Exam II Flashcards
What is ANOVA used for?
To study grouping variables that are not dichotomous.
Give an example of a grouping variable suitable for ANOVA.
Grade level, injury type, decade of life, or >2 treatment groups.
What is one strategy for comparing multiple groups?
Conduct t-tests between each pair of groups.
What is the problem with conducting multiple t-tests?
It increases the likelihood of a Type I Error.
What happens as the number of comparisons increases?
The greater the error rate.
True or False: ANOVA is only applicable for dichotomous grouping variables.
False.
Fill in the blank: ANOVA is often used when studying grouping variables that are _______.
not dichotomous.
What type of test is ANOVA classified as?
Omnibus test
An omnibus test assesses whether there are any statistically significant differences among the means of three or more independent groups.
What is a key characteristic of ANOVA?
General, not specific
ANOVA does not indicate which specific groups are different, only that at least one group differs.
What is a common phrase associated with ANOVA to describe its function?
One of these things is not like the others
This phrase highlights the goal of ANOVA to identify differences among group means.
What defines the three or more groups being compared?
Grouping Variable
What is another term often used for a Grouping Variable?
Factor
Is the Grouping Variable usually an independent variable?
Yes
What is a Measurement/Outcome Variable?
A variable that is usually the dependent variable in a study.
What types of scales can a Measurement/Outcome Variable be?
Interval, ratio, or ordinal.
What does One-Way ANOVA compare?
The means of three or more independent groups defined by one factor (grouping variable)
One-Way ANOVA is used to determine if there are statistically significant differences between the means of the groups.
Is One-Way ANOVA a parametric or non-parametric test?
Parametric test
It assumes a normal distribution of the data.
What assumption does One-Way ANOVA make about the groups?
Homogeneity of variance between the groups
This means that the variance among the groups should be approximately equal.
What statistics should reports of One-Way ANOVA include?
Mean and SD for each group, F-statistic, numerator df, denominator df, p-value, and effect size
These statistics help in interpreting the ANOVA results.
What does ANOVA compare to determine if group means are different?
Within and between group variance
ANOVA assesses how much variation exists within each group and how much variation exists between different groups.
True or False: ANOVA can only compare two groups.
False
ANOVA is designed to compare means across three or more groups.
What is the primary purpose of ANOVA?
To determine if the means of the groups are different from one another
ANOVA helps to identify whether observed differences in sample means are statistically significant.
What tests are conducted to determine which group(s) are different from which other(s) after ANOVA?
Post-hoc or ‘follow-up’ tests
What action is taken if the computed f-ratio is greater than 2.70?
Reject the null hypothesis
This decision is based on the comparison of the computed f-statistic with the critical value. If your computed F-ratio is greater than the critical F-value, you reject the null hypothesis (H₀), meaning there is a statistically significant difference between group means.
What is a grouping variable?
Defines the two points of comparison
Is the independent variable
What is the Outcome Variable?
Interval or ratio level data
Measured at each of two points of comparison
What do statistical tests do?
Compares the means of two related groups
What is a paired t-test?
A statistical test used to compare the means of two related groups.
What is an independent t-test?
A statistical test used to compare the means of two independent groups.
Why is a paired t-test usually more powerful than an independent t-test?
Because variation between samples for pairs is typically smaller than for independent samples.
What does ‘more powerful’ mean in the context of statistical tests?
It means the test is more likely to detect a true effect or difference when it exists.
What contributes to a less noisy estimate in a paired t-test?
Smaller variation between paired samples.
What is a key difference between F-statistics and t-statistics?
T-statistics can be positive or negative, while F-statistics cannot.
This characteristic of t-statistics allows for the specification of an expected direction of the difference.
What does the ability of t-statistics to be positive or negative allow for?
It allows for the specification of an expected direction of the difference.
Specifying an expected direction may make it slightly easier to reach significance.
True or False: F-statistics can indicate a direction of the difference.
False.
F-statistics cannot be positive or negative; they are always non-negative.
What does N-Way ANOVA compare?
The means of four or more independent groups defined by two or more grouping variables, each of which has two or more levels
What test is used to test for homogeneity of variance between groups?
Levene’s test
Levene’s test assesses whether different samples have equal variances, which is an important assumption in many statistical analyses.
What does Repeated-Measures ANOVA compare?
The means of three or more related groups defined by one factor
What assumption does Repeated-Measures ANOVA make about the data?
It assumes ‘compound symmetry’
What does Friedman’s ANOVA by Rank compare?
The distribution of the values in three or more related groups
Is Friedman’s ANOVA by Rank a parametric or nonparametric test?
Nonparametric test (no assumption about distribution)
What is treatment variance?
The variance due to the independent variable
Treatment variance measures how much of the variation in the dependent variable can be attributed to the manipulation of the independent variable.
Define blocks variance.
The individual variation
Blocks variance accounts for differences among subjects that are not related to the treatment being studied.
What does error variance represent?
All variance not explained by treatment or individual variation
Error variance indicates the randomness or noise in the data that cannot be attributed to the experimental conditions or individual differences.
What is the Least Significant Difference (LSD) test?
A post hoc test for repeated-measures ANOVA that does not adjust for multiple comparisons
Carries a high risk of making a type I error.
