Biostatistics: Measures of Central Tendency and Variance in Medical Laboratory Settings Module 5 1

Objectives Define: – Mode – Mean – Median – Confidence limits – Gaussian curve – Standard Deviation – Coefficient of Variation Upon completion of this lesson you will be able to: 5-2

Prepare a frequency distribution table Calculate mean, standard deviation and %CV Identify median and mode Discuss how the values of mean, median and mode influence the validity of statistical data Evaluate data to determine if normal vs. non- normal distribution curve 5-3 Objectives Upon completion of this lesson you will be able to:

Statistics Used with Laboratory Data Measures of central tendency – Mean – Median – Mode 5-4

Variability of measurements Measures of Variation: – Standard Deviation, (s) – Coefficient of Variation (CV) 5-5 Statistics Used with Laboratory Data

Ideal: repeat analysis of a sample would produce the same value each time Real world: there will always be a certain amount of variability in repeated measurements Variability in measurements caused by Heterogeneity of the sample over time Variation in the technique of the analyst Heterogeneity of reagents over time Instrument variation 5-6 Variability of Measurements

Visualized with a bar graph Frequency Distribution table of repeated measurements – Reflects how easy it was to repeat the measurement and obtain the same value Want distribution plot to display central tendency and a bell shaped curve – Bell shaped curve also called Gaussian Curve – Represents normal distribution pattern of values 5-7 Variability of Measurements

Frequency Distribution of Values 5-8

Comparison 5-9

Statistics Used to Measure Central Tendency Mean Median Mode 5-10

Mean = average of all data points Mean = sum of data points =  (xi) number of results N 5-11 Statistics Used to Measure Central Tendency

Median = the middle data point observed once the data are arranged in descending or ascending order Mode = the value that occurs with the greatest frequency 5-12 Statistics Used to Measure Central Tendency

Normal Gaussian Distribution Symmetric about the mean Obtained when the Mean = Median = Mode – The Frequency distribution graph makes a bell- shaped curve. 5-13

Example Determine the mean, median and mode for the following values: – 6,11,8,5,6,7,9,10,11,8,6 We will use that information to determine if this data is normally distributed. 5-14

6,11,8,5,6,7,9,10,11,8,6 Mean = Median = Mode = Normal or skewed distribution? Let’s take time to perform this Example

6,11,8,5,6,7,9,10,11,8,6 Mean = 87/11 = 8 Median = 8 Mode = 6 Normal (nearly normal) distribution 5-16 Example

Measures of Variation Desirable to have repeated measure data show a slim distribution about the mean, reflecting low variability and low random error Standard Deviation (SD or s) 5-17

Standard Deviation Standard Deviation (SD or s) – Measurement statistic that describes the average distance each data point in a normal distribution is from the mean – Expressed with same units as the measured analyte – SD or s = √∑(x i -mean) 2 N –

A large standard deviation: – Large variation in data – Wide bell shaped curve of frequency distribution A small standard deviation: – Small variation in data – Narrow bell-shaped curve of frequency distribution 5-19 Standard Deviation

Variance Standard deviation squared is variance. What is the variance of the following? – Standard Deviation = 4 – Variance = ?

One SD unit approx 34% total distance of the x-axis on a normal distribution curve 5-21 Standard Deviation

CV is the standard deviation (SD or s) expressed as a percentage of the mean CV = s X 100 mean 5-22 Coefficient of Variation (CV)

Used to evaluate precision or reproducibility of repeated measures Allows comparison without influence from magnitude of data base 5-23 Coefficient of Variation (CV)

A low CV value indicates the distribution of values about the mean is tight rather than broad Acceptable: CV <5% – Modern instrumentation CV <3% – Manual methods CV ~8-10% – Other methods CV >10% Can be used to monitor personnel pipetting technique 5-24 Coefficient of Variation (CV)

Which of the following two methods is more precise (reproducible) showing the least amount of variability and thus the least amount of random error? First we must calculate both CVs. Glucose Method A Glucose Method B Mean = 500 mg/dl Mean = 100 mg/dl SD = 20 mg/dl SD = 6 mg/dl CV= CV = Example

Given the CV we calculated which of the following two methods is more precise (reproducible) showing the least amount of variability and thus the least amount of random error? Glucose Method A Glucose Method B Mean = 500 mg/dl Mean = 100 mg/dl SD = 20 mg/dl SD = 6 mg/dl CV = 4 CV = 6 Method A is more precise 5-26 Example

Confidence Intervals Confidence Intervals also referred to as – Acceptable range – Established limits – Confidence limits Defined as the limits between which we expect a specified proportion or percentage of a population of values to lie Most of the data in a normal distribution lies close to the mean 5-27

Confidence limits are the standard deviations expressed as percentages – 68% – 95.5% – 99.7% Indicate the percentage of values falling within that area of the curve 5-29 Confidence Intervals

Mean - 1 SD = 34.1% Mean +1 SD = 34.1% Mean + 1 SD = 68.2% of data This is the sum of % from above 5-29 Confidence Limits

Mean - 2 SD = = % Mean +2 SD = = % Mean + 2 SD = 95.5 % of data 5-30 Confidence Limits

Mean - 3 SD = = % Mean +3 SD = = % Mean + 3 SD = 99.7 % of data 5-31 Confidence Limits

Summary Distribution of Values Mean Median and Mode Standard Deviation Coefficient of Variation Confidence intervals 5-32