PSYCH 210

analysis of variance (ANOVA)

a hypothesis test typically used with one or more nominal (and sometimes ordinal) independent variables (with at least three groups overall) and a scale/continuous dependent variable.

F statistic

is a ratio of two measures of variance: (1) between-groups variance, which indicates differences among sample means, and (2) within-groups variance, the average of the sample variances.

between groups variance

an estimate of the population variance, based on the differences among the means.

within groups variance

an estimate of the population variance, based on the differences within each of the three (or more) sample distributions.

one-way ANOVA

a hypothesis test that includes both one nominal independent variable with more than two levels and a scale dependent variable

between groups ANOVA

a hypothesis test in which there are more than two samples, and each sample is composed of different participants.

within groups ANOVA

a hypothesis test in which there are more than two samples, and each sample is composed of the same participants. (This test is also called a repeated-measures ANOVA.)

homoscedastic

populations are those that have the same variance.

heteroscedastic

populations have different variances

source table

presents the important calculations and final results of an ANOVA in a consistent and easy-to-read format.

eta squared

estimate of the proportion of variance in the dependent variable that is accounted for by the independent variable.

omega squared

is an estimate of the proportion of variance in the dependent variable that is accounted for by the independent variable; it is less biased than eta squared

post hoc test

is a statistical procedure carried out after the null hypothesis has been rejected in an analysis of variance in which we make all possible pairwise comparisons among the means of the groups in the studyfami

familywise type I error rate

the probability of obtaining at least one Type I error when conducting a set of comparisons. We refer to this set of comparisons as the family.

Tukey HSD Test

widely used post hoc test that determines the differences between means in terms of standard error; the HSD is compared to a critical value.

sphericity assumption

which requires the average difference between pairs of scores to be similar across conditions.

two way ANOVA

a hypothesis test that includes two nominal independent variables, regardless of their numbers of levels, and a scale/continuous dependent variable.

factorial ANOVA

a statistical analysis used with one scale/continuous dependent variable and at least two nominal independent variables

cell

a box that depicts one unique combination of levels of the independent variables in a factorial design

main effect

occurs in a factorial design when one of the independent variables has an influence on the dependent variable.

quantitative interaction

an interaction in which the effect of one independent variable is strengthened or weakened at one or more levels of the other independent variable, but the direction of the initial effect does not change.

qualitative interaction

an interaction of two (or more) independent variables in which one independent variable reverses its effect depending on the level of the other independent variable.

marginal mean

the mean of a row or a column in a table that presents the cells of a study with a two-way ANOVA design.mi

mixed design ANOVA

used to analyze the data from a study with at least two independent or predictor variables; at least one variable must be within-groups and at least one variable must be between-groups

multivariate analysis of variance (MANOVA)

a form of ANOVA in which there is more than one dependent variable.

analysis of covariance (ANCOVA)

a type of ANOVA in which a covariate is included so that statistical findings reflect effects after a continuous variable has been statistically removed.

covariate

continuous variable that we suspect associates, or covaries, with the independent variable of interest.

multivariate analysis of covariance (MANCOVA)

an ANOVA with multiple dependent variables and a covariate

pearson correlation coefficient

statistic that quantifies a linear relation between two scale variables

partial correlation

is a technique that quantifies the degree of association between two variables that remains when the correlations of these two variables with a third variable are mathematically eliminated.

psychometrics

is the branch of statistics used in the development of tests and measures.

test-retest reliability

refers to whether the scale being used provides consistent information every time the test is taken.

coefficient alpha

a commonly used estimate of a test’s or measure’s reliability, or internal consistency, and is calculated by taking the average of all possible split-half correlations.

simple linear regression

a statistical tool that lets us predict a person’s score on an outcome variable from their score on one predictor variable.

regression to the mean

the tendency of scores that are particularly high or low to drift toward the mean over time.

standardized regression coefficient

a standardized version of the slope in a regression equation, is the predicted change in the outcome variable in terms of standard deviations for an increase of 1 standard deviation in the predictor variable

residual

is the difference between the predicted value of the outcome (Ŷ) and the observed value of the outcome (Y).

standard error of the estimate

a statistic that indicates the average vertical distance between a regression line and the actual data points.

proportionate reduction in error

a statistic that quantifies how much more accurate predictions are when we use the regression line instead of the mean as a prediction tool

adjusted r squared

is a less biased and more conservative estimate of effect size for the regression equation than is r2

orthogonal variables

predictor variables that make separate and distinct contributions in the prediction of an outcome variable, as compared with the contributions of the other predictor variables.

multiple regression

a statistical technique that includes two or more predictor variables in a prediction equation.

chi square test for goodness of fit

a nonparametric hypothesis test that is used when there is one nominal variable

chi square test for independence

a nonparametric hypothesis test that is used when there are two nominal variables

adjusted standardized residual

the difference between the observed frequency and the expected frequency for a cell in a chi-square research design, divided by the standard error

Cramer’s V

is the standard effect size used with the chi-square test for independence

nonparametric test

 inferential statistical analyses that are not based on a set of assumptions about the population

single sample t test

• hypothesis test in which we compare a sample from which we collect data to a population for which we know the mean but not the standard deviation

paired sample t test

used to compare two means when the samples are paired, or related in a clear way, including when the same participant is in both samples

independent samples t test

• used to compare two means for a between groups design, a situation in which each participant is assigned to only one condition

nominal variable

A variable used for observations that have categories, or names, as their values.

ordinal variable

A variable used for observations that have rankings (i.e., 1st, 2nd, 3rd, …) as their values.