seesaw evident; in all other methods the correlations between fat and sugar(s) were positive. Examination of the effects of using percentage energy values to describe the macronutrient composition demonstrated that the fat‐sugar seesaw is only an inevitable mathematical consequence, rather than the result of dietary choice. Comparing diet composition in percentage terms alone can therefore be misleading. It is only when examined as absolute values (weight), as well as percentage contributions to energy, that the interrelationships between macronutrients can be studied fully.

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Section: Introductionmentioning

confidence: 99%