1. BIOSTATISTICS I Stephen McCurdy, M.D., M.P.H. Department of Public Health Sciences U.C. Davis School of Medicine

2. BIOSTATISTICS “THERE ARE THREE KINDS OF LIES: LIES, DAMN LIES, and STATISTICS.” ~Benjamin Disraeli

3. BIOSTATISTICS “To be perfectly intelligible, one must be INACCURATE. To be perfectly accurate, one must be UNINTELLIGIBLE.” ~Bertrand Russell

4. BIOSTATISTICS Statistics summarize a large body of data into a few numbers. Information is lost or disguised. “The challenge of statistics is to tell the truth clearly: to be (reasonably) accurate and intelligible.” ~Stephen McCurdy ~Stephen McCurdy

5. Biostatistics Statistics I: Descriptive statistics Statistics 2: Confidence intervals Statistics 3: Fundamentals of testing Statistics 4: Which test to use? Statistics 5: Multivariate methods

6. BIOSTATISTICS Objectives -Role of Statistics for describing data -Define, population, sample, individual -Discern continuous vs. categorical data -Understand how to summarize data

7. BIOSTATISTICS Descriptive Statistics: Summarize to describe a body of information (e.g. average height for men and women)

8. BIOSTATISTICS Analytic Statistics: Summarize to help us analyze and make inferences. (e.g. are men taller than women, on average?)

9. BIOSTATISTICS To be intelligible, two compromises are needed:  Take a sample instead of the entire population Population: all adults in the world Sample: adults in your study > Summarize instead of giving “raw data” for each subject

10. BIOSTATISTICS Types of Data Continuous Any values in a range are OK Order is important Categorical Only some values are OK Order may or may not matter

11. BIOSTATISTICS Blood Sugar [K + ] Birth weight Age[DPH] Continuous Data Examples:

12. BIOSTATISTICS Categorical Data Gender Vital Status Sick vs. not-sick Examples:

13. BIOSTATISTICS Summarizing: Categorical Data

14. BIOSTATISTICS Continuous vs. Categorical

15. BIOSTATISTICS Summarizing: Continuous Data  Mean  Median  Mode    “Central Tendency”

16. BIOSTATISTICS What’s wrong with a mean? PersonIncome 1234567$6,200$7,100$5,400$5,900$8,000$7,300$6,800 Central Tendency Mean: $6,671 Median: $6,800 ($37,088) ($6,950) $250,000 8

17. BIOSTATISTICS Histogram of Annual Income

18. BIOSTATISTICS Summarizing: Continuous Data Range Quartiles Standard Deviation (SD) 25 th %-ile 50 th %-ile   75 th %-ile  “Dispersion”

19. BIOSTATISTICS Summarizing: Continuous Data The “Standard Deviation (SD)” Mean Birth-wt = 3.5 kg Std Dev. = 1.0 kg Mean ±1 SD 3.5 ±1kg 2.5 – 4.5 kg = 66% Mean ± 2 SD 3.5 ±2 kg 1.5 – 5.5 kg = 95% 3.5

20. BIOSTATISTICS PersonIncome 1234567$6,200$7,100$5,400$5,900$8,000$7,300$6,800 What’s wrong with the SD? Dispersion 0%-ile - $5,400 25%-ile - $5,775 50%-ile - $6,800 75%-ile - $7,475 100%-ile-$8,000 S.D. : $894 ($86,033) 8 $250,000 ($5,900) ($6,950) ($7,300) ($250,000)

21. BIOSTATISTICS Take – home messages: > Look at your data > For continuous data, summarize with mean (for central tendency) and SD (for dispersion) only for normal bell – shaped distributions (otherwise, use median and percentiles)