Chapter 16
Statistical Analysis
DR. JOE NJOROGE
}
Descriptive Statistics
}
Inferential Statistics
}
Other Multivariate Techniques
}
Quick Quiz
Descriptive Statistics
}
Descriptive Statistics – statistical computations describing either the
characteristics of a sample or the relationship among variables in a sample.
}
Data Reduction
}
Measures of Association
}
Proportionate Reduction of Error (PRE) – a logical model for assessing the
strength of a relationship by asking how much knowing values on one variable
would reduce our errors in guessing values on another variable.
Descriptive Statistics
}
Nominal Variables
}
Lambda (λ)
}
Ordinal Variables
}
Gamma (γ)
}
Interval and Ratio Variables
}
Pearson (r)
Descriptive Statistics
}
Regression Analysis – a method of data analysis in which the relationships among
variables are represented in the form of an equation, called a regression
equation.
}
Linear Regression Analysis – a form of statistical analysis that seeks the
equation for the straight line that best describes the relationship between two
ratio variables.
}
Multiple Regression Analysis – a form of statistical analysis that seeks the
equation representing the impact of two or more independent variables on a
single dependent variable.
Descriptive Statistics
Descriptive Statistics
}
Linear Regression
}
Regression Line
}
Unexplained Variation
}
Explained Variation
Descriptive Statistics
}
Multiple Regression
}
Partial Regression Analysis – a form of regression analysis in which the effects
of one or more variables are held constant, similar to the logic of the
elaboration model.
}
Curvilinear Regression Analysis – a form of regression analysis that allows
relationships among variables to be expressed with curved geometric lines
instead of straight ones.
Inferential Statistics
}
Inferential Statistics – the body of statistical computations relevant to making
inferences from findings based on sample observations to some larger population.
Inferential Statistics
}
Univariate Inferences
}
Cautions about Making Inferences
•
The sample must be
drawn from the population about which inferences are being made.
•
The inferential
statistics assume several things: (a) simple random sampling, (b) sampling with
replacement, (c) 100 percent completion rate
•
Inferential statistics
are addressed to sampling error only, not nonsampling error.
}
Tests of Statistical Significance
}
Statistical Significance – a general term referring to the likelihood that the
relationship observed in a sample could be attributed to sampling error alone.
}
Tests of Statistical Significance – a class of statistical computations that
indicate the likelihood that the relationship observed between variables in a
sample can be attributed to sampling error alone.
}
The
Logic of Statistical Significance
•
Assumptions regarding the independence of two variables in the population study
•
Assumptions regarding the representativeness of samples selected through
conventional probability-sampling procedures
•
The observed joint distribution of sample elements in terms of the two variables
}
Level of Significance – in the context of tests of statistical significance, the
degree of likelihood that an observed, empirical relationship could be
attributed to sampling error.
}
A relationship is
significant at the .05 level if the likelihood of its being only a function of
sampling error is no greater than 5 out of 100.
}
Chi-Square
}
Based on the null hypothesis.
}
Computation:
}
For each cell in the
table, subtract the expected frequency for that cell from the observed
frequency.
}
Square the quantity.
}
Divide the squared
difference by the expected frequency.
}
Chi-Square Table
Inferential Statistics
}
t-Test
}
Measure for judging the statistical significance of differences in group means.
}
Logic:
}
The value of t
will increase with the size of the differences between means.
}
The value of t
will also increase with the size of the sample involved.
}
The value of t
will be larger when variations of values within each group are smaller.
}
Caution…
}
There are no objective tests of substantive significance (only objective
significance).
}
Statistical significance is only appropriate for samples, and not for whole
populations.
}
Tests of significance are based on the same sampling assumptions used to
computer confidence intervals.
Other Multivariate Techniques
}
Path Analysis – a form of multivariate analysis in which the causal relationship
among variables are presented in a graphic format.
}
Time-Series Analysis – an analysis of changes in a variable over time.
}
Factor Analysis – a complex algebraic method for determining the general
dimensions of factors that exist within a set of concrete observations.
}
Analysis of Variance (ANOVA) – method of analysis in which cases under study are
combined into groups representing an independent variable, and the extent to
which the groups diff from one another is analyzed in terms of some dependent
variable. Then, the extent to which the groups differ is compared with the
standard of random distribution.
}
Discriminant Analysis – method of analysis similar to multiple regression,
except that the dependent variable can be nominal.
}
Log-Linear Models – data analysis technique based on specifying models that
describe the interrelationships among variables and then comparing expected and
observed table-cell frequencies.
}
Geographic Information Systems (GIS) – analytic technique in which researchers
map quantitative data that describe geographic units for a graphic display.