The following is meant as an indication of the material I expect we will cover this semester. (Sometimes we do not get through it all.) Since this material all builds upon the material covered in Psyc 2013, some of this will be review. It will be assumed that you have mastered that material, however, whether reviewed by me in Psyc 2023 or not. I have tentatively linked topics to classes, however, we will go through this as quickly, or as slowly as necessary. Changes to the schedule will be noted in class.

Some Problems with probabilistic reasoning: (adapted from Stanovitch)
1) man who statistics (salience of individual cases)
2) insufficient use of probabilistic information (Baye's theorem)
3) cognitive illusions
4) failure use sample size information
5) tendency to explain chance events
6) gambler's fallacy (tendency to see independent events as dependent)
7) conjunction fallacy

Four factors to consider in evaluating external validity:
1) Population studied and how sampled
2) Operational Definitions
3) Parameter values (both independent and control variables)
4) Demand characteristics (both internal & external)
other threats to validity: statistical validity
Power: avoidance of type II (b error) depends upon:
1) increases as the probability of making type I error increases (trade off between the two)
2) increases as the magnitude of the hypothesized effect increases
3) increases as the size of the sample increases (with n=102, an r of ± .16 is significant at a =.05)

Simple Analytic experiments: involve control, manipulation & measurement: importance of operational definitions
"intro psyc" problem: a legitimate problem, but often overstated

• convenient
• good for a first study (at least),
• in much basic research the subject population studied is not important
• replication occurs among other undergraduate populations
• not wrong, just incomplete (external validity questionable)

• trend to move toward experimental methods from case studies and/or observational or survey methods to correlational to experimentation

• within: increases power, statistical reliability and internal validity use when too few subjects or measures
• concerns with order (carryover) effects: (due to: learning, fatigue, habituation, sensitization, contrast or adaptation)
• counteract by:

terminology: independent, dependent, intervening, control, and confounding (or "extraneous") variables

• Multiple dependent variables often used, assesses generalizability

• within group variance:

• between group variance: same, but also includes effects of the IV

Errors: type I (a - alpha), type II (b - beta): how controlled
1 tailed vs 2-tailed tests (decide a priori)
Between and within subjects t-test (pooled and unpooled error calculations)
Many different inferential statistics: Each intended for specific conditions

• type of measure (nominal, ordinal, interval of ratio)
• shape of the distributions
• experimental design

Analysis of Variance (ANOVA)
ANOVA followed by t-tests only if the ANOVA is significant (importance of placebo controls)
ANOVA: partitions variance: i) subject variables, ii) experimental error, iii) value of the IV

• significant ANOVA indicates that some of the differences among groups did not occur by chance

• 3 stages: 1) identify each causal factor of interest, 2) decide how many levels of each, 3) determine all possible combinations
• terminology: factor = independent variable
• can examine both the main effects (by collapsing across the other IVs) and interactions: with a 2 factor design, have 3 independent questions to answer: main effects for IV₁ and IV₂ and the interaction between them (gives 8 possible outcomes). If any are significant the direction or nature of the differences must be described
• if there is (are) no interaction then the results are said to be additive
• these are still analytic experiments: characterized (ideally) by: random selection of subjects, random assignment of subjects to groups, and concurrent contrast and control with a measured DV.

Factorial designs: #levels IV₁ x #levels IV₂ x #levels IV₃àetc.

• Review of terminology: independent, dependent, intervening, control, and confounding variables
• Interpreting data from 3 factor experiments and/or experiments with three or more levels of one or more IV (e.g., in class 3x3 experiment on impression formation: occupation x personality), Tomlinson et al (1978) pupil size experiment
• Fazio & Backler: software tutorial on main effects and interaction (available in library)

Three specific experimental designs.

• longitudinal designs
• cross-sectional designs
• cohort-sequential designs (cross-sequential in text)

Habituation-Dishabituation techniques a paradigm technique in infancy research

• if show dishabituation, must be able to discriminate
• asymmetries in dishabituation can reveal preferences
• research on categorical perception of colours (Bornstein) and phonemes (speech sounds)

WHY?: ethical reasons or an interest in organismic variables

• prospective and retrospective designs
• find naturally occurring groups and follow them forward (prospective) or trace their histories (retrospective)

Partial solutions:
Matching: 1) subject for subject (preferable but more difficult) or 2) distribution by distribution

• in both cases can selectively drop individuals and bias the sample further

Retrospective studies also have additional problems in that they rely on memory so the partial solutions are more difficult to employ successfully

• more efficient (cheaper and faster) May be necessary with very rare grouping variables of interest (e.g., rare diseases)

• even with measurement and matching, internal validity is still questionable (The additional problems of retrospective designs were well illustrated by McFarland's (1988) study of cyclical variability in moods)

• relative risk ratio (prospective studies) - illustrated by breast cancer data
• relative odds ratio (approximates the relative risk) -- retrospective studies

