A study examined the effect of a low-carbohydrate diet compared to a low-fat diet on body weight. A sample of 150 overweight but otherwise healthy adults from a large city was enrolled in the study and randomly assigned in a 1:1 ratio to either the low-carbohydrate (40 g/d) or the low-fat (

Question

A study examined the effect of a low-carbohydrate diet compared to a low-fat diet on body weight.  A sample of 150 overweight but otherwise healthy adults from a large city was enrolled in the study and randomly assigned in a 1:1 ratio to either the low-carbohydrate (40 g/d) or the low-fat (<7% saturated fat) diet.  At 12 months, a greater body weight change was reported in the low-carbohydrate diet group compared to the low-fat diet group, with a mean difference in body weight change of −3.5 kg (p = 0.01, predetermined significance level = 0.05).  Which of the following is the most accurate interpretation of the results of this study?

Quizplus · Accepted Answer

Statistical tests contrast a null hypothesis (H₀) and an alternative hypothesis (H_a), in this case: H₀ is a claim of no difference between populations (eg, no difference in mean body weight between the low-carbohydrate population and the low-fat population). H_a is a claim of a difference between populations (eg, difference in mean body weight between the 2 populations). Statistical inference uses data from samples (eg, 75 adults in the low-carbohydrate sample, 75 adults in the low-fat sample) to draw conclusions about underlying populations. Sample estimates or differences (eg, sample mean, difference in mean between 2 samples) generally vary with distinct samples (eg, if a different sample of 75 adults was chosen for each group) and may be close but not equal to the underlying population value. One way to account for sampling variation is to calculate the p-value, which is the probability of obtaining a sample value at least as large as the one observed when the population value claimed in H₀ is assumed to be true. The magnitude of the p-value compared to a predetermined significance level (eg, 0.05 [or 5%] commonly used as the threshold) determines whether there is convincing evidence against H₀. A low p-value (eg, <0.05) occurs when the sample value significantly disagrees with the population value claimed in H₀ and provides convincing evidence against H₀ (ie, H₀ is probably wrong). Results are considered statistically significant. A high p-value (eg, ≥0.05) occurs when the sample value is close to the population value claimed in H₀ and provides convincing evidence in favor of H₀ (ie, H₀ might be correct). Results are considered not statistically significant. In this case, the given p-value = 0.01; therefore, there is a 1% chance (ie, 0.01) of observing a mean difference in body weight change (ie, sample estimate) of at least −3.5 kg between the low-fat and the low-carbohydrate samples when no difference between the populations is assumed (ie, H₀ is assumed to be true) (Choice B). (Choices A, D, and E) The p-value of 0.01 is less than 0.05; therefore, the observed mean difference is statistically significant at the 5% level. The p-value is not associated with individual observations in a sample. It accounts for sampling variation (ie, random variation) not bias (ie, systematic variation). Educational objective: The p-value is the probability of obtaining a result (ie, sample estimate) at least as large as the one observed when the population value claimed in the null hypothesis is assumed to be true. A p-value <0.05 typically indicates that results are statistically significant.

A Study Examined the Effect of a Low-Carbohydrate Diet Compared