Transcript Statistics - University of Delaware

Statistics
March 2009
Tim Bunnell, Ph.D. & Jobayer Hossain, Ph.D.
Nemours Bioinformatics Core Facility
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Overview
• Class goals
– Master basic statistical concepts
– Learn analytic techniques & when to apply
them
– Learn how to interpret analysis results
– Develop familiarity with R and related tools
– Gain understanding that will transfer to a
broad range of other statistics tool
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Overview
• Class structure
– 8 sessions
– 1.5 hours per session
– Several homework assignments
• Class website
– http://www.medsci.udel.edu/open/StatClass/March2009
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R
• Installing
– Download from Class website
• Pick right (Mac versus Windows) version
– Run installer program
• Go with all the defaults
• Running R
– Live Demonstration
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R Concepts
• Command line similar to
– Windows Command Shell
– Mac Terminal
– Unix/Linux Shell
• Uses ‘>’ as prompt
• Accepts
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Constants (e.g., 2 3 156 -99.0, etc.)
Variables (e.g., Height, Weight, SubjID,…)
Operations (e.g., ‘+’ ‘-’ ‘*’ ‘/’ ‘^’ ‘>’ ‘<‘ ‘==‘ ‘<-’)
Functions (e.g., sum(c(1,2,3)), mean(c(1,2,3))…)
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R Concepts
• Variable types
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Scalar (a = 128)
Vector (a = c(3, 2, 9, 5))
Matrix (dim(a) = c(2,2))
Data Frame - collection of vectors.
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Similar to spread sheet
‘rows’ are indexed
‘cols’ named and indexed
E.g., df$a is the column of data frame df named ‘a’ and
df$a[5] is the 5th element of ‘a’.
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Statistics
• Science of data collection, summarization, analysis
and interpretation.
• Descriptive versus Inferential Statistics:
– Descriptive Statistic: Data description
(summarization) such as center, variability and
shape for quantitative variable (e.g. age) and
number (frequency) and percentage for
categorical variable (e.g. gender, race etc).
– Inferential Statistic : Drawing conclusion beyond
the sample studied, allowing for prediction.
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Statistical Description of Data
• Statistics describes a numeric set of data by its
• Center (mean, median, mode etc)
• Variability (standard deviation, range etc)
• Shape (skewness, kurtosis etc)
• Statistics describes a categorical set of data by
• Frequency, percentage or proportion of each
category
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Statistical Inference
sample
population
•Statistical inference is the process by which we acquire
information about populations from samples.
•Two types of estimates for making inferences:
–Point estimation.
–Interval estimate.
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Population and Sample
• Population: The entire collection of individuals or
measurements about which information is desired.
• Sample: A subset of the population selected for study.
– Primary objective is to create a subset of population
whose center, spread and shape are as close as that of
population.
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Parameter v.s. Statistic
• Parameter:
– Any statistical characteristic of a population.
– Population mean, population median, population standard
deviation are examples of parameters.
– Parameter describes the distribution of a population
– Parameters are fixed and usually unknown
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Parameter v.s. Statistic
• Statistic:
– Any statistical characteristic of a sample.
– Sample mean, sample median, sample standard deviation
are some examples of statistics.
– Statistic describes the distribution of population
– Value of a statistic is known and is varies for different
samples
– Are used for making inference on parameter
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Parameter v.s. Statistic
• Statistical Issue
– Estimate a population parameter using a
sample statistic.
– E.g., the sample mean is an estimate of
the population mean.
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