![]() Imagine you’ve been given three test scores and some information about the test. In this section, you will learn how to calculate z-scores manually and using Google Sheets. There are three steps involved in calculating the z-score: find the population mean, find the population standard deviation, and apply the z-score formula. z-score = (x - μ) / σ How to Calculate the Z-Score? ![]() To get the z-score, subtract the population mean from the raw score and divide the result by the population standard deviation. There are three variables to consider when calculating a z-score: the raw score (x), the population mean (μ), and the population standard deviation (σ). The z-score’s unit of measure is the dataset’s standard deviation, and the sign indicates whether the value is above or below the mean. DOI: 10.13140/RG.Z-scores, which are sometimes referred to as standard scores, measure the distance between specific values - raw scores - and the mean of the dataset. You may not modify, adapt, translate or create derivative works based upon the software.Ĭiteable Reference: Lenhard, W. We do not grant you the right to sublicense or distribute the software. Negligent behavior of Psychometrica and its suppliers. You agree to hold Psychometrica harmless from any and all liabilities, losses, actions, damages, or claims (including all reasonable expenses, costs, and attorneys fees) arising out of using the software if they are not deliberately intended or caused by grossly The software and any authorized copies that you make are the intellectual property of Psychometrica. The Norm Scale Calculator may be used free of charge for private, non commercial usage. Higher scores indicate a better result, lower scores a worse one. A person with percentile 50 therefore shows an average result. ![]() They specify, which percentage of the reference population scores equal or worse.Ī percentile of 50 means that 50% of the reference population score equal or worse. Percentiles, on the other hand, provide a different kind of information. = 10), Standard Values (SW score a norm scale used in German speaking countries M = 100, SD = 10), and The Norm Score Calculator also offers the transformation into z-scores ( M = 0, SD = 1), 115 and more is usually referred to as above average, under 85 is below average. Probably the most well known scale is the IQ scale with a mean of 100 and a standard deviation of 15.Ī score of 100 means that the result is completely on average. They all more or less yield the same information and can directly be transformed into one another. There are a number of different norm scales. its width).Ī normal score is an individual's distance from the population mean quantified in terms of standard deviations. The standard deviation is a measure for the variability within the distribution (i.e. ![]() Normal distributions are characterized by their mean M and their standard deviation SD. This means that many people have scores around the arithmetic mean and only few people have scores deviating extremely from the population mean. The conversion of individual test results into normal scores is usually based on the assumption that personal traits or abilities are normally distributed within the population. Normal scores help to compare attributes of individuals to a representative population and to determine if the scores lie within the normal range or if they are exceptional. Statistical Interpretation of Norm Scores *The Norm Score Calculator uses Chart.js. Please have a look at further calculators for confidence intervals and discrepancy analysis Please fill in a score into the according text field and press return or simply use the slider:Ĭonfidence Interval around the estimated true score: ** The online Norm Score Calculator simplifies the conversion of different types of norm scores (e.g., IQ-scores, T-scores, Standard Scores, Wechsler Subtest Scales and percentiles) into one another. R package for generating continuous test norms in psychometrics and biometrics and for analyzing the model fit ![]()
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