w7 dmitriy-zinovev descriptive stats

8/4/2019 W7 Dmitriy-Zinovev Descriptive Stats

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Descriptive Statistics

and Inferential StatisticsCSC 426 Week 7

Dmitriy Zinovev


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Agenda

Data Preparation


Inferential Statistics


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Data Preparation

Logging the Data

Checking the Data For Accuracy

Data Transformations


4/19


Univariate Analysis

Accesses properties of a single variable

Distribution

Center

Spread

Correlation

Shows ties between variables


5/19

Univariate Analysis (distribution)


6/19

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


9/19

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


10/19

Correlation

Need to determine whether there is arelationship between variables


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Correlation (cont.)

Magnitude

Direction


12/19

Correlation (cont.)

Calculation

Test significance of produced value Significance level

Degree of freedom


13/19

Correlation (cont.)

Situations when there is only 1 variable inthe model are rare in real life. Need tocompute correlation matrix.


14/19

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.


15/19

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


17/19

Inferential Statistics (Dummyvariables.)

Define different groups.


18/19

Research design

Experimental Analysis.

Quasi-Experimental Analysis.


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QUESTIONS?

w7 dmitriy-zinovev descriptive stats

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