PSYC 424 Final Exam

What is the difference between controlling for a pre-test score as a covariate in an ANCOVA and simply analyzing pre-post difference scores in a one way ANOVA?

- ANCOVA uses one additional degree of freedom (more complexity), BUT it may be more powerful because of the ruction in the SSE due to the covariate (more accuracy)

Power generally ___________ from a one-way ANOVA to a factorial ANOVA because the additional factor(s) reduce error in the criterion variable.

- INCREASES - power increases going from a one-way to a factorial ANOVA bc of the reduction of error from the inclusion of additional factors

Does the omnibus model comparison test NEED to be significant to make inferences about specific contrast-coded tests? Are unequal cell sizes between conditions ALWAYS problematic when using orthogonal contrast codes?

- No, does not need to be significant - No, it is not always problematic

**What is the homogeneity of a regression assumption?

- The relationship between a [continuous predictor variable and the outcome variable] is invariant across all levels of any categorical predictor variables - Note: [regression correlation]

What gets added to the denominator of the confidence interval associated with a slope parameter when testing multiple regression (relative to simple regression)?

- Tolerance (1-R^2p) NOTE: tolerance = (1-PREp)

What is the correct procedure for contracting contrast codes in a 3x2 design?

- develop a set of orthogonal one-way contrast codes for each categorical variable. Then construct interactions by multiplying all possible pairs of contrast codes, one from each variable.

What must be included in the model to obtain the simple slopes in the above figure? (IV: SAT, DV: GPA, IV: gender and major)

- dummy codes representing both gender and college - a continuous variable representing SAT scores - all categorical by continuous products of the predictors (i.e., interactions)

What does the standard error of prediction represent?

- how variable, spread out, or dispersed the errors of prediction are at each level of Xi; we assume this to be constant across all values of Xi

Controlling for an orthogonal continuous variable in a factorial design (in which cov. has a sig association with DV) will...

- increase statistical power bc we have reduced the sum of squared errors (SSE)

**In general, there is redundancy when...

- redundancy occurs when it is possible to predict one or more of the Xij with some combination of the other predictor variables

**What do orthogonal polynomial contrasts assess?

- the TREND in the category means across levels of the categorical independent variable

What are the problems with overall model tests (relative to focused model tests)?

- they can be ambiguous (because we do not know which predictors are useful) and can lack statistical power (because we estimate parameters for predictors that are potentially useless)

**How many predictors are needed to represent a four-level categorical variable?

- three - Note: predictors NOT parameters - need one less group than you need codes (K-1) -----> ???? fact check that

What reason(s) might we have for conducting an ANCOVA?

- to adjust for pre-existing differences by controlling for a partially redundant continuous predictor variable - to test mediation by controlling for a partially redundant continuous predictor variable - to increase power by controlling for an orthogonal (independent) continuous predictor

What is tolerance (1-R^2p)?

- tolerance is a measure of Xp's UNIQUENESS from the other predictors

What is the difference between a factorial ANOVA and a one-way ANOVA?

- trick question silly professor, we analyze data from a two-way to higher order factorial design by applying the same one-way ANOVA techniques to an appropriate set of contrast codes

**What question does an interaction term ask?

- whether the difference between the means of some focal variable is different across levels of another variable (as opposed to the mean difference being equal regardless of the other variables) - whether the effect of some focal predictor is moderated by another variable - whether the effect of one categorical variable depends on the level of another variable

What is a simple effect?

Comparisons between categories of one variable within or at a single level of another variable

The intercept (b0) represents _______ when using dummy codes and ______ when using contrast codes

The intercept (b0) represents the REFERENCE GROUP MEAN when using dummy codes The intercept (b0) represents the THE GRAND MEAN when using contrast codes.

Which of the following is a valid a priori value of Bp in the compact model? a) 0 b) any a priori value of Bp is statistically valid (even if we usually use zero) c) 1 d) -1

b) any a priori value of Bp is statistically valid (even if we usually use zero)

**Which of the following is NOT a necessary condition for an orthogonal contrast? a) there must be K-1 contrast codes where K represents levels of the independent variable b) one level of the categorical independent variable must be coded as zero c) each contrast code must sum to zero d) if we multiply across each level of all the contrast codes, these products sum to zero

b) one level of the categorical independent variable must be coded as zero

Which of the following statements about the cross-product of XY is NOT true? a) positive values come from observations that are above or below the mean on both variables b) the sign of the slope is determined by the sign of the variance (and not the crossproduct itself) c) negative values come from observations that are above the mean on one variable but below the mean on the other variable d) each observation gets a weight in determining the slope based on its distance form the joint mean

b) the sign of the slope is determined by the sign of the variance (and not the crossproduct itself)

Which of the following would produce a narrower and more precise confidence interval (and thus increase statistical power)? a) reduce the type 1 error rate (alpha) and thus increase F-critical b) increase the variability of our errors of prediction (MSE) c) Increase sample size (n) d) sample less widely across our predictor variable (sx^2)

c) Increase sample size (n)

**Which of the following statements about type 1 error rates when testing mean differences using one-way ANOVA is NOT true? a) b) c) d)

d) as long as alpha=.05, the probability of of finding a false positive will always be less than or equal to 5% no matter how many mean comparisons we make between levels of the categorical independent variable