1. Statistical Core Didactic
Introduction to
Biostatistics
Donald E. Mercante, PhD
LSU-HSC School of Public Health Biostatistics

2. Randomized Experimental Designs
LSU-HSC School of Public Health Biostatistics

3. Randomized Experimental Designs
Three Design Principles:
1. Replication
2. Randomization
3. Blocking
LSU-HSC School of Public Health Biostatistics

4. Randomized Experimental Designs
1. Replication
Allows estimation of experimental error, against which, differences in trts are judged.
LSU-HSC School of Public Health Biostatistics

5. Randomized Experimental Designs
Replication
Allows estimation of expt’l error, against which, differences in trts are judged.
Experimental Error:
Measure of random variability.
Inherent variability between subjects treated alike.
LSU-HSC School of Public Health Biostatistics

6. Randomized Experimental Designs
If you don’t replicate . . .
. . . You can’t estimate!
LSU-HSC School of Public Health Biostatistics

7. Randomized Experimental Designs
To ensure the validity of our estimates of expt’l error and treatment effects we rely on ...
LSU-HSC School of Public Health Biostatistics

8. Randomized Experimental Designs
. . . Randomization
LSU-HSC School of Public Health Biostatistics

9. Randomized Experimental Designs
2. Randomization
leads to unbiased estimates of
treatment effects
LSU-HSC School of Public Health Biostatistics

10. Randomized Experimental Designs
Randomization
leads to unbiased estimates of
treatment effects
i.e., estimates free from systematic differences due to uncontrolled variables
LSU-HSC School of Public Health Biostatistics

11. Randomized Experimental Designs
Without randomization, we may need to adjust analysis by
stratifying
covariate adjustment
LSU-HSC School of Public Health Biostatistics

12. Randomized Experimental Designs
3. Blocking
Arranging subjects into similar groups to
account for systematic differences
LSU-HSC School of Public Health Biostatistics

13. Randomized Experimental Designs
Blocking
Arranging subjects into similar groups (i.e., blocks) to account for systematic differences
- e.g., clinic site, gender, or age.
LSU-HSC School of Public Health Biostatistics

14. Randomized Experimental Designs
Blocking
leads to increased sensitivity of statistical tests by reducing expt’l error.
LSU-HSC School of Public Health Biostatistics

15. Randomized Experimental Designs
Blocking
Result: More powerful statistical test
LSU-HSC School of Public Health Biostatistics

16. Randomized Experimental Designs
Summary:
Replication – allows us to estimate Expt’l Error
Randomization – ensures unbiased estimates of treatment effects
Blocking – increases power of statistical tests
LSU-HSC School of Public Health Biostatistics

17. Randomized Experimental Designs
Three Aspects of Any Statistical Design
Treatment Design
Sampling Design
Error Control Design
LSU-HSC School of Public Health Biostatistics

18. Randomized Experimental Designs
1. Treatment Design
How many factors
How many levels per factor
Range of the levels
Qualitative vs quantitative factors
LSU-HSC School of Public Health Biostatistics

19. Randomized Experimental Designs
One Factor Design Examples
Comparison of multiple bonding agents
Comparison of dental implant techniques
Comparing various dose levels to achieve numbness
LSU-HSC School of Public Health Biostatistics

20. Randomized Experimental Designs
Multi-Factor Design Examples:
Factorial or crossed effects
Bonding agent and restorative compound
Type of perio procedure and dose of antibiotic
Nested or hierarchical effects
Surface disinfection procedures within clinic type
LSU-HSC School of Public Health Biostatistics

21. Randomized Experimental Designs
2. Sampling or Observation Design
Is observational unit = experimental unit ?
or,
is there subsampling of EU ?
LSU-HSC School of Public Health Biostatistics

22. Randomized Experimental Designs
Sampling or Observation Design
For example,
Is one measurement taken per mouth, or are multiple sites measured?
Is one blood pressure reading obtained or are multiple blood pressure readings taken?
LSU-HSC School of Public Health Biostatistics

23. Randomized Experimental Designs
3. Error Control Design
concerned with actual arrangement of the expt’l units
How treatments are assigned to eu’s
LSU-HSC School of Public Health Biostatistics

24. Randomized Experimental Designs
3. Error Control Design
Goal: Decrease experimental error
LSU-HSC School of Public Health Biostatistics

25. Randomized Experimental Designs
3. Error Control Design
Examples:
CRD – Completely Randomized Design
RCB – Randomized Complete Block Design
Split-mouth designs (whole & incomplete block)
Cross-Over Design
LSU-HSC School of Public Health Biostatistics

26. Inferential Statistics
Hypothesis Testing
Confidence Intervals
LSU-HSC School of Public Health Biostatistics

27. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Start with a research question
Translate this into a testable hypothesis
LSU-HSC School of Public Health Biostatistics

28. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Specifying hypotheses:
H0: “null” or no effect hypothesis
H1: “research” or “alternative” hypothesis
Note: Only the null is tested.
LSU-HSC School of Public Health Biostatistics

29. Errors in Hypothesis Testing
When testing hypotheses, the chance of making a mistake always exists.
Two kinds of errors can be made:
Type I Error
Type II Error
LSU-HSC School of Public Health Biostatistics

