Statistics & Psychometrics Flashcards
Construct
Any property/characteristic/element which is not directly observable but can be inferred due to empirical evidence
E.g. energy & sound & time
Psychological constructs
Produce instruments to measure psychological constructs e.g. depression
Construct supported by theory
Behaviour is only unit which is observable in constructs
Doesn’t mean all behaviour is objective & rational
Discrete & continuous variables
Discrete; finite range of values
Continuous; infinite ranges e.g. time, distance
Dichotomous & polytomous variables
Dichotomous; discrete variables that can assume only 2 values e.g. yes/no
Polytomous; discrete variables that can assume more than 2 values e.g. likert scale
Levels of measurement
Categorical; nominal & ordinal
- nominal= identity, count, mode, ch-square
- ordinal= identity, rank order, same stats plus median & rank order correlation
Quantitative; interval & ratio
- interval= identity, rank order, additivity, same stats plus mean, SD & ANOVA
- ratio= identity, rank order, additivity, same stats as interval
What is measurement?
Assign magnitudes to a certain property of an object or class of objects, according to pre-established rules & with the help of the numerical systems, so that’s its validity can be proved empirically
Measurement complexity
The relationship ‘twice as’ applies only to the numbers, not the attribute being measured
Likert scales involve arbitrary decisions, the statistical analysis should say something about reality
Measurement theory
A branch of applied mathematics that is useful in measurement & data analysis
The fundamental idea of MT is that measurements are not the same as the attribute being measured
Hence, if you want to draw conclusions about the attribute, you must take into account the nature of the correspondence between the attribute & the measurements
Isomorphism principle
Measurement theory
Nature has properties parallel to the structures of mathematical logical systems
Quality of Measurement
Measurement theory
Quantification= allows accurate descriptions of phenomena as well as comparison with other phenomena Communication= summarise info accurately & objectively, only provides info about what we wish to measure Standardisation= ensures equivalence between objects with different characteristics Objectivity= reduces potential ambiguities
Quantities (units)
Measurement theory
Fundamental(F)= mass, length, time
Derived(D)= density(D)=mass(F)/volume(F)
Law= for every action, there’s an equal & opposite reaction (Newton’s 3rd law)
Theory= measurable attributes based only on scientific theories
The error
Measurement Theory
Error corresponds to the distance between the object to be measured & the points in the instrument responsible for measuring it, the larger the gap, the higher the error & lower the validity
Stats; studies the number as representing something different from it, description of natural phenomena & no longer original concept
Maths; the number 1 is only 1 (uniqueness quantification)
Measurement; the number 1 can be +/-1, the number becomes a range & being an interval, has variability (variance), that is, error
Error types/where they come from
Measurement theory
Instrument errors; content validity
Individual biases & errors; halo effect, severity, leniency error, stereotyping
Systematic errors; come from non-controlled factors
Random errors; caused by unknown & unpredictable changes in test administration
Sampling error; arise from erroneous inferences about pops from samples (non-representative samples)
The theory of error
Impossible to determine causes of all possible errors in a measure
Random errors occurrence is governed by the probability laws, as an random phenomena
Mean= most probably value of a single quantity observed many times under same condition
Dispersion= extent to which a distribution is stretched or squeezed
Normal distribution/ probability density function/ cumulative distribution function
ND= Related traits to psychological constructs are distributed around the mean, want to estimate area under curve PDF= normal, platatonic, katatonic CDP= could also be used for inferential purposes
Data transformation
Theory of error
Used if no ND
square root transformation
Cube root transformation
Log transformation
Residuals & error
Theory of Error
Residuals= amount by which an observation differs from its expected value in a sample
Error= amount by which ab observation differs from its expected value in a pop
SD= degree to which individuals in sample differ from sample mean
Standard error of the mean= how far the sample mean of the data is likely to be from the true pop mean
Degrees of freedom
Theory of error
Number of independent pieces of info used to estimate a parameter
Number of values in final calculation of a statistic that are free to vary
Degrees of freedom are usually n-1 (n=number of data points)
Why calculating SEM is important
From SEM, the confidence interval (CI) can be computed
CI is a range of values where the true value lies in
Normality tests
2 different distributions, expected & observed
Larger gap=lower precision & accuracy of measurement
Statistics
Applied mathematics that provides methods for collecting, organising, describing, analysing & interpreting data for their use in decision making
It is the science of learning from data, which in turn, can provide info for decision-making in the presence of uncertainties
The path of quantitative research
1) Object/event (variable)
2) uncertain behaviour (random variable)
3) theory (epistemological perspective)
4) hypotheses (test of theoretical assumptions) & measurement theory (mathematical assumptions)
5) statistical analyses
6) results (description & generalisation/inference)
Relationship between variables
Causality= experimental research, IV manipulation & random samples
Association= non-experimental research, non-causal relationships, random or non-random samples
Correlation
Magnitude & direction of the relationship between an IV (predictor) & DV (criterion)
Linear regression= y=ax+b
Shows a relationship, not a comparison between variables
Not a statistical technique for hypothesis testing, can be used after hypothesis testing to calculate effect size
Correlation coefficients
-0.3
Curvilinear relationship
As one variable increases, so does the other variables, but only up to a certain point, after which, as one variable continues to increase, the other decreases
e.g. Yerkes Dodson law
Spurious Correlation
Coincidental correlation
Can be misleading
Correlations need to be theoretically driven
Measurement theory
Accuracy= closeness of a measured value to a standard or known value e.g. sample with mean IQ score of 120 is not accurate
Precision= closeness of 2 or more measurements to each other e.g. IQ score in 3 different sessions
Regression Analysis
A statistical technique for estimating the relationships among variables
Can be used to predict the DV when the IV is known
Latent variable models
Latent variables= constructs are unobserved, hidden or latent variables inferred from the data collected on related observable variables
Structural equation modelling= a multicast stats analysis technique used to analyse structural relationships among observable & unobserved (latent) variables, implies a structure for the covariances between the observed variables
Relationship between the observable & unobservable quantities is described by a mathematical function
