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Biostatistics 3

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									Biostatistics 3



Stephen McCurdy, M.D., M.P.H.
Department of Public Health
 Sciences
School of Medicine
University of California, Davis
Davis, CA USA
Biostatistics

 Statistics 1: Descriptive statistics
 Statistics 2: Confidence intervals
 Statistics 3: Fundamentals of testing
 Statistics 4: Which test to use?
 Statistics 5: Multivariate methods
Biostatistics

   “There are three kinds of lies:
                lies,
            damn lies,
                and
            statistics.”
                 ~Benjamin Disraeli
Biostatistics

  “To be perfectly intelligible, one
       must be inaccurate.
To be perfectly accurate, one must
        be unintelligible.”
                   ~Bertrand Russell
Biostatistics

 Statistics I: Descriptive statistics
 Statistics 2: Confidence intervals
 Statistics 3: Fundamentals of testing
 Statistics 4: Which test to use?
 Statistics 5: Multivariate methods
Take Home Message
Mean: “Best guess” for true central
   tendency (for normal distribution)
SD: Dispersion of data and for making a
    confidence interval for mean (for normal
    distribution)
95% CI = mean    2 SEM
              SEM = SD
                           n
Biostatistics

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

Our descriptive approach
characterizes the cholesterol                 M      F
levels for men and women:           N        51     28
                                    Mean     152    158
                            M
                            F       Median   146    159
[N]
                                    SD       35.8   23.6
                                    SE       5.0    4.5
      130 140 150 160 170 180 190            142-   149-
                                    95% CI
              Cholesterol                    162    167
Analytic Question

The next question is analytic:
Is there a true difference in cholesterol
between men and women,
– or –
could the difference we saw be due to simple
chance?
Objectives

 Learn the three–step process for
  statistical testing
 Discuss p value, Type I and Type II errors,
  and power
Three-Step Process

1. Begin with the Null Hypothesis
2. Test the Hypothesis
   Look and use intuition
   Then get the P value
3. Conclude
   Reject Null Hypothesis if P < 0.05 (or 5%)
   — Otherwise —
  Accept Null Hypothesis
Step 1:
Begin with Null Hypothesis
“No true, underlying difference”
(i.e., the difference we saw was due to simple
random chance.)
Step 2:
Test the Null Hypothesis
If no true difference exists, how likely is it
that the observed difference would occur
from chance variation?
Test

Is the observed difference likely to due to
chance (“Luck of the Draw”) alone?
1. Use your intuition!
   (Hint: Look at the data.)
2. Put a number on (quantify) your intuition.
   (Hint: Let the computer calculate an
   “exact” likelihood.)
The P Value

The “P Value” tells us how likely it is to see a
difference at least as great as the observed
difference by chance alone.
―P‖ stands for Probability
Step 3:
Accept or Reject Null Hypothesis
 If observed difference is “small” and could
  easily occur by chance:
  Accept Null Hypothesis

 If observed difference is “too large” and is
  unlikely to be due to simple chance
  (p <.05):
 Reject Null Hypothesis
You Can Still Be Wrong!

1. Conclude there is a true difference when
   none exists: Type I () Error
2. Conclude there is no true difference when
   one does exist: Type II (ß) Error
Power

Power is the ability of a study to detect a true
difference between groups. (Power varies
between 0 to 100%.)
Power improved with:
 Large sample size
 Large difference
 “Tight” distribution within groups

								
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