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Intermediate Statistics 1
 

Intermediate Statistics 1

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    Intermediate Statistics 1 Intermediate Statistics 1 Presentation Transcript

    • Intermediate Statistics Professors:Ramaswami & Walker
    • This Morning’s Session
      • Review of Course Outline
      • Review of Course Expectations
      • Review of First Stat’s course
      • Break
      • Introduction to Generalized Linear Techniques
      • Introduction to Regression
      • Break
      • Simple Regression
    • Purpose of the course
      • To assist you to develop the tools and knowledge on how to: (a) be intelligent consumers of data; (b) be able to run your own analysis; © understand how to interpret data and (d) be able to derive logical inferences based on data
    • Focus of the Course
      • Generalized Least Square techniques
      • Interpretation using SPSS Outputs
      • Knowing SPSS (Statistical Package for the Social Sciences)
    • Course Requirements
      • Mid-term examination
      • Final examination
      • Always have handouts in class
      • Have a calculator
      • Politeness
      • Cooperative ethos
      • Working independently on exams
    • Review of First Stats Course
      • What are the different types of measurement?
      • What is correlational analysis
      • Interpret the following findings:
    • Example 1:
      • In a study that examined the relationship between number of days present in school and students’ sense of belonging among 135 high school students the following Pearson Correlation statistics was obtained:
      • r=.64; p<=.000
    • Example 2
      • The relationship between time on task and obtaining a grade of C+ or lower was found to be r= -.32; p <= .048 for 50 students in an alternative education program for disruptive students.
    • What are generalized least square models?
      • Generalized least square models are models that seek to minimize differences between what we observe and what we calculate.
      • These models are able to accomplish this, by fitting the data such that the squared deviations between observed and fitted data are minimized.
    • Example
      • Refer to example on the board-
    • Techniques to be Studied
      • Regression (Simple, multiple, hierarchical)
      • Analysis of Variance (one-way)
      • Univariate Analysis of Variance to include Analysis of Covariance
      • Possibly- Chi- Square
    • Regression
      • History- in France, applied to the study of astronomy- orbits of bodies around the sun (least squares method)
      • Term regression coined in the 19 th C to describe a biological phenomenon- children of exceptional individuals tended to be less intelligent than their parents- Darwin’s cousin Francis Galton- “regression towards mediocrity”. Work later extended by Pearson and Yukle
    • Assumptions of Regression
      • Sample must be representative of the population.
      • The dependent variable must be continuous.
      • The independent variables must be linearly related but not strongly
      • The independent variable should be continuous although categorical variables can be used.
      • Values of the independent variables are normally distributed
    • The Basic Regression Model
      • Predicted Y= a+ B1(X1)+ B2(X2)……..error
      • Where B1 represent the impact of X1 on Y
      • a represents the constant or the intercept.
      • Y is our outcome variable
      • X is our independent variable
    • What do the terms mean?
      • B is called the slope or the regression coefficient. It is the change in the dependent variable for a unit change in x or the predictor variable
    • Example of slope
      • Education Income
      • 16 years 20,000
      • 18 years 20, 500
      • 20 years 21,000
      • 22 years 21,500
      • 24 years 22, 000
    • Questions that can be asked in regression
      • What is the impact of the predictor (independent) variables on the outcome (dependent variable)?
      • Is the impact significant?
      • Is the regression model significant?
      • What percent of the variance in the outcome variable is explained by the predictor (s) variable (s).
    • Key Terms in SPSS Regression Outputs
      • R Square
      • Adjusted R Square
      • Regression model
      • Standardized Coefficients(Beta)
      • Unstandardized Coefficients (B)
      • Fvalue
      • T value
      • P value