# Measures of Variability

**OVERVIEW**

Measures of variability describe the average dispersion of data around a mean

most common = range, standard deviation and the standard error of the mean

Summary

- range
- percentiles
- standard deviation
- standard error
- confidence intervals
- z-transformation

**RANGE**

- smallest & largest values in a sample

**PERCENTILES**

- tell me what percentage of scores are less than your one.
- median = 50th percentile
- interquartile range = middle 50% of observations around the median
- to calculate percentile = (desired percentile/100) x (number of numbers + 1)

**STANDARD DEVIATION (SD)**

- a measure of the average spread of individual values around the sample or population mean
- calculated by squaring the differences between each value and the sample mean, summing them then dividing the result by n – 1 to give the variance
- SD = the square root of the variance
- SD important because:

- reporting the SD along with the mean, gives an indication at a glance as to whether the sample mean represents a real trend in the sample
- if the sample is randomly selected and large -> it can be assumed to be close to that of the population
- the SD is used to calculate the standard error (see below)
- any data point from a normal distribution can be described as a multiple of standard deviations from the population mean

- tables will then tell us the proportion of the distribution with values more extreme than that (z transformation)

**STANDARD ERROR**

- Standard error is an estimate of the spread of sample means around the population mean
- it is estimated from the data in a single sample
- it is an estimated prediction based on the number in the sample and the sample sd

SE = SD / square root of n

- thus, the variability among sample means will be increased if there is
- (a) a wide variability of individual data and
- (b) small samples

- SE used in parametric tests to quantify the difference between a sample mean & its proposed population mean, i.e. how far the two are apart in multiples of the SE (z-transformation)
- SE is used to calculate confidence intervals

**CONFIDENCE INTERVALS**

- CI is the range around a sample mean within which you predict the means of the sample’s population lies
- the range in which you predict the ‘true’ value lies

Calculation

- 95% of sample means should lie between 1.96 standard error of the mean above & below their sample mean
- thus, if the sample is large enough and is normally distributed as long as the sample was randomly selected then it should also represent the 95% CI for the population mean
- the population mean doesn’t fall within this range -> there is a 95% chance that the samPle is from a different population

Information provided

- an indication of the precision of the sample mean as an estimate of the population mean
- the wider the CI, the greater the imprecision, the greater the potential difference between the calculated sample mean & ‘true’ mean

Causes of wide CI’s

- small sample
- large variance within samples

CI vs P value

- p gives a probability of a specific hypothesis being right or wrong
- CI’s allow more scope for reader judgement on significance

## Critical Care

Compendium

Chris is an Intensivist and ECMO specialist at the Alfred ICU in Melbourne. He is also a Clinical Adjunct Associate Professor at Monash University. He is a co-founder of the Australia and New Zealand Clinician Educator Network (ANZCEN) and is the Lead for the ANZCEN Clinician Educator Incubator programme. He is on the Board of Directors for the Intensive Care Foundation and is a First Part Examiner for the College of Intensive Care Medicine. He is an internationally recognised Clinician Educator with a passion for helping clinicians learn and for improving the clinical performance of individuals and collectives.

After finishing his medical degree at the University of Auckland, he continued post-graduate training in New Zealand as well as Australia’s Northern Territory, Perth and Melbourne. He has completed fellowship training in both intensive care medicine and emergency medicine, as well as post-graduate training in biochemistry, clinical toxicology, clinical epidemiology, and health professional education.

He is actively involved in in using translational simulation to improve patient care and the design of processes and systems at Alfred Health. He coordinates the Alfred ICU’s education and simulation programmes and runs the unit’s education website, INTENSIVE. He created the ‘Critically Ill Airway’ course and teaches on numerous courses around the world. He is one of the founders of the FOAM movement (Free Open-Access Medical education) and is co-creator of litfl.com, the RAGE podcast, the Resuscitology course, and the SMACC conference.

His one great achievement is being the father of three amazing children.

On Twitter, he is @precordialthump.

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