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Meeting 1: Chapter 3 Individual Differences and Correlations (The Nature…
Meeting 1: Chapter 3 Individual Differences and Correlations
The Nature of Variability
Interindividual differences
--> difference that exist between people
some of these interindividual differences are between people in the same experimental group
some of these interindividual differences are between people who are in different experimental groups
Intraindividual differences
-->
differences thtat emerge in one personover time or under different cirumstanes
The Importance of individual difference
At the heart of research in the behavioral science (e.g.Why are some people more aggressive than others?)
Fundamental to psychological measurement
Psychometric concepts such as reliability and validity are entirely dependent on the ability to quantify the differences among people
Not only for traditional psychological tests, but for all research
research in experimental psychology involves exposing people to different experiences and then measuring the effects of these experiments on their behavior
Process of quantification of psychological measurement
distribution of scores
variability --> differences among the scores within a ditribution
Variability and Distribution of Scores
Quantifying the amount of variability within a distribution of scores is key element of behavioral research.
Central Tendency --> what is the typical most representative score in the distribution
arithmetic mean is a value that represents the typical score
Variability --> measurement rests on this concept
when calculated you get the degree to which the individual score differs from the mean
Size Depends on; --> The degree to which scores in the distribution differ
-->The metric of the scores in the distribution
Factors to consider when interpreting the variance
1.Variance can not be smaller than 0
No simple small/ large interpretation possible
the variance of distribution scores is most interpretative and meaningful when it's put into a context
the importance of variance and standard deviation lies mainly in their effects on other values that are more directly interpretive
Standard deviation
Simply the square root of variance
reflects variability as the degree to which the scores in a distribution deviate
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Distribution Shapes and Normal Distributions
the very meaning of test scores sometimes hinges on the assumption the the scores are normally distributed
theoretical ideal
In a symmetric distribution the mean is the same as median
Total surface of probability density function is always 1
In a positively skewed distribution the mean is larger than the median
Quantifying the Association Between Distributions
Direction of association --> do people who obtain a high score on one variable also do so on the other?
Covarience--
>association between the variability in the two distribution scores
Only informative about the direction
Correlation-->not only direction but also magnitude
magnitude of the association -->
two variables weakly correlated or not ?
Consistency -->useful concept when thinking about associations
Variance covariance matrix --> variances presented diagonal, covariances around
covariances are symmetric, values below the diagonal are identical to the above
Variance and Covariance of Composite scores
Composite scores-->scores made up of several variables
Variance composite score is the same as summing all cells of variance covariance matrix.
association between two composite scores relevant to the reliability
Interpretation of test scores
When a person takes a psychological test, he or she receives test scores that can be expressed in different forms
Two key points with a reference distribution
Deviation from the mean
knowing that your raw score is above/below the mean tells you something about your performance relative to the class
deviation relative to the other scores
only when normally distributed can approached by the cumulative distribution function
z scores (standard scores)
degreee to which a test score is above or below the mean test score
useful for computing correlation coefficients
Converted standard scores --> easier to understand
two step process = new mean + new standard deviation
e.g. SAT,ACT,GRE,LSAT
Percentile rank --> percentage of people with a given score or lower
normal distribution --> z scores--> p
allows to link specific standard scores to percentiles
not normal distribution= frequency table & continuity correction
Normalized scores --> scores into normally distributed scores
normalization transformations or area transformations
percentile ranks 2. percentile ranks--> standard scores 3. standard scores -->scores with a given matric
Test Norms
tests are normed to provide a better interpretation by the test user
reference sample
large group of people used in construction of a test
representatives of the refrence sample
selecting individuals
probability sampling --> representative sample
nonprobability sampling --> no assurance
Binary Items
-->
comprised of dichotomous responses
the average score will range between 0-1, representing the proportion of "yes"
if test scores have no variance, scores cannot be correlated with any other sets of scores
Brane Bencic 424918 / 2.5.2 Course and Practical: Psychometrics: An Introduction / Meeting 1 / Tutor: Nelleke Deijkers / Source: Furr, R.M. & Bacharach, V.R. (2014). Psychometrics: An introduction. Second Edition. Thousand Oaks, CA: Sage Publications. ISBN 9781452256801.
