T-Tests and ANOVA Flashcards
What is a t-test?
A statistical test used to compare the means of two groups to determine if there is a significant difference between them.
What are the types of t-tests?
One-sample t-test
Independent (two-sample) t-test
Paired-samples (dependent) t-test
When is a one-sample t-test used?
When comparing the mean of a single sample to a known population mean.
When is an independent t-test used?
When comparing the means of two independent groups (e.g., males vs. females).
When is a paired-samples t-test used?
When comparing means from the same group at different times (e.g., pre-test vs. post-test).
What assumptions must be met for a t-test?
The dependent variable is continuous.
The data are normally distributed.
The groups have equal variances (for independent t-tests).
Observations are independent.
What is the formula for the t-statistic in an independent t-test?
t=
(X1-X2)
—————–
Sqr of (S2/n1)+(S2/n2)
Where:
Xs are Sample Means
S are standard deviations
n are sample sizes.
What is the null hypothesis in a t-test?
That there is no significant difference between the group means (𝐻0:𝜇1=𝜇2).
What is ANOVA?
Analysis of Variance (ANOVA) is a statistical test used to compare the means of three or more groups to determine if there is a significant difference.
What are the types of ANOVA?
One-way ANOVA
Two-way ANOVA
Repeated measures ANOVA
When is a one-way ANOVA used?
When comparing the means of three or more independent groups based on one independent variable.
When is a two-way ANOVA used?
When analyzing the effect of two independent variables on a dependent variable.
What is the null hypothesis in an ANOVA test?
That there is no significant difference between the group means (𝐻0:𝜇1=𝜇2=𝜇3).
What does a significant ANOVA result indicate?
At least one group mean is significantly different from the others.
What is the F-ratio in ANOVA?
The ratio of variance between groups to variance within groups, used to determine statistical significance.
What assumptions must be met for ANOVA?
The dependent variable is continuous.
The data are normally distributed.
Homogeneity of variance (equal variances across groups).
Observations are independent.
What follow-up test is used if ANOVA is significant?
Post Hoc tests like Tukey’s HSD to identify specific group differences
What is the formula for the F-statistic in ANOVA?
F=variancebetweengroups/variancewithingroups
What is repeated measures ANOVA?
A test used when the same participants are measured multiple times under different conditions.
How does ANOVA differ from t-tests?
ANOVA compares multiple groups, while t-tests compare only two groups.
What is the assumption of homogeneity of variance in ANOVA?
The assumption that all groups have equal variances.
What does a large F-statistic indicate?
A greater difference between group means relative to within-group variation.
When should ANOVA not be used?
When data do not meet assumptions such as normality and homogeneity of variance.
What are non-parametric alternatives to the t-test and ANOVA?
Mann-Whitney U test (for t-test alternative)
Kruskal-Wallis test (for ANOVA alternative)
