stats final

When should you use a factorial ANOVA?

When you have two or more Independent Variables (IVs) and one continuous Dependent Variable (DV).

What does a '2 x 2' factorial design mean?

It means there are 2 IVs with 2 levels each.

What is the rule for naming factorial designs?

Always put the larger number last (e.g., 2 x 4).

What are 'levels' in ANOVA?

The groups within an IV (e.g., 'Noise' vs 'No Noise').

Can an IV have only one level?

No.

What is a between-subjects design?

Different people are in each group.

Why is between-subjects design commonly used?

It avoids order effects and practice effects.

What is a repeated measures design?

The same people are in every group.

What is a drawback of repeated measures?

It can introduce bias.

What is a mixed factorial design?

A combination of between-subjects and repeated measures designs.

What is a main effect?

The effect of one IV on the DV, ignoring other IVs.

What is an interaction effect?

When the effect of one IV on the DV depends on the level of another IV.

How do you identify no interaction on a graph?

The lines are parallel.

How do you identify an interaction on a graph?

The differences between groups are not consistent across levels (non-parallel lines).

What is counterbalancing?

A method used in repeated measures to reduce order effects.

How is counterbalancing done?

By randomly assigning the order of conditions (e.g., rolling dice).

What is a bivariate correlation?

Measuring the relationship between two variables and identifying patterns.

What types of variables are required for correlation?

Interval or ratio variables.

What is the correlation coefficient (r)?

A value between +1 and -1 showing strength and direction.

What does a positive correlation mean?

As one variable increases, the other increases.

What does a negative correlation mean?

As one variable increases, the other decreases.

What does an r value of 0.0 mean?

No relationship.

What are Cohen's cutoffs for correlation strength?

.1-.3 = weak, .3-.5 = moderate, .5+ = strong.

Does correlation equal causation?

No.

What is direction of causality?

You don't know which variable causes the other.

What is the third variable problem?

An outside variable may influence both variables.

What is covariance?

How much two variables differ from their means together.

What are cross-product deviations?

The product of each variable's deviation from its mean.

What is the coefficient of determination (r²)?

The percentage of variance in the DV explained by the IV.

Example: If r = .94, what is r²?

.88 (88% explained).

What is the coefficient of alienation?

1 − r² (the unexplained variance).

How do you test if a correlation is significant?

Use a t-test on r.

How are degrees of freedom calculated for correlation?

n − 2.

When do you fail to reject the null hypothesis?

When t-statistic is smaller than the critical value.

What is univariate analysis?

Observing one DV.

What is multivariate analysis?

Observing two or more DVs.

What is a quadratic (curvilinear) relationship?

A relationship that changes direction (U-shaped or inverted U).

What are unique relationships in correlation?

Relationships examined while controlling for a third variable.

What is partial correlation?

Removes the third variable's influence from both IV and DV.

What is semi-partial correlation?

Removes the third variable's influence from only one predictor.

Which is always smaller: partial or semi-partial?

Semi-partial.

What is an example of APA correlation reporting?

There is a significant positive relationship between exam scores and hours spent studying, r(18) = 0.82, p < .001.

What are the two pieces of information in a correlation?

Strength and direction.

What are 'Storm Chips'?

A special brand of chips on the East Coast of Canada.

When is linear regression used?

When both IV and DV are continuous.

What is the purpose of linear regression?

To predict one variable from another.

What is the line of best fit?

The line that best represents the data.

What is the regression equation?

Y = a + (b × X)

What does Y represent?

The predicted outcome (DV).

What does a represent?

The intercept.

What does b represent?

The slope.

What does X represent?

The predictor (IV).

What are residuals?

The difference between actual and predicted values.

What is the goal with residuals?

Minimize them (Sum of Squared Errors).

What is an unstandardized coefficient (b)?

The relationship in original units.

What is a standardized coefficient (Beta)?

The relationship in standard deviation units.

What is multiple regression?

Predicting a DV using two or more IVs.

What is the purpose of multiple regression?

To see total and unique contributions of IVs.

What is R (multiple correlation)?

Correlation between DV and all IVs together.

What is R² in multiple regression?

Variance explained by all IVs.

What is adjusted R²?

A corrected version of R² accounting for number of predictors.

What is simultaneous regression?

All IVs entered at once.

What is hierarchical regression?

IVs entered in a chosen order.

What is stepwise regression?

Computer selects IV order based on variance explained.

What is a mediator?

Explains why a relationship exists.

Example of a mediator?

Cell phone use → distraction → accidents.

What is full mediation?

When the IV-DV relationship disappears after adding mediator.

What is a moderator?

Changes strength or direction of a relationship.

What does a moderator tell us?

When or for whom a relationship occurs.

Example of a moderator?

Stress → symptoms, weaker with high social support.

What is a moderator in regression terms?

An interaction effect.

What is linearity?

Relationship must be a straight line.

What is homoscedasticity?

Residuals are consistent across all levels.

What is independence of errors?

Observations don't influence each other.

What is normality?

Residuals are normally distributed.

Where do you find R and R² in SPSS?

Model Summary table.

What does the ANOVA table show in SPSS?

Whether the model is significant.

What does the coefficients table show?

Individual predictor significance (b or Beta).

What is centering?

Subtracting the mean to make it 0.

Why is centering used?

To make moderation easier to interpret.

What is multicollinearity?

IVs are too highly correlated (above .80-.90).

Why is multicollinearity bad?

It's hard to tell which IV is influencing the DV.

What are outliers?

Extreme data points far from the line.

Why are outliers a problem?

They can distort the slope and predictions.

What correlation coefficient best reflects age predicting 6.25% of the variance in number of wrinkles?

0.25

What do chi-square tests compare?

Observed vs expected frequencies

What is the formula Ŷ = mx + b?

The formula for a simple regression

What does a U-shaped or inverted U-shaped pattern in the data suggest?

The presence of a quadratic relationship between variables

What type of statistical tests are used for one DV, and what type for two or more DVs?

Univariate tests for one DV, multivariate tests for two or more DVs

What does the squared semi-partial correlation represent?

Unique variance explained in the outcome

If observed frequencies are very different from expected frequencies, what will the chi-square value be?

Large

What is the expected frequency for women who liked to watch soaps, given the provided data?

131.19

In a multiple regression model, if R² = .52, what is the most accurate interpretation?

52% of the variance in the outcome is explained by the predictors

What analysis would be used to assess differences in the proportion of students from private high schools admitted to UMD compared to public high schools?

Chi-square

For what type of data are parametric tests most appropriate?

Interval or ratio data

When interpreting a regression output, what does a beta (β) of 2.45 mean?

For every unit increase in the predictor variable, scores on the outcome variable increase by 2.45 units.

Give an example of a study that would use a 2x2 chi-square test to analyze the data.

A researcher asks faculty whether their usual coffee order is plain coffee or specialty coffee and whether they typically respond to emails with "Sounds good!" or a full paragraph. A 2x2 chi-square would test whether email response style differs by coffee preference.

What is the covariance?

The sum of the cross-product deviations for two variables.

What type of analysis is used for a study with three study strategies and three time points?

A 3 × 3 mixed-design factorial ANOVA.

Is it possible to have a significant interaction effect if both main effects are not significant?

False.