Statistics and Experimental Design: T-tests, ANOVA, and Factorial Designs

What is the simplest form of an experiment?

An experiment with one independent variable manipulated in two ways and one outcome measured.

What is the purpose of a T-test?

To test a hypothesis about the means of two populations and determine if they are significantly different.

What are the two types of T-tests?

Independent samples T-test and dependent (paired samples) T-test.

What is the independent samples T-test used for?

To compare the means of two independent samples on a variable.

What are the assumptions of the independent T-test?

Normality and homogeneity of variance.

What is the dependent (paired samples) T-test used for?

To compare the average scores of a single sample on two variables.

What does the null hypothesis state in the context of T-tests?

Under the null hypothesis, we expect the means from two random samples to be very similar.

What is the significance of the standard error in T-tests?

It measures how means fluctuate and helps compare differences between sample means.

What is the effect size in the context of T-tests?

A measure of the size of an effect observed in some statistic, indicating practical significance.

What does a non-directional hypothesis imply?

It indicates that there is a difference between groups but does not specify the direction of the difference.

What is the purpose of ANOVA?

To compare means of two or more groups on one dependent variable to see if groups are significantly different.

What is a one-way ANOVA?

ANOVA that can only have one independent variable (IV) and one dependent variable (DV).

What is the difference between experiments and natural observation?

In experiments, the predictor variable is manipulated in a controlled way, while in natural observation, differences between means may not be caused by the predictor.

What is the purpose of dummy variable coding in regression models?

To represent categorical variables numerically for analysis, using one less than the number of categories.

What is the significance of the pooled variance estimate?

It is used when sample sizes are unequal in T-tests.

What does the term 'grand mean' refer to in ANOVA?

The average of all group means considered as a whole.

What is a dose-response hypothesis in the context of an experiment?

It predicts that as exposure time increases, the outcome (e.g., happiness) will also increase.

What is the significance of reporting the independent T-test results?

It provides statistical evidence of differences between groups, including means, standard errors, and effect sizes.

What is the role of significance testing in T-tests?

To determine if the observed differences between sample means are statistically significant.

What does the term 'mANOVA' stand for?

Multivariate Analysis of Variance, used to compare multiple dependent variables across groups.

What is the purpose of calculating the mean square within and mean square residual?

To find the amount of variation within each sample.

How do you find the average amount of variation in ANOVA?

By dividing the sum of squares by the degrees of freedom.

What does the F-statistic represent in ANOVA?

The ratio of mean square model to mean square residual, indicating the variability explained by the model compared to the error.

What is the formula for calculating the F value?

Mean square model divided by mean square residual.

What does model sum of squares indicate?

The variability due to the predictor variable or experimental manipulation.

What is residual sum of squares?

The variability that cannot be explained by the model.

What is the definition of degrees of freedom in the context of ANOVA?

The number of values that are free to vary, typically one less than the number of values used to calculate the sum of squares.

How do you calculate the model degrees of freedom?

It is equal to the number of groups minus one (k-1).

What is the purpose of post-hoc tests in ANOVA?

To determine where significant differences lie between group means after finding a significant F-statistic.

What does the Bonferroni method adjust?

The significance level when conducting multiple comparisons.

What assumptions must be met for ANOVA?

Assumption of random sampling, normality, and homogeneity of variance.

What is omega squared (ω²) used to measure?

The effect size in ANOVA, indicating the proportion of variance accounted for by the treatment level.

What does a significant F value indicate?

That the experimental manipulation has had a significant effect on the outcome variable.

What is the interpretation of an effect size of 0.138 in ANOVA?

It indicates a large association.

What is the significance of the t-test in the context of ANOVA?

It compares means between groups to identify specific differences.

What does the term 'planned contrasts' refer to?

Hypothesis-driven comparisons made before the experiment.

What is the purpose of trend analysis in ANOVA?

To assess the direction and strength of relationships between variables.

What is the difference between independent and dependent groups in ANOVA?

Independent groups are those that are not related, while dependent groups are related or matched in some way.

What is the significance of the summary table in ANOVA?

It summarizes the results, including sums of squares, degrees of freedom, mean squares, F-statistic, and p-values.

What does it mean if SSR is greater than SSE?

It indicates that the model explains more variability than the error, suggesting a significant effect.

What is a factorial design?

An experimental design where more than one predictor variable has been manipulated.

What does 'N-way' refer to in factorial designs?

It refers to designs with N predictors.

What is an independent design in experimental research?

A design where different entities are used in all conditions.

What is a repeated measures design?

A design where the same entities are used in all conditions.

What is a mixed design in experimental research?

A design with different entities in all conditions of at least one independent variable, and the same entities in all conditions of at least one other independent variable.

What was the independent variable in the 'beer-goggles effect' study?

Alcohol dose and face type.

What were the levels of the alcohol dose in the study?

Placebo (alcohol-free beer), low dose (4% ABV), and high dose (7% ABV).

What is the outcome variable in the beer-goggles effect study?

Median rating of attractiveness of 50 photos on a scale from 0 to 10.

What does a two-way ANOVA analyze?

It analyzes the interaction between two independent variables and their main effects.

What does a non-parallel line on an interaction graph indicate?

It indicates some degree of interaction between the independent variables.

What does a post-hoc test do?

Identifies where differences between the study groups exist.

What are 2 things the Bonferroni correction is used for?

Adjusting p-values when conducting multiple comparisons and controlling for Type I error.

What does the residual sum of squares (SSR) represent?

Individual differences in performance or variance that cannot be explained by the manipulated factors.

What is the main effect in the context of ANOVA?

The overall effect of an independent variable on a dependent variable.

What type of design does a one-way ANOVA adopt?

An independent groups design.

What is the significance of crossing lines in an interaction graph?

Crossing lines suggest a possible significant interaction between independent variables.

What is the effect size measure represented by partial eta squared?

It quantifies the proportion of total variance that is attributed to a particular effect.

What is the difference between independent and dependent t-tests?

Independent t-tests compare means from different groups, while dependent t-tests compare means from the same group under different conditions.

What does it mean if a study reports a significant effect size of r = .72?

It indicates a highly significant result with a substantial effect.

How is a t-statistic calculated?

By dividing the mean difference by the standard error of the mean.

What does the term 'main effect of alcohol' refer to?

The effect of alcohol on the attractiveness ratings in the study.

What is the purpose of simple effects analysis?

To examine the effect of one independent variable at each level of another independent variable.

What does the term 'interaction effect' refer to?

The effect that occurs when the relationship between one independent variable and the dependent variable changes depending on the level of another independent variable.

What is the total sum of squares (SST) in ANOVA?

The total variance in the data, which is the sum of the variance within groups (SSW) and the variance between groups (SSB).