PYB210 Statistics

Theory

An abstract statement about reality that pertains to a whole hypothetical universe and typically proposes a relationship between cause and effect.

Hypothesis

A concrete, testable prediction derived from a theory about what should be observed in a specific sample.

Independent Variable (IV)

The variable that is manipulated in an experiment.

Dependent Variable (DV)

The effect variable that is measured to see if it changes as a function of the independent variable.

Operationalization

The process of translating fuzzy theoretical concepts into concrete, observable things that can be measured or manipulated in the real world.

Internal Validity

The extent to which a researcher can be confident that the change in the DV was actually caused by the manipulation of the IV.

External Validity

The extent to which the results of a study can be generalized back to the broader population or other real-world scenarios.

Nuisance Variable

An extraneous variable that is irrelevant to the research goal but creates "noise" or error in the data.

Confounding Variable

A specific type of extraneous variable that systematically varies with the IV and provides a plausible alternative explanation for the results.

Demand Characteristics

Cues in an experiment that lead participants to infer the researcher's hypothesis and adjust their behavior accordingly.

Double-Blind Technique

A method where neither the participant nor the experimenter knows which condition the participant is in, preventing expectancy effects.

Probability Sampling

A category of sampling where every member of the population has an equal or known chance of being selected, reducing selection bias.

Stratified Random Sampling

A strategy where the population is divided into important demographic subgroups (strata), and participants are randomly sampled from within those groups.

Convenience Sampling

Selecting participants who are easily accessible, which is inexpensive but often introduces bias.

Snowball Sampling

A method where initial participants recruit further participants from their own social or professional networks.

Reliability

The consistency, repeatability, or accuracy of a measurement.

Validity (Measurement)

The extent to which an instrument actually measures the specific construct it is intended to measure.

Cronbach’s Alpha

• A common measure of internal consistency reliability that represents the average of all possible inter-item correlations.

• Produces a coefficient from 0 to 1, 0.70 is acceptable but >= 0.8 is desirable.

Test-Retest Reliability

Administering the same test to the same participants at two different time points to check for stability over time.

Face Validity

The degree to which a measure appears, "on the face of it," to be measuring what it claims to measure.

Mean

A measure of central tendency representing the mathematical average of a set of scores.

Standard Deviation

A measure of the average amount that scores in a distribution deviate from the mean.

Variance

The average of the squared deviations from the mean; it represents the "stuff" of statistics that researchers try to explain.

Standard Error of the Mean

An estimate of how much a sample mean is likely to deviate from the true population mean.

Null Hypothesis (H0)

The assumption that there is no effect or relationship in the population and that observed differences are due to chance (flukes).

Type I Error (α)

Falsely rejecting the null hypothesis; concluding there is a significant effect when there is actually nothing going on in the population.

Type II Error (β)

Falsely accepting the null hypothesis; failing to detect a real effect that exists in the population.

Statistical Power

The probability of correctly rejecting the null hypothesis (1−β); the ability of a study to detect a true effect or relationship in the population if one actually exists.

ANOVA (Analysis of Variance)

A technique used to compare means across three or more groups by partitioning total variance into "between-groups" and "within-groups" sources.

F-Ratio

• The ratio of between-groups variance (treatment effect) to within-groups variance (error)

• F = 0, suggests IV has had no effect

• F > 1, ideal result as the difference between groups is larger than the error.

• F < 1, hypothesis is as wrong as possible

Omnibus Test

The initial ANOVA test that indicates whether there is any difference between group means, but does not specify which groups differ.

Homogeneity of Variance

The assumption that the variances of the different groups being compared are approximately equal.

Sphericity

An assumption specific to repeated-measures ANOVA stating that the variances of the differences between all pairs of conditions are equal.

Planned Comparisons (A Priori)

Specific mean comparisons that were hypothesized before the data were collected; these generally do not require a significant omnibus F.

Post-Hoc Tests

Comparisons made after a significant omnibus F is found to explore which specific means differ; these require adjustments for Type I error inflation.

Tukey’s HSD

• A post-hoc test that maintains the family-wise Type I error rate at .05

• Used to follow up a significant omnibus F-test and when no a-priori contrasts made

Eta Squared (η2)

An effect size measure in ANOVA representing the proportion of total variance in the DV that is explained by the IV.

Pearson’s r

A statistic describing the strength and direction of a linear relationship between two continuous variables, ranging from -1 to +1.

Regression

A statistical method used to predict a score on a criterion variable based on one or more predictor variables.

Regression Coefficient (b)

The slope of the regression line; it indicates the amount of change in the DV for every one-unit increase in the IV.

Y-Intercept (a)

The predicted value of the DV (Y) when the IV (X) is zero; the point where the regression line crosses the vertical axis.

Residual

The difference between a participant's actual observed score and their predicted score from the regression equation.

Standard Error of the Estimate

The average amount of error or "margin of error" in predictions made using a regression equation.

Qualitative Research

Methods aimed at scoping research space and finding "what you don't know" rather than testing pre-defined hypotheses.

Indigenous Methods

Research approaches where the researcher is a "respectful student" and the participants are the "experts".

Informed Consent

The ethical requirement that participants must be fully aware of research risks and voluntarily agree to participate.

Duty of Care

The researcher’s ongoing responsibility for the well-being of participants throughout the study and for any unforeseen consequences.

De-identified Data

A dataset where personally identifying information (names, IDs) has been replaced by random unique codes

Multi-stage cluster sampling

• Clusters/sub-groups are randomly selected followed by a random selection of participants from within those clusters.

• Often used when it is not possible to sample every subgroup within a population, helping to reduce bias

Multi-phase sampling

• Data first collected from a large sample to create a wide scope of information

• Specific sub-groups then later used for smaller follow-up projects

Welch test

A robust alternative to ANOVA used when the assumption of homogeneity of variance is violated

Greenhouse-Gessier

• A correction for degrees of freedom used in repeated-measures ANOVA when the assumption of sphericity is breached

• Calculates epsilon (e) value which measures the extent of the sphericity violation from 0 to 1 (where 1 is perfect sphericity).

Variance between-groups

Represents variance due to the effect of the IV e.g. the differences between the means of each condition

Variance within-groups (error)

Represents the difference between individual scores within each condition (isn’t to do with the manipulation, simply error)

Bonferroni’s Test

• Post-hoc test used to control for Type I error inflation when performing multiple comparisons by dividing the desired alpha level (e.g. a=0.05).

• Considered “too conservative” which increases risk for Type II error.

Huynh-Feldt adjustments

• A correction test used when sphericity is breached

• Used when Mauchley’s test indicates the assumption of sphericity has been violated (p<0.05).

• Recommended to be used when e>0.75,

• More conservative test, not often used, Greenhouse-Gessier preferred