STATISTICS

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STATISTICS

• Clinical Research Unit
• Seminar Series
• Department of Ophthalmology
• University of Alabama at Birmingham

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Lecture Goals

• Overview of types of data
• Overview of descriptive statistics
• Overview of inferential statistics

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Types of Data

• Nominal (categorical, non-ordered) examples r
  ace, gender
• Ordinal (categorical, ordered) examples scale
  s (excellent--poor)
• Interval (continuous) examples age, visual
  acuity

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Types of Data Nominal Variables
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Types of Data Ordinal Variables
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Types of Data Interval Variables
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Descriptive Statistics

• Most commonly used measures
• Mean
• Median
• Proportion
• Variation

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Descriptive Statistics
Distribution of visual field impairment scores
among 147 glaucoma patients (Parrish et al.,
Arch Ophthal1998)
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Descriptive Statistics EXAMPLE
Mean
(56.20.0517.589.0)/147 24.5 Median
50th percentile (0.0,0.0,0.5,0.5,100.0)
12.0 Standard deviation
24.2 Proportion (lt50 impairment) p x /
N 75.0
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Inferential AnalysisWhat is the question?

• Is DRUG A better than DRUG B?
• Is DISEASE Y associated with EXPOSURE X?
• What factors are associated with survival among
  patients with DISEASE Y?

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Inferential AnalysisChoosing the right test
or nonparametric equivalent
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Inferential Analysist-test
USEAGE To test whether the means of 2 groups
are different. ASSUMPTIONS Independent samples,
Normal distribution, Variance assumptions NULL
HYPOTHESIS Ho ?1?2 or ?1-?2 0 TEST
STATISTIC
Degrees of freedom n1n2-2
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Inferential Analysist-test

Ho ?A-?B 0 Ha
?A-?B gt0 GROUP A GROUP B Sample size
n1100 n2100 Sample mean y10.58
y20.53 Sample std. dev. s10.21
s20.19 Pooled std. dev.
sp0.0401
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Statistical Significance The t Distribution
Pprobability
0
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Statistical Significance The t Distribution
Pprobability
0 1.78
Area under curve gt1.78 p-value
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Inferential Analysist-test

• ADDENDUM
• Nonparametric alternatives sign test,
  Wilcoxon signed-rank test, Wilcoxon rank sum
  test
• Paired data assumption of independence

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Inferential Analysiscorrelation
USEAGE To asses the strength of an association
between two variables. ASSUMPTIONS Normal
distribution, Linear association NULL
HYPOTHESIS Ho ? (rho) 0 TEST STATISTIC
r-1 to 1
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r0 There exists no linear relationship
between the X and Y variables. rlt0 There
exists a linear relationship between the X and
Y variables. When X increases, Y decreases.
rgt0 There exists a linear relationship between
the X and Y variables. When X increases, Y
increases.
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Inferential Analysiscorrelation

• ADDENDUM
• Nonparametric alternatives Spearmans
  correlation
• R2 (Coefficient of determination) Amount of
  variation explained

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Inferential Analysischi-square
USEAGE To test whether a statistically
significant association exists between two
categorical variables. ASSUMPTIONS Data are
random samples from larger population. NULL
HYPOTHESIS Ho No association between variable
A and variable B. TEST STATISTIC
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Inferential Analysischi-square
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Is this significant? P(?2 6.25) lt 0.025
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What does the chi-square statistic tell us about
the strength of the association? NOT
MUCH. Measures of associationare often
calculated fordata of this type. The oddsratio
(OR) is perhaps themost common.
What does this mean? Persons on treatment B had
74 lower mortality compared to those on A (or
mortality 3.8-times higher on treatment A).
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Inferential Analysischi-square

• ADDENDUM
• Nonparametric alternatives Fishers exact
  test
• Strength of association Odds ratio
• Other uses of chi-square statistic

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Et cetera...

• Multivariable analysis (regression
  models)
• Confidence intervals
• Sample size and power