Statistics Lecture 1: Basic Statistical Concepts

• Basic statistical concepts, as covered in Lecture 1

Learning Objectives

• Understanding mean, median, and mode is important
• Grasping Gaussian distribution and variance is important
• Differentiating accuracy vs. precision is key
• Being able to apply standard deviation (SD) and coefficient of variation (CV) is essential

Mean

• The mean is the average of a set of numbers
• For example, given cholesterol test results of 0.521, 0.520, 0.524, 0.522, and 0.518, the mean = 0.524
• It is calculated by dividing the sum of the values by the total count
• The mean helps ensure consistent lab results and detect errors

Median

• The median is the middle number when values are arranged in order
• For example, given the numbers 0.518, 0.520, 0.521, 0.522, 0.524, the median = 0.521
• If there is an even amount of numbers, the average of the two middle values constitutes the median
• The median is utilized when outliers exist in lab test results

Mode

• The mode is the most frequently occurring number in a dataset
• For example, given the numbers 25, 24, 22, 30, 26, 23, 22, 21, the mode = 22, as it appears twice
• It is useful in detecting common lab values or errors

Gaussian Distribution – The Normal Curve

• When mean, median, and mode are equal, a bell-shaped curve is shown
• Blood glucose levels in healthy individuals typically form a normal distribution
• It is used in laboratory statistics to analyze test accuracy

Accuracy vs. Precision

• Accuracy refers to how close results are to the true value
• Precision refers to how consistent repeated results are
• For example, a glucose meter giving readings close to the actual value but varying each time is accurate but not precise
• A hemoglobin test repeating the incorrect value each time, is precise but not accurate
• Labs require both accuracy and precision to ensure reliable diagnoses

Variance & Standard Deviation

• Variance shows how spread out data is
• Standard Deviation (SD) is the square root of variance and easier to interpret
• Low SD = consistent results
• High SD = possible lab test errors
• In a lab, if the SD of hemoglobin tests is too high, the test may need recalibration

Coefficient of Variation (CV%)

• CV% = (SD ÷ Mean) × 100
• Helps compare two different test methods
• Lower CV% = more precise results
• If two cholesterol analyzers have CVs of 3% and 7%, the 3% is more reliable

Probabilities & SD Ranges

• Confidence in Results in a Normal Distribution:
• 68.2% of results fall within ±1 SD
• 95% of results fall within ±2 SD
• 99.7% of results fall within ±3 SD
• For a lab test for hemoglobin with a mean of 14 g/dL and SD of 1 g/dL, 95% of patients will have hemoglobin between 12 – 16 g/dL
• It helps determine normal vs. abnormal lab values