30. Errors in Hypothesis Testing
Reality 
 Decision
H0 True
H0 False
Fail to Reject H0 
Type II ()
Reject H0
Type I ()
LSU-HSC School of Public Health Biostatistics

31. Errors in Hypothesis Testing
Type I Error
Rejecting a true null hypothesis
Type II Error
Failing to reject a false null hypothesis
LSU-HSC School of Public Health Biostatistics

32. Errors in Hypothesis Testing
Type I Error
Experimenter controls or explicitly sets this error rate - 
Type II Error
We have no direct control over this error rate - 
LSU-HSC School of Public Health Biostatistics

33. Randomized Experimental Designs
When constructing an hypothesis:
Since you have direct control over Type I error rate, put what you think is likely to happen in the alternative.
Then, you are more likely to reject H0, since you know the risk level ().
LSU-HSC School of Public Health Biostatistics

34. Errors in Hypothesis Testing
Goal of Hypothesis Testing
Simultaneously minimize chance of making either error
LSU-HSC School of Public Health Biostatistics

35. Errors in Hypothesis Testing Indirect Control of β
Power
Ability to detect a false null hypothesis
POWER = 1 - 
LSU-HSC School of Public Health Biostatistics

36. Steps in Hypothesis Testing
General framework:
Specify null & alternative hypotheses
Specify test statistic and -level
State rejection rule (RR)
Compute test statistic and compare to RR
State conclusion
LSU-HSC School of Public Health Biostatistics

37. Steps in Hypothesis Testing
test statistic
Summary of sample evidence relevant to determining whether the null or the alternative hypothesis is more likely true.
LSU-HSC School of Public Health Biostatistics

38. Steps in Hypothesis Testing
test statistic
When testing hypotheses about means, test statistics usually take the form of a standardize difference between the sample and hypothesized means.
LSU-HSC School of Public Health Biostatistics

39. Steps in Hypothesis Testing
test statistic
For example, if our hypothesis is
Test statistic might be:
LSU-HSC School of Public Health Biostatistics

40. Steps in Hypothesis Testing
Rejection Rule (RR) :
Rule to base an “Accept” or “Reject” null hypothesis decision.
For example,
Reject H0 if |t| > 95th percentile of t-distribution
LSU-HSC School of Public Health Biostatistics

41. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
P-values
Probability of obtaining a result (i.e., test statistic) at least as extreme as that observed, given the null is true.
LSU-HSC School of Public Health Biostatistics

42. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
P-values
Probability of obtaining a result at least as extreme given the null is true.
P-values are probabilities
0 < p < 1 <-- valid range
Computed from distribution of the test statistic
LSU-HSC School of Public Health Biostatistics

43. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
P-values
Generally, p<0.05 considered significant
LSU-HSC School of Public Health Biostatistics

44. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
LSU-HSC School of Public Health Biostatistics

45. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Example
Suppose we wish to study the effect on blood pressure of an exercise regimen consisting of walking 30 minutes twice a day.
Let the outcome of interest be resting systolic BP.
Our research hypothesis is that following the exercise regimen will result in a reduction of systolic BP.
LSU-HSC School of Public Health Biostatistics

46. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Study Design #1: Take baseline SBP (before treatment) and at the end of the therapy period.
Primary analysis variable = difference in SBP between the baseline and final measurements.
LSU-HSC School of Public Health Biostatistics

47. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Null Hypothesis:
The mean change in SBP (pre – post) is equal to zero.
Alternative Hypothesis:
The mean change in SBP (pre – post) is different from zero.
LSU-HSC School of Public Health Biostatistics

48. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Test Statistic:
The mean change in SBP (pre – post) divided by the standard error of the differences.
LSU-HSC School of Public Health Biostatistics

49. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Study Design #2: Randomly assign patients to control and experimental treatments. Take baseline SBP (before treatment) and at the end of the therapy period (post-treatment).
Primary analysis variable = difference in SBP between the baseline and final measurements in each group.
LSU-HSC School of Public Health Biostatistics

50. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Null Hypothesis:
The mean change in SBP (pre – post) is equal in both groups.
Alternative Hypothesis:
The mean change in SBP (pre – post) is different between the groups.
LSU-HSC School of Public Health Biostatistics

51. LSU-HSC School of Public Health Biostatistics
Hypothesis Testing
Test Statistic:
The difference in mean change in SBP (pre – post) between the two groups divided by the standard error of the differences.
LSU-HSC School of Public Health Biostatistics

52. Interval Estimation
Statistics such as the sample mean, median, and variance are called
point estimates
-vary from sample to sample
-do not incorporate precision

53. Interval Estimation X ——————>  (popn mean) S2 ——————> 2
Take as an example the sample mean:
X ——————> 
(popn mean)
Or the sample variance:
S2 ——————> 2
(popn variance)
Estimates
Estimates

54. Interval Estimation
Recall, a one-sample t-test on the population mean. The test statistic was
This can be rewritten to yield:

55. Interval Estimation Confidence Interval for :
The basic form of most CI :
Estimate ± Multiple of Std Error of the Estimate

56. Interval Estimation Example: Standing SBP
Mean = 140.8, S.D. = 9.5, N = 12
95% CI for :
140.8 ± (9.5/sqrt(12))
140.8 ± 6.036
(134.8, 146.8)