What is a key characteristic of the Modified Bonferroni t test?
It is more conservative than the LSD test
With a larger number of groups, there is an increased risk of type II error.
What is the Sidak test used for?
It is a post hoc test for repeated-measures ANOVA that is somewhat less conservative
It is a better choice when comparing larger numbers of groups.
True or False: The LSD test adjusts for multiple comparisons.
False
The LSD test does not adjust for multiple comparisons.
Fill in the blank: The LSD test carries a high risk of making a _______.
type I error
Fill in the blank: The Modified Bonferroni t test has an increased risk of _______ with a larger number of groups.
type II error
What are carryover effects in the context of repeated-measures ANOVA?
Carryover effects occur when some or all of the effects of a treatment given at one time are still evident at the time of the second treatment.
This can lead to confounding results as the impact of previous treatments may influence responses to subsequent treatments.
What are position effects in repeated-measures ANOVA?
Position effects occur when the order in which the treatments are given affects the outcome or all of the effects of a treatment given at one time are still evident at the time of the second treatment.
This can lead to confounding variables that impact the validity of the results.
What does the correlation coefficient quantify?
Strength and direction of association between two variables.
What is the Pearson correlation coefficient used for?
Parametric statistic for normally distributed variables at interval or ratio scale.
When should the Spearman correlation coefficient be used?
If distributional assumptions are violated or if one or both of the variables is ordinal.
Fill in the blank: The Pearson correlation coefficient is represented by the symbol _______.
r
Fill in the blank: The Spearman correlation coefficient is represented by the symbol _______.
rho
What does r = -1 indicate?
Perfect negative correlation
As one variable increases in value, the other decreases.
What does r = +1 indicate?
Perfect positive correlation
As one variable increases, the other variable also increases.
What does r = 0 indicate?
No relationship between variables
An increase in one variable does not relate to changes in the other.
What does it mean if r is close to zero?
Weak correlation
A weak correlation indicates that the relationship between the variables is not strong.
What does it mean if r is closer to |1|?
Stronger correlation
A value closer to |1| indicates a stronger relationship between the variables.
What does the square of the correlation coefficient, r2, indicate?
The percentage of shared variance between the two variables
In statistical analysis, r2 is a key measure of how well one variable can predict another.
Which measurement scales are required for Pearson Correlation?
Interval or ratio measurement scales.
What type of distribution is assumed in Pearson Correlation?
Normal distribution.
What type of relationship does Pearson Correlation assess?
Linear relationship.
What is the effect of outliers on Pearson Correlation?
Minimal ‘influence’ by outliers.
What type of measurement scales does the Spearman correlation apply to?
Ordinal, interval, or ratio measurement scales
Spearman correlation is a non-parametric measure that can be used with various types of data.
How important is the distribution of data for Spearman correlation?
Distribution less important
Unlike Pearson correlation, Spearman correlation does not assume normal distribution.
What type of relationship does Spearman correlation assess?
Monotonic, but not necessarily linear, relationship
A monotonic relationship means that as one variable increases, the other variable tends to either increase or decrease, but not necessarily at a constant rate.
How does Spearman correlation treat outliers?
Outliers less important
Spearman correlation is less affected by outliers compared to linear correlation methods.
What does Phi assess?
The correlation of two dichotomous variables
Phi is a measure used in statistics to determine the association between two binary variables.
What is Point-Biserial used for?
To assess the correlation of one dichotomous variable with one continuous variable
Point-Biserial correlation is a special case of Pearson correlation.
What type of test is Kendall’s Tau?
A nonparametric test of correlation that can be used as an alternative to Spearman
Kendall’s Tau is particularly useful for small sample sizes and when data does not meet normality assumptions.
What does the Contingency coefficient assess?
The association between two nominal variables
This coefficient is commonly used in chi-square tests to examine relationships in categorical data.
What is the purpose of the ‘Universal’ measure (eta)?
To measure relationships that are not monotonic
Eta can capture relationships where the direction of the association changes for different values.
What does partial correlation describe?
The relationship between two variables after controlling for the influence of a third
Partial correlation helps to isolate the direct connection between two variables by removing the effect of a third variable.
How does semipartial correlation differ from partial correlation?
It controls the influence of the third variable on only one of the two variables
Semipartial correlation is useful for understanding how a third variable affects one variable while not affecting the other.
What is multiple correlation used for?
To assess the correlation between one variable and a combination of other variables
Multiple correlation is useful in situations where a single outcome variable is influenced by several predictors.
What does canonical correlation quantify?
The correlation between compound dependent variables (DVs) and independent variables (IVs)
Canonical correlation is a powerful multivariate technique that explores the relationships between sets of variables.
What does simple linear regression model?
The association of one DV and one IV
DV stands for dependent variable and IV stands for independent variable.
What does multiple linear regression (MLR) model?
The association between one DV and multiple IVs
MLR extends simple linear regression by incorporating multiple independent variables.
What is multicollinearity?
Highly correlated independent variables (IVs) likely provide redundant information.
Multicollinearity can complicate the interpretation of regression coefficients.
What issue may occur if multicollinearity is present in a model?
Model estimates may become unstable.
Unstable estimates can lead to unreliable predictions and interpretations.
