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Chapter 13

CCJS 300 Chapter Notes - Chapter 13: Phi Coefficient, Nonparametric Statistics, Parametric Statistics


Department
Criminology and Criminal Justice
Course Code
CCJS 300
Professor
Alan Lehman
Chapter
13

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-Statistics summarize data
-Two types of statistics:
-Descriptive statistics: summarizes or describes data or shows relationships between variables
-Inferential statistics: enable generalization or interference of sample findings to larger
populations
-Measures of central tendency: summary statistics that describe the typical, middle, or average
score (mode, median, mean)
-Mode: most frequently occurring score, simplest measure of central tendency
-Median: midpoint, most appropriate for ordinal data
-Mean: average score, most familiar measure of central tendency
-Measures of dispersion: spreadoutness of the data
-Range: simplest measure of dispersion, represents the highest and lowest scope or the
difference between them
-Standard deviation: highly useful, plus or minus one standard deviation always equals
68 percent of a normal curve
-Normal distribution: bell-shaped curve that describes a variety of phenomena. For
example, a large sample of a population will be normally distributed and resemble a
normal curve
-Standard deviation units (z score): measure the deviation from the mean relative to the
standard deviation
-Chi-square: a test of the independence of the relationship between nominal-level variables
-Unstable in the 2x2 case
-Harder with a larger number of cells
-Degrees of freedom: the number of cells that are free to vary
-Chi-square based measures of association:
-Phi coefficient and phi-square: a PRE (proportionate reduction in error) measure in
knowledge of one variable enables one to predict the second
-Contingency coefficient: a chi-square-based measure of relationship in which a zero
equals no relationship, but the upper limit is less than one
-Cramer’s V: a useful chi-square-based measure of relationship appropriate for a 2x2
table
NATURE AND TYPES OF STATISTICS
-Parametric statistics: assume some interval level of measurement and a normal population
(better for interval data)
-Nonparametric statistics: distribution free statistics in which few assumptions are made
regarding the normality of the population (better for nominal and ordinal data)
-Null hypothesis: assumes that there is no difference between the groups being compared or no
relationship in the population
-Tests of significance: assesses whether the differences between observed and expected values
could be due to chance (sampling error) or are statistically significant
-Level of statistical significance is set by the researcher in terms of the amount of risk or
willingness to be in error in rejecting the null hypothesis
-T test: used to compare the sample means of two groups, developed for the benefit of
students
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