Transcript HCAD Review of Statistics

HCAD Advanced
Statistics
Dr. Mary Whiteside
Review
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Concepts of statistics
Data & sources
Graphs
Numeric descriptions of data
Probability
Random variables
 Discrete – binomial
 Continuous – normal
Sampling distributions
Inferences
 Estimation
 Hypothesis testing
Concepts of statistics
Variability
 Randomness
 Significance
 Uncertainty
 Probability
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Data and sources
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Data
 Times series vs. cross sectional
 Categorical (nominal, qualitative) vs. numeric
 For numeric: discrete vs. continuous; ordinal, vs.
interval or ratio
Sources
 Experiments
 Observational studies
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Random samples
Convenience samples
Self selected samples
Samples from a process
Graphs
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Time series
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Line
Bar
Cross sectional
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Categorical
• Pie
• Bar
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Numeric
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Histogram
Box and whiskers
Stem and leaf
Ogive
Numeric descriptions
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Symmetric distributions
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m = mu = Mean=median=mode
Standard deviation = sigma = s
Empirical rule for mound shaped
• 95% in 2 standard deviations
• 99.7% in 3 standard deviations
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Skewed distributions
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R mode < median < mean
L mean < median < mode
Five points: min Q1 Q2 Q3 max
Probability
Five laws
 Conditional probabilities
 Prior and posterior probabilities
 Approaches to probability
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Equal likelihood
 Relative frequency
 Mathematical
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Problem of false positives
Random variables
Discrete = counting numbers as
values
 Continuous = measuring numbers as
values
 Binomial as an example of a discrete
distribution
 Normal as an example of a
continuous distribution
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Sampling distributions
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Frequently normal due to the Central Limit
Theorem
Based on an assumption of underlying
normality
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t
F
C2
Binomial
Exact
Inference
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Confidence interval estimation
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Precision
Cost
Confidence
Hypothesis testing
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Reject H0 when evidence is sufficient at the
given significance level
Fail to reject H0 when evidence is insufficient
• No evidence
• Some evidence but not enough
Inferences are for
parameters
p = the population proportion or the
probability of success in a binomial
process
 m = the population mean of the
Expected Value of a random variable
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