![]() Īnthropometric measurements may have different distributions for different populations. Using the most precise methods to calculate z-score is important because of the risk of misclassification and its additional consequences. The use of z-scores in medicine and paediatrics is widespread to accurately assess growth through anthropometric measurements such as height, weight and Body Mass Index (BMI). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Ĭompeting interests: The authors have declared that no competing interests exist. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.ĭata Availability: The data underlying the results presented in the study are available from CDC ( ).įunding: The study presented in this paper was developed in the context of the M圜yFAPP Project, funded by the European Union under the Grant Agreement number 643806. Received: SeptemAccepted: NovemPublished: December 20, 2018Ĭopyright: © 2018 Martinez-Millana et al. PLoS ONE 13(12):Įditor: David Meyre, McMaster University, CANADA (2018) Optimisation of children z-score calculation based on new statistical techniques. This means that the relative frequency or probability that an event occurs below 1.5 is 0.9332 or 93.32%.Īdjust to Z to find the corresponding probability.Citation: Martinez-Millana A, Hulst JM, Boon M, Witters P, Fernandez-Llatas C, Asseiceira I, et al. Knowing that the area under the standard normal distribution is 1: If we refer to the standard normal table it can be observed that for Z = 1.5: We can find the probability of a value being less than 1.5 by finding the area of the blue shaded area below. What is the probability that X is less than 1.5? Let X be a random variable taken from a standard normal distribution. To find the probability value for a z-score of -1, we need to find the area under the standard normal curve between − ∞ and -1. ![]() The area under the standard normal distribution curve represents the cumulative probability and as such the total area under the curve is 1. The standard normal distribution has a mean μ = 0, and standard deviation σ = 1. The probability density function of a normal (Gaussian) random variable X is given by:į x = 1 σ ⋅ 2 ⋅ π ⋅ &ExponentialE − x − μ 2 2 ⋅ σ 2 ![]() The square root of the variance, &sigma, is called the standard deviation. The variance, &sigma 2, is the expected value of the square of the difference between the value of the X and its mean. For any distribution X, the mean, denoted &mu, is the expected value of X. The values contained in the standard normal distribution table can also be calculated by hand. Once this z-score is known, its respective probability can be looked up in the standard normal distribution table. For more on standardizing data samples, see the Scale command. Z-scores are calculated by first subtracting the mean of the data set from every observation, then dividing by the standard deviation, such that every standardized observation is a measure of how many standard deviations a given observation is from the sample mean. ![]() It is common practice to convert any normally distributed data to the standard normal distribution as the standard normal distribution table contains a value for every standardized z-score. More specifically, the table contains values for the cumulative distribution function of the standard normal distribution at a given value, x. A standard normal distribution table, also known as the unit normal table or Z table, is used to find the probability that a statistic is observed below, above, or between values in the standard normal distribution, the so-called p-value.
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