Transcript Lecture6 - University of Idaho

PSYC512: Research Methods
Lecture 6
Brian P. Dyre
University of Idaho
PSYC512: Research Methods
Lecture 5 Outline
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Questions about material covered in Lecture 5
 Scientific Method: Proof and disproof & Strong
Inference
 Operational definitions
Issues in Measurement
 Choosing Measures
 Scales of Measurement
 Variables: Reliability and validity
 sampling
PSYC512: Research Methods
Choosing Measures
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Research tradition
e.g., operant conditioning—lever pressing
e.g., cognition—accuracy and reaction time
e.g., sensation and perception—discrimination
accuracy
e.g., personality—surveys, inventories (self-reports)
Theory
e.g., the psychophysical postulate – discrimination
accuracy
e.g., Serial vs. parallel processes in visual search – RT
Availability of new techniques
Availability of equipment
PSYC512: Research Methods
Features of Measures: Scale of
Measurement (Stevens, 1946)
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Four types: nominal, ordinal, interval, and ratio
Nominal scales
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set of unique cases, types, or categories with NO ORDER
Only non-parametric operations are valid: counting frequencies,
modes, chi-square, point-biserial correlation
Ordinal scales
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different categories that can be ranked along a continuum
more or less, but not how much more or less
Only non-parametric operations are valid : counting
frequencies, modes, medians, chi-square, rank-order
correlation
PSYC512: Research Methods
Features of Measures: Scale of
Measurement (Stevens, 1946)
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Interval
 intervals of the scale are equal in magnitude
 Necessary but not sufficient condition for parametric statistical
tests
 valid operations: all mathematical operations, means, standard
deviations, etc. may be calculated
 If other distributional assumptions are met: linear and non-linear
regression, t-tests, ANOVA are also valid
 no fundamental zero—no ratio statements allowed
Ratio
 Like interval but also has a fundamental zero point—allows ratio
statements such as “A is twice as much as B”
Generally interval or ratio scales should be used if possible
 More powerful and flexible statistical tests
 More precision in evaluating quantitative hypotheses
PSYC512: Research Methods
Features of Measures:
Sensitivity
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Sensitivity: measure must show changes in response
to changes in the independent variable
Range effects
 Ceiling effects: variable reaches its highest
possible value and gets truncated (test is too
easy)
 Floor effects: variable reaches its lowest possible
value and gets truncated (test is too hard)
PSYC512: Research Methods
Features of Measures:
Reliability
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the ability of a measure to produce consistent results when
repeated measurements are taken under identical conditions
Types:
 precision: physical measurement (1/noise)
 margin of error: sampling in surveys
 interrater reliability: observers viewing the same behavior
 Test-retest, parallel forms and split-half reliabilities:
psychological tests
PSYC512: Research Methods
Other Features of Measures
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Accuracy
 does a measure produce results that agree with a
known standard?
 Accuracy vs. Precision
Validity
 Measurement validity: the extent to which your
measure indeed measures what it is intended to
measure
 Types: Face validity, Content validity, Criterionrelated validity (concurrent vs. predictive),
Construct validity
Relationship between reliability and validity
PSYC512: Research Methods
Probability and Statistics
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Why are probability and statistics important?
Used to assess variability in data
 Treatment Variance
 Variability due to different levels of independent
variable
 Good variance that we want to maximize
 Error Variance
 Variability in data due to factors other than the
treatment
 Bad variance that we want to minimize
Probability and Statistics are simply tools used to assess and
compare these sources of variability
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PSYC512: Research Methods
Visualizing Variability: Distributions
of Frequency and the Histogram
Histograms: used to represent
frequencies of data in different
classes or categories
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Frequency
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PSYC512: Research Methods
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Displaying Histograms:
Stem and Leaf Plots
Stem and Leaf plots are used to display histograms
graphically (on their side) using only typed characters
Stem
Leaf
(hypothetical histogram for IQ)
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012234445555667777889
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PSYC512: Research Methods
Distributions of Probability Density
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Similar to frequency
histogram except y-axis
now represents
probability density
(mass) rather than
frequency
Probability density =
Frequency/N
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Probability Density
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Some Types of Distributions
Gamma
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Probability Density
Probability Density
Normal
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PSYC512: Research Methods
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Measures of the Center of a
Distribution
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Measures of center represent the general
magnitude of scores in a distribution
Mode: most frequent score
Median: the middle score of an ordered
distribution
Mean (average):
where X is the data and
N is the total number of
observations
X
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PSYC512: Research Methods
Measures of the Spread of a
Distribution
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Measures of spread are used to assess the
consistency of scores in a distribution
Range = max score – min score
Interquartile range = score(Q3) – score(Q1)
Variance (s2) and standard deviation (s)
where X is the data,
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and N is the total number
s2  
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PSYC512: Research Methods
More on Variance
Standard Deviation (s) = sqrt(variance)
where X is the data,
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X 
m is the mean of the data,
s
and N is the total number
N
of observations
Why N instead of N-1? Populations vs. Samples
 Remembering how to compute variance
“the mean of the squares – square of the means”
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PSYC512: Research Methods
Describing Distributions
Parametrically: Statistical Moments
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Any distribution based on interval or ratio data can be
summarized by its statistical moments
First Moment: Mean—location of distribution on x-axis
Second Moment: Variance—dispersion of distribution
Third Moment: Skewness—symmetry of distribution
Fourth Moment: Kurtosis—degree of “peakedness”
PSYC512: Research Methods
Estimators
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Sample statistics estimate population parameters
 Mean: M or X vs. M
 Variance: s2
vs. s2
Properties of Estimators
 Sufficiency: uses all information in sample (mean and variance
are sufficient, mode and range are not)
 Unbiasedness: expected value approaches real value with
increased sampling
 Efficiency: tightness of cluster of sample statistics relative to
the population parameter
 Resistance: influence of outliers on sample statistic
PSYC512: Research Methods
Next Time…
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Topic: descriptive statistics, variables, sampling,
and more on hypothesis testing
Be sure to:
 Read the assigned readings (Howell chapters
3-4)
 Continue searching and reading the scientific
literature for your proposal
PSYC512: Research Methods