PSYC 200 Final Review

what are df for expected frequencies?

(R-1)(C-1)

what is pearson's r?

degree of shared variance/covariance

what is variance partitioning?

difference between variability and variance -variability → spread of raw scores (SS) -variance → average squared difference of scores from mean (SS^2)

what are the two components of a correlation statistic?

direction and magnitude

what is phi?

effect size for chi square (2x2 only)

what is another word for within subjects variance?

error variance

how do you interpret correlation values?

-0-0.10 → none -0.10-0.29 → weak -0.30-0.49 → moderate -0.5 greater → strong

how do you interpret omega-squared effect sizes?

-0.01-0.05 → small -0.06-0.15 → medium →0.14 → large

what is a planned comparison?

-a priori, beforehand -specific hypotheses comparing groups before collecting data -need theoretical guidance -directional or non-directional -t tests on groups of interest (limit to avoid type 1)

what is a post-hoc test?

-after the fact -no strong theoretical basis to make specific comparison beforehand -only performed if omnibus has significant difference -corrects for inflated alpha from multiple t-tests by using a familywise error rate -tukey's hsd → corrects for inflated type 1 error rate

what is the chi square test of independence?

-analysis of contingency tables (2 way table displaying frequency classified by each variable) -tests whether placement on variable influences placement on variable 2 -is position in one variable contingent on position in another variable? -marginals → total for each row and column -categories mutually exclusive

what is ANOVA?

-analysis of variance -variance is basic unit of analysis -F (always positive because you can never have no variance) -want between variance to be higher to distinguish groups -want error variance to be minimized - less noise you can't control

on a line graph, how do you interpret main effects?

-average slope -if slope = 0 → no main effect -draw dot for average at A1 and A2 and if the line between the dots is 0 → no main effect

what is a cell? how do you determine the number of cells in a factorial ANOVA?

-cell = condition -levels of A x levels of B

how do you do factorial ANOVA notation?

-classify by # IV and # levels -ex: 2x3 → 2 IV, one with 2 levels and one with 3

what measures pairwise effect size?

-cohen's d calculated for each comparison -ONLY calculated if the pairwise comparison was significant

on a line graph, how do you interpret interaction effects?

-compare slopes of two lines -if lines are parallel → no interaction effect -if you SEE a crossover → interaction effect BUT no main effect

what is the familywise error rate?

-corrects for inflated alpha from multiple t tests in post hoc -prob of making at least one type 1 error -posthoc is unplanned → error inflated, running more tests than expected -should equal alpha

what is tukey's hsd?

-corrects for inflated type 1 error rate in post-hoc -compares all possible pairs of groups -corrects for familywise error rate -always positive -tells you WHERE the difference is if omnibus test tells you there IS a difference

what is a correlation measure of covariance?

-degree of shared variance → pearson's r -as one variable changes, how is the other affected?

what is a mixed ANOVA?

-design with within and between subjects (at least one of each) -within factor is often time (pre-post test) -# x # format, specify w/in or between -IV → nominal/ordinal, need 2+ (one within, one between) -DV → continuous (same across all IV and levels/times) -strong and powerful design

what is the f sampling distribution?

-distribution of ratio of variances -probability of getting each f value under chance -distribution varies by degrees of freedom (n affects shape because two different df types) -always positive -positively skewed -1 tailed test -median is about 1 -becomes more normal/symmetrical as N increases

what is fisher's lsd?

-doesn't correct for multiple comparisons -further compare means of groups after omnibus -create confidence intervals for all pairwise differences while controlling individual error rate -uses individual error rate and # comparisons to calculate confidence level for all CIs -simultaneous confidence level → probability that all CIs contain true difference

what are non-parametric tests?

-don't have assumptions about makeup of population (don't meet normality) -don't use continuous DVs (like mean/variance)→ use frequencies instead (categorial) -parametric tests are preferred to non (more powerful)

what are main effects in a factorial ANOVA?

-focus on one IV at a time -how levels of IV vary from other levels in same IV -main effect of A → average across all levels of factor B -there's a main effect for EACH IV

what happens when you put cells into a factorial table?

-gives you marginal means → mean of factor A regardless of B -grand mean → mean of all participants regardless of group

why are parametric tests preferred to non-parametric?

-greater magnitude of effect understanding -sensitive to detecting effects -simultaneous testing multiple variables -robust w/ violations (only severe violations lead us to non-p)

what is homoscedasticity?

-homogeneity of variance between levels -all members of group affected by treatment similarly

what are the assumptions of a mixed ANOVA?

-homogeneity of variance for mixed designs → box's test of equality of covariances (rarely met) -normality and sphericity

what are interaction effects in a factorial ANOVA?

-how levels of one IV vary across levels of another IV -interactions → effect not the same at all levels of other IV -can break down into simple effects to explore nature of interaction

what is the difference between correlation and causation?

-in a correlation, third unknown variable could cause relation between X and Y -there could also be a spurious relation → relation due to chance alone

what are assumptions of chi square?

