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Standard Deviation

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more...

Introduction to z Scores

Introduction to z Scores

A z score (or standardized value) is measured in units of the standard deviation. It tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
z scores help...

Introduction to z Scores

Introduction to z Scores

A z score (or standardized value) is measured in units of the standard deviation. It indicates how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
z scores help...

Calculating Standard Deviation

Calculating Standard Deviation

The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. Further, the standard deviation is always a positive value or zero.
The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high variation.
Let us...

Comparing Experimental Results: Student's t-Test

Comparing Experimental Results: Student's t-Test

The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...

Testing a Claim about Standard Deviation

Testing a Claim about Standard Deviation

A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...

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Related Experiment Video

Updated: Jun 18, 2026

Muscle Imbalances: Testing and Training Functional Eccentric Hamstring Strength in Athletic Populations

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The standard difference score: a new statistic for evaluating strength and conditioning programs.

Robert W Pettitt¹

¹Department of Human Performance, Minnesota State University, Mankato, Minnesota, USA. robert.pettitt@mnsu.edu

Journal of Strength and Conditioning Research

|November 20, 2009

Summary

This study introduces the standard difference score (SDS), a novel statistic for strength and conditioning programs. SDSs help identify individual athletes with extreme performance changes, potentially indicating overtraining, which traditional statistics miss.

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Area of Science:

Sports Science
Exercise Physiology
Performance Analytics

Background:

Inferential statistics assess overall team response to training programs.
Current methods fail to detect individual anomalies like overtraining.
Need for a statistic to identify extreme individual performance changes.

Purpose of the Study:

Introduce the standard difference score (SDS) as a new statistic for evaluating strength and conditioning.
Demonstrate SDS's utility in identifying athletes with unusual responses.
Provide a practical tool for strength and conditioning specialists.

Main Methods:

Calculate standard difference scores (SDSs) from changes in raw performance scores.
Utilize SDSs as standard scores (z-scores) for individual performance.
Aggregate SDSs to detect extreme changes across a battery of tests.

Main Results:

SDSs are simple to calculate, sort, and plot.
SDSs can be aggregated to identify athletes with extreme performance changes.
SDS evaluation with skewness can replace conventional exploratory statistics.

Conclusions:

The standard difference score (SDS) offers a valuable method for individualized athlete monitoring.
SDSs enhance the ability to detect potential overtraining or non-response.
This statistic provides a practical alternative to complex statistical software for performance analysis.