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Descriptive Statistics
and Inferential StatisticsCSC 426 Week 7
Dmitriy Zinovev
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Agenda
Data Preparation
Descriptive Statistics
Inferential Statistics
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Data Preparation
Logging the Data
Checking the Data For Accuracy
Data Transformations
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Descriptive Statistics
Univariate Analysis
Accesses properties of a single variable
Distribution
Center
Spread
Correlation
Shows ties between variables
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Univariate Analysis (distribution)
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Univariate Analysis (Center)
Mean
Non-stable to extreme observations
Very useful in case of a normal distribution Median
Great for visual comparison between distributionsVery useful in case of skewed distribution
ModeMost frequent value in the distribution
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Univariate Analysis (Spread)
5 number summary Min smallest observation
Q1 median of the first half of a distribution
Median median of a distribution
Q3 median of the second half of a distribution
Max biggest observation
1.5 IQR rule
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Univariate Analysis (Spread cont.)
Standard Deviation
Shows relation of observations to the mean of adistribution
Calculate a distance to mean for each value Square the results
Divide a sum by the size of a distribution 1 (variance)
Take a square root from variance
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Univariate Analysis (Spread cont.)
Standard Deviation Empirical rule
approximately 68% of the scores in the sample fall withinone standard deviation of the mean
approximately 95% of the scores in the sample fall withintwo standard deviations of the mean
approximately 99% of the scores in the sample fall withinthree standard deviations of the mean
http://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg -
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Correlation
Need to determine whether there is arelationship between variables
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Correlation (cont.)
Magnitude
Direction
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Correlation (cont.)
Calculation
Test significance of produced value Significance level
Degree of freedom
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Correlation (cont.)
Situations when there is only 1 variable inthe model are rare in real life. Need tocompute correlation matrix.
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Inferential Statistics
Used for drawing conclusion about thepopulation from a sample
Estimation
Estimate true value of the parameter from asample
Hypothesis testing
Determine if there is a difference in a parametervalue for two groups.
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Inferential Statistics (Generallinear model )
General linear model family of statistical models thatproduce most of inferential statistics
y = b0 + bx + e
y outcome
b0 intercept
x predictors
b coefficient estimates
e error component
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Inferential Statistics (Generallinear model cont.)
Foundation for many statistical analyses
t-test
Checks if means of two groups are different from each otheron defined confidence level
ANOVA
Checks if there is a difference between more than two groups
ANCOVA
Adjusts the use of ANOVA by including covariates into theanalysis
Regression analysis
Creates a model for predicting dependent variable
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Inferential Statistics (Dummyvariables.)
Define different groups.
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Research design
Experimental Analysis.
Quasi-Experimental Analysis.
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QUESTIONS?