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SOC202H1 Chapter Notes -Guesstimate, Systematic Sampling, Rank


Department
Sociology
Course Code
SOC202H1
Professor
Scott Schieman

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CH2 ORGANIZING DATA TO MINIMIZE STATISTICAL ERROR
Accuracy of scientific ideas tested by empirical predictions
Errors known degrees of imprecision
o Error reduction relies on understanding predictive relationships
among variables
o STATISTICAL ERROR Know degrees of imprecision in the procedures
used to gather and process information
Controlling Sampling Error
Statistical analysis involves sampling
o Sampling Error inaccuracy in prediction about a population that
results from the fact that we do not observe every subject in the
population
Observation a measurement of a single person
Summary Calculation summing up a group of measurements, based on a
set of observations
o Research interests usually w/ summary statements of the group
Usually small # subjects to draw conclusions on larger pop.
A POPULATION a large group of people (or objects) of particular interest
that we desire to study and understand
A SAMPLE a small group of the population; the sample is observed and
measured and then used to draw conclusions on the population
A PARAMETER a summary calculation of measurements made on all
subjects in a population
o Determine true parameter need survey entire population
A STATISTIC a summary calculation of measurements made on a sample
to estimate a parameter of the population
o A estimate, tool to draw conclusions about a population in general
Conclusion from sample not absolutely correct, only estimations
Degree of error/confidence in predictions determinable w/ logic
o Statistical Generalization conclusions about a population made w/
proper statistical procedures
o Statistical Estimate report of a summary measurement based on:
1. Systematic sampling & precise measurements
2. Reported w/ known degrees of error & confidence
o Guesstimate a report of a summary measurement based on limited
and usually subjective personal experiences, anecdotal evidence, or
hasty casual observation
Stereotype a false generalization, guided by feelings
Probability Theory the analysis and understanding of chance occurrences
o allows compute confidence/accuracy degrees w/ conclusion on pop.
o Allows compute error how often statistic will incorrectly predict
the parameter
Sample Size  the number of cases or observations in a sample
o The number of persons or objects observed
o Large sample smaller sample error, measured in +/- value
REPRESENTATIVE SAMPLE a sample in which all segments of the
population are included in the sample in their correct proportions in the
population
o More representative smaller sample error
o Non-Representative Sample some segments of the population are
overrepresented or underrepresented in the sample
o SIMPLE RANDOM SAMPLE every person (or object) in population has
the same chance of being selected for the sample
Controlling Measurement Error
Observation & measurement key in research
o Measurement Error inaccuracy in research, which derives from
imprecise measurement instruments, difficulties in the classification of
observations and the need to round numbers.
Operational Definition set of procedures/operations to measuring a
variable
o Formulation guided by identifying common measurement errors &
doing everything possible to minimize them
Levels of Measurement: Careful selection of Statistical Procedures
Measurement the assignment of symbols, either names or numbers, to
the differences
o Score The measurement of a particular sample subject on a single
variable –ex. Subject A’s Age, GPA, Gender
o Unit of Measure a set interval or distance between quantities
LEVEL OF MEASURE OF A VARIABLE Identifies the variable’s
measurement properties, which determine the kind of mathematical
operations (addition, etc.) that can be appropriately used with it and the
statistical formulas that can be used w/ it in testing theoretical hypotheses
o NOMINAL VARIABLES name categories codes merely indicate a
difference in category, class, quality, or kind
No meaningful rank in magnitude, numbers arbitrarily chosen
No sense of degree w/ nominal variables
Dichotomous Variable variable with only two categories
o ORDINAL VARIABLES Nominal w/ allowing ranks (high to low)
Can be named categories or numerical scores
Ex. Social class (upper-lower), education level (senior, junior)
Ex. Likert scoring to survey questions
o INTERVAL VARIABLES Numerical scores w/ defined unit of measure
Allow add, subtract, multiple, divide scores, compute averages
Differences in amount, quantity, degree numerically
Ex. Fahrenheit, interval between degrees same
Vs. Ordinal, has set unit of measure
Subtraction btwn ordinal = difference in rank not distance
btwn scores
o RATIO VARIABLES Interval w/ true zero point, zero means none
Ex. Weight, height, GPA, distance, population size
Interval may have zero but is arbitrary
Check ratio vs. interval, check if a ratio is meaningful
Ratio the amount of one observation in relation to another
Ex. Weight, 40g to 20g has 2:1 ratio
Ex. 1st, 2nd & 3rd, 3rd isn’t 3rd times worse than 1st
Dummy Coding change nominal/ordinal into interval/ratio w/ artificial
numerical scores ex. Index coding
Unit of measure for interval/ratio variables only
o Fixes set interval for the numerical values used as scores for an
interval/ratio variable ex. Kg, cm, mL
o Different from level of measurement
Coding and Counting Observations
Codebook a concise description of the symbols that signify each score of
each variable
o Use number symbols for categories b/c easier counting & sorting
o Response coding may introduce measurement error, req. precision
All variables coded follow 2 principles:
o Principle of Inclusiveness for every given variable, there must be a
score/code for every observation made (exhaustive)
Ex. Race: white, black, Asian, other (residual category)
Req. supply codes for missing data (Missing Values)
Disregarded when compute statistic for a variable
o Principle of Exclusiveness for a given variable, every observation can
be assigned one and only one score
Two scores cannot overlap
Frequency Distributions
Frequency Distribution a list of all observed scores of a variable and the
frequency for each score (or category)
o Frequency (f) # of observations or cases for each value
o PROPORTIONAL FREQUENCY DISTRIBUTION a list of the proportion
of responses for each category or score of a variable
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
o PERCENTAGE FREQUENCY DISTRIBUTION a list of the percentage of
responses for each category or score of a variable
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Coding and Counting Interval/Ratio Data
Precise Measurement one in which the degree of measurement error is
sufficiently small for the task at hand, specified by rounding error
o Specification: how much measurement error can be tolerated w/o
encountering practical problems or drawing faulty scientific concl.
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