How a Z-Score Can Help You Compare Data—Here's How to Calculate It

Table of ContentsView AllTable of ContentsWhat Does a Z-Score Tell You?Z-Score vs. Standard DeviationHow to Calculate the Z-ScoreZ-Scores and IQ TestingZ-Score and Other Psychological Tests

Table of ContentsView All

View All

Table of Contents

What Does a Z-Score Tell You?

Z-Score vs. Standard Deviation

How to Calculate the Z-Score

Z-Scores and IQ Testing

Z-Score and Other Psychological Tests

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“You can’t compare apples to oranges.” Although the saying is cliché, the message behind it is clear. Comparing two things that are completely different is hard to do. You need a way to make the objects equal so it can give you a fair comparison.

Similarly, when analyzing numbers, experts have to find a way to make the numbers comparable. This allows them to draw parallels between the information. Finding the Z-score can help make sense of different types of data.

“Z-scores are a handy way to determine how a specific value compares to the average,” explains Nathan Brunner, CEO ofSalarship. “Researchers find the Z-score very useful because it is standardized, which allows them to perform standardizedstatistical testsand compute prediction intervals,” he notes.

Finding the Z-score can help make sense of different types of data.

We’ll look at what the Z-score is, when having a Z-score is helpful, and how you can calculate the score.

Depression Statistics Everyone Should Know

A Z-score gives you a composite number for a specific set of data. It helps provide standardized numbers for data that may otherwise be hard to compare. The American Psychological Association notes that it is “the standardized score that results from applying a Z-score transformation to raw data.”By using the formula to get a standardized number, you can compare that finding to other sets of data.

What Does ‘Cognitive’ Mean in Psychology?

You may be thinking that since the Z-score finds the average of several sets of data as a part of its formula, it is like finding the standard deviation. That’s not exactly the case.

“The Z-score and standard deviation are related but different concepts. The standard deviation measures the spread or variability of the whole dataset. A larger standard deviation indicates greater variability, while a smaller standard deviation indicates less variability,” Brunner notes.

The Z-score gives a way to compare information. The standard deviation tells you the difference between the two sets of information.

Calculating the Z-score starts with you having the raw data that you want a composite number for. With that data, you will need to find the mean or average number, as well as the standard deviation value for all the data.

The standard deviation is a bit more detailed.

You would use the following formula: Z-score = (the initial data point – mean)/standard deviation.

Brunner uses an example of finding out how a student’stest scoreof 90 compared with the scores his peers received, which are 75, 80, 85, 90, and 95. First, we find out the mean of this data set, which is 85. Then you calculate the standard deviation, which is approximately 7.9. Plugging the numbers into the formula, the Z-score is (90-85)/7.9, which equals 0.63.

If following the math is confusing, aZ-score calculatorcan help you find your answer.

Interesting information, but where is it applicable?

IQ test scores are highly prized for admission to certain clubs and organizations. Researchers note that Z-scores help you to understand the actual value of the IQ test, as well as where the test score falls in comparison to otherIQ scores.

How to Convert a Z-Score to IQ

Which Z-Score Indicates a Genius-Level IQ?

While this number can fluctuate, Brunner provides insight on a high-level z-score.

“Some psychologists consider an IQ of 145 or above to be genius-level. The z-score is (145 - 100) / 15 = 3 for this value. This is extremely restrictive as only 0.135% of the population has an IQ of 145 or above,” he states.

What’s the Average IQ?

Z-scores and the information they provide can also be beneficial in the mental health arena.

Studies have shown that when comparing the impact of different levels of stress on subjects’mood, hormones, and cognition, Z-scores were extremely useful.

The scores helped to create a uniform way to compare the information.

Another study found that using Z-scores to provideneurofeedbackand biofeedback in older adults with memory issues helped to target methods of treatment.

Experts say Z-scores can also help with tracking changes in patient’s depression andanxietylevels.

Ultimately, being able to take raw data and put it into a form that is useful for understanding and processing information is valuable. Z-scores serve as that beneficial tool on a variety of platforms.

How to Find the Mean, Median, and Mode

4 SourcesVerywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.American Psychological Assocation.APA Dictionary of Psychology.Andrade C.Z scores, standard scores, and composite test scores explained. Indian Journal of Psychological Medicine. 2021;43(6):555-557.Caldwell JA, Niro PJ, Farina EK, McClung JP, Caron GR, Lieberman HR.A Z-score based method for comparing the relative sensitivity of behavioral and physiological metrics including cognitive performance, mood, and hormone levels.PLoS One. 2019;14(8):e0220749.Meeuwsen KD, Groeneveld KM, Walker LA, Mennenga AM, Tittle RK, White EK.Z-score neurofeedback, heart rate variability biofeedback, and brain coaching for older adults with memory concerns.Restor Neurol Neurosci. 39(1):9-37.

4 Sources

Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.American Psychological Assocation.APA Dictionary of Psychology.Andrade C.Z scores, standard scores, and composite test scores explained. Indian Journal of Psychological Medicine. 2021;43(6):555-557.Caldwell JA, Niro PJ, Farina EK, McClung JP, Caron GR, Lieberman HR.A Z-score based method for comparing the relative sensitivity of behavioral and physiological metrics including cognitive performance, mood, and hormone levels.PLoS One. 2019;14(8):e0220749.Meeuwsen KD, Groeneveld KM, Walker LA, Mennenga AM, Tittle RK, White EK.Z-score neurofeedback, heart rate variability biofeedback, and brain coaching for older adults with memory concerns.Restor Neurol Neurosci. 39(1):9-37.

Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.

American Psychological Assocation.APA Dictionary of Psychology.Andrade C.Z scores, standard scores, and composite test scores explained. Indian Journal of Psychological Medicine. 2021;43(6):555-557.Caldwell JA, Niro PJ, Farina EK, McClung JP, Caron GR, Lieberman HR.A Z-score based method for comparing the relative sensitivity of behavioral and physiological metrics including cognitive performance, mood, and hormone levels.PLoS One. 2019;14(8):e0220749.Meeuwsen KD, Groeneveld KM, Walker LA, Mennenga AM, Tittle RK, White EK.Z-score neurofeedback, heart rate variability biofeedback, and brain coaching for older adults with memory concerns.Restor Neurol Neurosci. 39(1):9-37.

American Psychological Assocation.APA Dictionary of Psychology.

Andrade C.Z scores, standard scores, and composite test scores explained. Indian Journal of Psychological Medicine. 2021;43(6):555-557.

Caldwell JA, Niro PJ, Farina EK, McClung JP, Caron GR, Lieberman HR.A Z-score based method for comparing the relative sensitivity of behavioral and physiological metrics including cognitive performance, mood, and hormone levels.PLoS One. 2019;14(8):e0220749.

Meeuwsen KD, Groeneveld KM, Walker LA, Mennenga AM, Tittle RK, White EK.Z-score neurofeedback, heart rate variability biofeedback, and brain coaching for older adults with memory concerns.Restor Neurol Neurosci. 39(1):9-37.

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