Statistics & Psychometrics

Question 1

Construct

Answer 1

Any property/characteristic/element which is not directly observable but can be inferred due to empirical evidence
E.g. energy & sound & time

Question 2

Psychological constructs

Answer 2

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

Question 3

Discrete & continuous variables

Answer 3

Discrete; finite range of values

Continuous; infinite ranges e.g. time, distance

Question 4

Dichotomous & polytomous variables

Answer 4

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

Question 5

Levels of measurement

Answer 5

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

Question 6

What is measurement?

Answer 6

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

Question 7

Measurement complexity

Answer 7

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

Question 8

Measurement theory

Answer 8

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

Question 9

Isomorphism principle

Answer 9

Measurement theory

Nature has properties parallel to the structures of mathematical logical systems

Question 10

Quality of Measurement

Answer 10

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

Question 11

Quantities (units)

Answer 11

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

Question 12

The error

Answer 12

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

Question 13

Error types/where they come from

Answer 13

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)

Question 14

The theory of error

Answer 14

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

Question 15

Normal distribution/ probability density function/ cumulative distribution function

Answer 15

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

Question 16

Data transformation

Answer 16

Theory of error

Used if no ND

square root transformation

Cube root transformation

Log transformation

Question 17

Residuals & error

Answer 17

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

Question 18

Degrees of freedom

Answer 18

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)

Question 19

Why calculating SEM is important

Answer 19

From SEM, the confidence interval (CI) can be computed

CI is a range of values where the true value lies in

Question 20

Normality tests

Answer 20

2 different distributions, expected & observed

Larger gap=lower precision & accuracy of measurement

Question 22

Statistics

Answer 22

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

Question 23

The path of quantitative research

Answer 23

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)

Question 24

Relationship between variables

Answer 24

Causality= experimental research, IV manipulation & random samples

Association= non-experimental research, non-causal relationships, random or non-random samples

Question 25

Correlation

Answer 25

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

Question 26

Correlation coefficients

Answer 26

-0.3

Question 27

Curvilinear relationship

Answer 27

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

Question 28

Spurious Correlation

Answer 28

Coincidental correlation
Can be misleading
Correlations need to be theoretically driven

Question 29

Measurement theory

Answer 29

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

Question 30

Regression Analysis

Answer 30

A statistical technique for estimating the relationships among variables

Can be used to predict the DV when the IV is known

Question 31

Latent variable models

Answer 31

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