Causality and ex-post-facto designs. No one quasi-analytic experiment will unambiguously show a causal relationship, however, with converging evidence from many such studies (5, 10 or 100?) can make causal statements (like "smoking causes cancer")

Subject Sampling

• types: random, stratified, proportional, systematic, cluster (multistage)
• Goal is an economic sample: big enough to ensure a valid sample (and sufficient power) and no more
• Volunteers

• A-B studies (e.g., homicides after prize fights, JFKÆs assassination, TV effects etc.)
• multiple baseline designs (can be used both within and between subjects)
• accounting for drifting baselines
• problems of internal validity (due to the confounding passage of time)

Quasi-analytic experiments: Bivalent correlation designs
for correlations: 1) select population and subjects of interest; 2) measure two variables of interest; 3) calculate the extent to which the two variables are systematically related
Graph data (scatterplot): predictor (assumed causal or IV) variable on abscissa (X-axis) and criterion or DV on ordinate (Y-axis)
Pearson's product moment correlation coefficient (for Interval or ratio data) measures the direction and degree of association.
r is the mean of z-score crossproducts: r=S (Z_xZ_y)/N, the extent to which deviations from the average on each measure are similar for each subject sampled

• statistical inference: for a given sample size: larger the absolute value of r, the less likely it is to have occurred by chance, similarly, for a given value of r, the larger the sample, the less likely it was to have occurred by chance.

• r² (coefficient of determination) = estimate of the proportion of variance shared by the two variables; extent to which they covary

• with standard scores and 1 IV, regression coefficient (b) = correlation coefficient (r) [r=b(s_x/s_y)]
• as the correlation grows less strong, Y' moves less in response to a given change in X,
• if r=0, best predictor of Y from X is the mean of Y, and the best predictor of X from Y is the mean of X

Problems interpreting the results of this type of research: third variable problem and directionality (not always an issue), regression artifact (e.g., Rushton), floor and ceiling effects, look for converging evidence

Correlation versus ex-post facto design: similar and can convert one to the other [e.g., assign dummy coding to the categorical (nominal) variable and calculate a point-biserial correlation coefficient]
Interpretation problems are not related to the statistical choice, rather due to the design
Causation not a simple concept: want to have:
1) an association between variables that recurs in different contexts (replication, convergent evidence),
2) have a plausible explanation showing how the predictor variable could cause the criterion variable, and
3) have no equally plausible 3rd variable that could cause the variance in the criterion variable.

While correlation doesn't imply causation, causation does imply correlation

Simpson's Paradox: when two groups are classified on some attribute (as in many ex-post facto designs), then are separated into subcategories, the group with the higher incidence (or scores) overall can have the same or even lower incidence within every one of the subcategories. e.g., 1) salaries and economics degrees, 2) race and imposition of death penalty

Partial correlation r_{YX2× X1}: allows you to examine the relationship between 2 variables with the effect of the third removed from both. Can be viewed as the average of the simple bivariate correlations across levels of the third, "nuisance" variable partialled out. variable.

• removes the systematic relationship statistically, by removing the linear trend, then correlate residuals.
• any number of measured variables can be partialed out as if controlled for experimentally
• partial correlation can be tested for statistical significance with n-j d.f. (where j= number of variables)

Semipartial correlations (sometimes called Part correlations) r_{Y(X2× X1)}:allows you to examine the relationship between 2 variables with the effect of the third removed from one.. (see later handout on multiple regression)

Multiple Correlation and Regression (see later handout)

Discrete trials designs - Psychophysics

• Psychophysics is concerned with four problems of : detection, identification, discrimination, and scaling
• absolute thresholds:

• S-shaped curves: called ogives
• operational definitions of thresholds: P_(yes)=.5
• thresholds vary within and between modalities

a mathematical, theoretical system that recognizing that observers are not merely passive receivers of stimuli, are also engaged in process of deciding whether they are confident enough to say they detect a signal.

• detecting the signal from the noise
• teasing apart sensory ability (i.e. delectability or sensitivity) and decision to say so (response bias).
• catch trials: reveals 2x2 matrix (outcome matrix): four possible outcomes: hit, miss, false alarm, correct negative
• Relations among these depends upon, 1) the nature of the stimulus and sensory ability, & 2) the subject's decision process
• can vary expectations or costs/benefits of outcomes (payoff matrix) to alter hit and false alarm rates (by varying the decision process without altering sensory ability or stimuli strength). If hits increase, so will false alarms
• Isosensitivity curves also called ROC (receiver operating characteristic) curves: more sharply bowed, more sensitive
• can also assume noise is normally distributed (with a variance of 1), so too will be the signal plus noise distribution (on average more intense, so shifted to the right)
• where distributions overlap, subjects must guess
• subjects select criterion (b ):say yes if and only if signal strength exceeds this (location has no effect on sensitivity)
• distance between distributions (in z-score units) = d' (sensitivity)
• calculate d' from hit and false alarm probabilities (using tables of areas under the normal curve)
• Importance of these techniques, e.g., study on acupunctural analgesia (Clark & Yang, 1974).