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BIOSTATISTICS III

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					                                                        Biostatistics
 BIOSTATISTICS III                          Statistics I: Descriptive statistics
                                            Statistics 2: Confidence intervals
       Stephen McCurdy, M.D., M.P.H.        Statistics 3: Fundamentals of testing
     Department of Public Health Sciences   Statistics 4: Which test to use?
        U.C. Davis School of Medicine       Statistics 5: Multivariate methods




         BIOSTATISTICS                                BIOSTATISTICS
                                            “To be perfectly intelligible, one must be
  “THERE ARE THREE KINDS OF LIES:             INACCURATE.
               LIES,
            DAMN LIES,                      To be perfectly accurate, one must be
                and                          UNINTELLIGIBLE.”
            STATISTICS.”                                       ~Bertrand Russell
                    ~Benjamin Disraeli




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




                                                                                         1
             Biostatistics                                   BIOSTATISTICS
                                                 Our descriptive approach characterizes the
Statistics I: Descriptive statistics             cholesterol levels for men and women:
Statistics 2: Confidence intervals
                                                           Men    Women
Statistics 3: Fundamentals of testing            N         51      28                       Men

Statistics 4: Which test to use?                 Mean     152     158
Statistics 5: Multivariate methods               Median   146     159
                                                                                       Women
                                                 SD       35.8    23.6
                                                 SE       5.0     4.5
                                                 95% CI 142-162 149-167
                                                                              130 140 150 160 170 180 190
                                                                                       Cholesterol




          BIOSTATISTICS                                      BIOSTATISTICS
The next question is analytic:                   Objectives:
  Is there a true difference in cholesterol       1. Learn the three–step process for
  between men and women,                             statistical testing
- OR -                                            2. Discuss p value, Type I and Type II
  could the difference we saw be due to              errors, and power
  simple chance?




          BIOSTATISTICS                                      BIOSTATISTICS
Three – Step Process:                            Step 1:
  1. Begin with the Null Hypothesis
                                                 Begin with “Null Hypothesis”
  2. Test the Hypothesis!!
    - Look and use intuition                         “No true, underlying difference”
    - Then get the P value
  3. Conclude:                                   (I.e., the difference we saw was due to
    Reject Null Hypothesis if P < 0.05 (or 5%)      simple random chance.)
            _____ Otherwise _____

    Accept Null Hypothesis




                                                                                                            2
          BIOSTATISTICS                                 BIOSTATISTICS
Step 2:                                      Test: Is the observed difference likely to
  Test the Null Hypothesis                    due to chance (“Luck of the Draw”)
                                              alone?
                                              1. Use your intuition!
 I.e., if no true difference exists, how          (Hint: Look at the data.)
 likely is it that the observed difference
                                              2. Put a number on (quantify) your
 would occur from chance variation?           intuition.
                                                  (Hint: Let the computer calculate an
                                                        “exact” likelihood.)




          BIOSTATISTICS                                 BIOSTATISTICS
                                             Step 3:
The “P Value” tells us how likely it is to   Accept or Reject Null Hypothesis
 see a difference at least as great as the
 observed difference by chance alone.        If observed difference is “small” and could
                                                easily occur by chance:
                                                Accept Null Hypothesis
                                             If observed difference is “too large” and is
(“P” stands for Probability.)                   unlikely to be due to simple chance (p <.05):
                                                Reject Null Hypothesis




          BIOSTATISTICS                                 BIOSTATISTICS
You can still be wrong!                      Power – the ability of a study to detect a true
                                              difference between groups. (Power varies
1. Conclude there is a true difference
                                              between 0 to 100%.)
                             α
  when none exists: Type I (α) Error
                                             Power improved with
2. Conclude there is no true difference       > sample size
  when one does exist: Type II (ß) Error      > Large difference
                                              > “Tight” distribution within groups




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