-independence of observations → each participant in only one cell -expected cell frequency → multiple samples would form a normal distribution of frequency around expected value -expected frequency MUST be 5+ in each cell (ideally 10+ for 2x2 or 1x2 tables)

what is the difference between chi square goodness of fit and independence?

-independence: looks for association between two variables within same population. compares two variables within a sample set to one another -goodness of fit: compares single observed variable to a theoretical population. want to know if observed frequencies are consistent with expected population frequencies -BASICALLY: goodness = 1 factor vs. independent = see if 2 or more factors independent of each other

what are confidence intervals?

-interval estimate -effect size → point estimate -magnitude of effect (NO direction)

what are concerns for chi square?

-large N → increased likelihood of obtaining significant effect even w/ no effect present -effect sizes → normal measures are difficult here because they reference SD units but you can't calculate SD in non-parametrics

what are the effects in a mixed ANOVA?

-main effect → each IV separately -interaction effect → all possible combinations of IVs

why use F?

-more than 2 levels of IV -could run multiple independent t-tests BUT this increases type 1 error/inflates alpha -f is better because you analyze data with minimal comparisons to reduce prob. of error

what is a factorial ANOVA?

-more than one IV (ex: 2 IV = 2-way ANOVA) -each IV can have 2+ levels

what are the characteristics of a one-way ANOVA?

-one IV with 2 levels (nominal or ordinal) -k = # levels of IV -DV is continuous -homoscedasticity assumption → homogeneity of variance between levels, all members of group affected by treatment similarly -assumes independence of observations → groups individual of one another, random assignment

what is the chi square goodness of fit test?

-one categorical variable -is frequency of responses the same across categories? (alternative → at least one group differs from another)

what is an omnibus test?

-one overall comparison in one-way ANOVA -always non directional hypothesis (tells you if there's a difference, not where)

what is effect size for factorial mixed ANOVA?

-overall: 1. eta squared 2. R squared 3. omega squared (preferred) -simple effects: 1. cohen's d

how are non-parametric tests different from parametric tests?

-parametric → continuous DV (mean/variance) -non-parametric → categorical DV (frequencies) -parametric preferred

what is a correlation coefficient?

-pearson's r -measure of relation between two continuous variables

what is hypothesis testing?

-point estimate -binary decision (presence/absence) -direction of effect (NO magnitude)

what is a simple effect in a factorial mixed ANOVA?

-probing an interaction effect → what levels of IV drive the interaction? -only run simple effects related to hypotheses (inflates alpha) -effect size → cohen's d

what is the difference between r and r^2?

-r → correlation coefficient → direction + magnitude -r^2 → coefficient of determination → degree of overlap/shared variance

what is a coefficient of determination?

-r^2 -correlation coefficient presented in terms of variance -variance accounted for -measure of magnitude (%) ***-proportion of total variability in X accounted for by Y

what are the properties of correlation values?

-range from -1 to 1 - 1 or -1 → perfect relation -0 → no relation -captures linear relations only (if relationship appears curvilinear → can't do correlation analysis)

what are cramer's v and phi?

-range from 0-1 -closer to 1 → stronger chi square effect

how do you interpret r?

-restricted range → distorts magnitude of r by deflating -outliers → distort best fit line and deflates r -correlation vs. causation → third unknown variable could cause relation between X and Y OR spurious relation due to chance alone

how do you graph a correlation?

-scatterplot (x on x axis, y on y) -best fit line shows trend if linear

what is a within subjects design repeated measures ANOVA?

-strengthens design → paired scores dependent on one another -IV → nominal/ordinal with 2+ levels (all participants experience all levels) -score for DV at each level of IV and DV → continuous

what are the three sources of variability in a mixed ANOVA?

-total → how each score varies from grand mean -between 1. between subjects → each group mean of between IV varies from grand mean 2. condition → mean of each level of within IV varies from grand mean 3. between x condition → mean for each group at each level varies from grand mean -within 1. subject → how individual scores vary around group mean 2. error → unexplained

how does a post-hoc test correct for inflated type 1 error rate?

-tukey's hsd

how do you get effect sizes for chi square since you can't calculate SD?

-use N and percentages -no standardization across sample, reliability across samples compromised

what is a planned comparison?

-when you have a directional hypothesis in a one-way ANOVA, testing with post-hoc

what are the 2 components of a correlation statistic?

1. direction → sign of # -positive (direct relation) -negative (indirect/inverse relation) 2. magnitude → size of # -quantifies how close points are to best fit line -perfect, strong, moderate, weak, none

what are odds ratios?

1. each variable: frequency for specific group/frequency in all other groups 2. pairs of odds: odds for group 1/odds for group 2

what are two effect size measures for one-way ANOVA?

1. eta squared → overestimates true value, biased (partial eta corrects for bias) 2. omega squared → preferred effect size for omnibus as it's conservative, less biased (amount of variance in DV that can be explained by IV as a percentage of variance)

what is the process of an omnibus test?

1. omega squared for post-hoc effect size 2. if significant effect → do pairwise comparisons -planned → dependent samples t-test -not planned → tukey's hsd 3. cohen's d for pairwise effect size

what three correlations can you get?

