Introduction to Statistics 101: Sadistics

1. Introduction to Statistics 101 Sadistics Thomas Rieg Clinical Investigation Department Naval Medical Center Portsmouth

2. Standard Error of Measurement • Difference between high and low • Reliability of 95% • Important for Comparing Means!

3. The End Email me at thomas.rieg@med.navy.mil Call me at 757-953-5939

4. I’m not a full time statistician I could play one on TV What this lecture is NOT A thorough course on statistics You WILL be dangerous! What I hope to achieve: A sampling of what you can do on your own A practical foundation for doing it Today Two Points: Determining your statistical test Inferential Statistics Sample Size Guestimation Goals

5. Experimental Methods • Naturalistic Observation • Already occurring variables

6. Experimental Methods • Naturalistic Observation • Already occurring variables • Correlational Approach • Not causal Leena von Hertzen, & Tari Haahtela. (2006). Disconnection of man and the soil: Reason for the asthma and atopy epidemic? Journal of Allergy and Clinical Immunoloty, 117(2), 334-344.

7. Causation • The more bars a city has the more churches it has as well • Religion causes drinking? • Intelligence and Shoe Size • Near Perfect Correlation: Kissing and Pregnancy

8. Experimental Methods • Naturalistic Observation • Already occurring variables • Correlational Approach • Not causal • Experimental Approach • Randomization, control, CAUSAL

9. Experimental Design • Non-Experimental (no control group) • Experimental Group • Receives manipulation of interest • Control Group • Receives sham treatment often called placebo” • Random sampling vs. Random assignment • Matching • Subject variables - Selection bias

10. Types of Variables • Independent (IV) - The presumed cause of the dependent variable - the input variable - the antecedent • The Manipulated Variable • Dependent (DV) - The presumed effect - the consequence - the output variable, • The Measured Variable • Extraneous (EV) - Tertiary related variable • The Confounding Variable

11. When we measure something (a variable) we assign a number to some quality that represents that variable some are perfectly clear height, weight, blood pressure, hemoglobin some are less clear quality of life, fatigue, pain, depression Scales of Measurement

12. Levels of Measurement • Non Parametric • Nominal Classification Discrete • Categories (male, female) • Ordinal Logical Order Discrete • Ordered responses (poor, fair, good, very good, excellent) • Parametric • Interval Equal Intervals Continuous • Meaningful distance between items (temperature) • Ratio Absolute Zero Continuous • Meaningful ratios and intervals between items (age, height)

13. Type of Statistical Test

14. Type of Statistical Test

15. Statistical Flaws • Inappropriate statistics, rounding, effect size, etc. • 25% Nature • 38% BMJ • 30% Nursing Research • 76% Neurology • 35% Psychology (APA Journals) • Your Discipline?

16. Two groups Used to Compare means Assumptions: Normally distributed, continuous outcomes Types Unpaired Equal variances Unequal variances Paired 1- or 2-tailed Caveats Not so good for tiny (N < 20 samples) Not good for 3+ samples Use ANalysis Of VAriance (ANOVA) instead t - Test

17. Humans differ in response to exposure to adverse effects Humans differ in disease symptoms Humans differ in response to treatment Therefore, diagnosis and treatmentis often probabilistically based Why Worry about Variation?

18. Variation • Everything Varies • Systematic Variation • i.e., shock and fear • Due to Independent Variable • Non-Systematic Variation • i.e., shock and fear • Chance Variation or Error Variation

19. Standard Deviation • Scatterplot • Mean = SX/N • Mean Line • Standard Deviation • Average of all of scoresfrom the mean line

20. World’s Coolest Graph

21. Difference of Means / Standard Deviation VAS Scores from 0-100 Significant Differences? μ1= 75.0, s1 = 6 μ2= 75.1, s2= 6

22. Significant Differences? μ1= 75 μ2= 80 SD = 6 SD = 6

23. Significant Differences? μ1= 75 μ2= 87 SD = 6 SD = 6

24. Need two SD’s Significant Differences? μ1= 75 μ2 = 105 SD = 6 SD = 6

25. 25 20 y c 15 n e u q e r 10 F 5 0 0 5 10 15 20 25 30 Measurement Are they different?

26. 25 20 y c 15 n e u q e r F 10 5 0 0 5 10 15 20 25 30 Measurement Smaller Standard Deviation

27. Remember Relationship F = between / within

28. Pascal’s Wager

29. Your Daily Wager

30. Hypothesis Testing

31. Error and Power • Type-I Error (also known as “α”) • Rejecting the null when the effect isn’t real • Type-II Error (also known as “β“) • Failing to reject the null when the effect is real • POWER (the flip side of type-II error: 1- β) • The probability of seeing a true effect if one exists

32. Power • Will increase if: • Alpha increases • The effect size is larger • The sample size increases • Random error is decreased

33. Power Quiz • Will increase if: • Alpha increases • The effect size is larger • The sample size increases • Random error is decreased • Question: How Can we do this? • Answer: Decrease Variability (EVs), Increase Control

34. Sample Size Estimation • One of the most useful aspects of power analysis is the estimation of the sample size required for a particular study • Too small an effect size and an effect may be missed • Too large an effect size too expensive a study • Different formulae/tables for calculating sample size are required according to experimental design

35. Sample Size: Components • Summary Measure of interest • (usually a descriptive statistic) • Significance Level (a) • Desired Power (1-b) • Effect Size: Smallest difference worth detecting (usually clinically) • Variability expected in sample or population

36. Power Chart Note: This power curve chart is for t test Ho: μ1 - μ2 = 0, independent samples, α = .05

37. Sample Size • Mean size of VAS: m1 = 6.5, m2 = 5.0 • Variability: s1 = 4.3cm, s2 = 5.1cm • Significance level: a = 5% • Power: 1 - b = 90% (never lower than 80%) • Effect size: m1 - m2 = 1.5cm n = 209

38. Small Effect • Use values: • Alpha = .05 • 1 - Beta = .80 • f = .100 • Then the total number of participants required is 1096 • (i.e., 274 per group) • Medium Effect • Use values: • Alpha = .05 • 1 - Beta = .80 • f = .250 • Then the total number of participants required is 180 • (i.e., 45 per group) • Large Effect • Use values: • Alpha = .05 • 1 - Beta = .80 • f = .400 • Then the total number of participants required is 76 • (i.e., 19 per group) Small, Medium, and Large Effects

39. Standard Error of Measurement • Difference between high and low • Reliability of 95% • Important for Comparing Means!

40. The End Email me at thomas.rieg@med.navy.mil Call me at 757-953-5939