1. positive → as X increases, Y increases or vice versa (same direction) 2. negative → as X increases, Y decreases or vice versa (inverse) 3. none → no relationship between X and Y (straight line)

what are the three sources of variability in a repeated measures ANOVA?

1. total variability -how each score varies from grand mean 2. condition variability -how mean of each level varies from grand mean 3. within subjects variability -subject → individual scores vary around level mean -error → remaining/unexplained -smaller SSw → smaller MSw → increased probability of detecting true effects

how many post-hoc tests could you conduct if you had a significant omnibus test for a single factor with 5 levels?

10 (5 main, 5 interactions)

how many F tests would you conduct with the following design: factor A (3 levels within subjects) factor B (2 levels between subjects) factor C (2 levels between subjects)

7: A, B, C, AxB, AxC, BxC, AxBxC

how many sources of variability would you have with this design: factor A (2 levels between subjects) factor B (3 levels within subjects) factor C (2 levels between subjects)

9: A, B, C, AxB, AxC, BxC, AxBxC, error, subject

what measure is a ratio of two variance estimates?

F

how do you determine your hypotheses for factorial ANOVA?

hypothesis for each component: 1. one for each main effect (A, B, C, ...) 2. one for each interaction (AxB, AxC, AxBxC, ...)

what is the difference between hypothesis testing and confidence intervals?

hypothesis → point estimate confidence → interval estimate

if F is close to 0, what does that say about the IV?

IV has no effect

how do you calculate Fobt?

MSb/MSw

how do you calculate expected frequencies?

RiCj/N R = row i = row # C = column j = column #

what are the two variance estimates you get from the three types of variability in variance partitioning?

SSb and SSw form two estimations of population variance: 1. between groups variance (MSb, mean squares) → variance due to IV (want this to be HIGH so IV has effect) 2. within groups variance (MSw, error variance) → want low to reduce individual noise

what are the sources of variability in an independent ANOVA?

SSt → SSb and SSw

what are the sources of variability in a repeated measures ANOVA?

SSt → SSb and SSw SSw → subject variability and error variability

what does repeated measures ANOVA assume?

sphericity -homogeneity of variance for difference scores -assumption met if p not sig.

what is omega squared?

amount of variance in DV that can be explained by IV as a percentage of variance

what does ANOVA stand for?

analysis of variance

how do you calculate F?

between groups variability/within subjects variability SSb/SSw

what type of data/scale of measurement do non-parametric tests use (parametric - continuous)?

categorical/nominal

if IV has no effect, what does F look like?

close to 0

what is the effect size measure for a planned comparison?

cohen's d

what table is used in the chi square test of independent to show frequencies by each variable simultaneously?

contingency table

what type of data/scale of measurement do parametric tests use (non-parametric - categorical/nominal)?

continuous

what is correlation measuring between X and Y, aka shared variance?

covariance

what are the three types of effect size measures for chi square?

cramer's v, phi, and odds ratio

what are three effect size measures for chi square?

cramer's v, phi, or odds ratios

why do we use F rather than conduct several t-tests?

inflation of alpha/type 1 error rate

what represents the number of groups or levels of a factor?

k

what are df for chi square?

k-1

what is a grand mean?

mean of all participants regardless of group

what is a marginal mean?

mean of factor A regardless of B

what is a chi square distribution?

non-directional hypothesis and 1-tailed evaluation that varies as a function of degrees of freedom

chi square is calculated using what two types of frequencies?

observed and expected

what is the effect size measure for an omnibus test?

omega squared

what is the one overall comparison test in a one-way ANOVA?

omnibus test

how do you determine your F ratios for factorial ANOVA?

one for each component: 1. main effect A → MSa/MSw 2. interaction of AxB → MSaxb/MSw

what test is used to analyze a single factor with 3 or more levels?

one-way ANOVA

what are three factors that could deflate r or affect interpretation of a correlation?

outliers, non-linear data, restricted range

what are the two types of multiple comparisons?

post-hoc and planned comparisons

what is a p-value?

probability you get the observed value due to chance under the null hypothesis

what is F (generally)?

ratio of two variance estimates

what type of chart visually assesses the relation between X and Y?

scatterplot

what is a correlation coefficient?

statistic showing relation between 2 variables

what source of variability accounts for individual variability and is removed from error variance in repeated measures designs?

subject variability

where does within subjects variance (aka error variance) come from?

subject variance

what tests do you conduct to follow up with a significant interaction effect?

tests of simple effects

how does variance partitioning give you two variance estimates?

three types of variability: 1. between groups (SSb) → group difference, effect of IV on DV 2. within groups (SSw) → individual difference, how do participants vary from mean of their group (error) 3. total variability (SSt) → sum of between and within, how do participants vary from overall mean regardless of group

we want this source of variance to be higher than the error variance.

treatment variance/explained variance/between groups variance (all same thing)

what relationship does correlation show?

two continuous variables (X and Y) related to each other

what type of ANOVA would you conduct if you had two factors, each with 3 levels?

two-way ANOVA

what is another word for error variance?

within subjects variance

what type of design has participants complete a single measure at three time points?

within subjects/repeated measures