T-Tests and ANOVA

Question 1

What is a t-test?

Answer 1

A statistical test used to compare the means of two groups to determine if there is a significant difference between them.

Question 2

What are the types of t-tests?

Answer 2

One-sample t-test

Independent (two-sample) t-test

Paired-samples (dependent) t-test

Question 3

When is a one-sample t-test used?

Answer 3

When comparing the mean of a single sample to a known population mean.

Question 4

When is an independent t-test used?

Answer 4

When comparing the means of two independent groups (e.g., males vs. females).

Question 5

When is a paired-samples t-test used?

Answer 5

When comparing means from the same group at different times (e.g., pre-test vs. post-test).

Question 6

What assumptions must be met for a t-test?

Answer 6

The dependent variable is continuous.

The data are normally distributed.

The groups have equal variances (for independent t-tests).

Observations are independent.

Question 7

What is the formula for the t-statistic in an independent t-test?

Answer 7

t=
(X1-X2)
—————–
Sqr of (S2/n1)+(S2/n2)

Where:
Xs are Sample Means
S are standard deviations
n are sample sizes.

Question 8

What is the null hypothesis in a t-test?

Answer 8

That there is no significant difference between the group means (𝐻0:𝜇1=𝜇2).

Question 9

What is ANOVA?

Answer 9

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.

Question 10

What are the types of ANOVA?

Answer 10

One-way ANOVA
Two-way ANOVA
Repeated measures ANOVA

Question 11

When is a one-way ANOVA used?

Answer 11

When comparing the means of three or more independent groups based on one independent variable.

Question 12

When is a two-way ANOVA used?

Answer 12

When analyzing the effect of two independent variables on a dependent variable.

Question 13

What is the null hypothesis in an ANOVA test?

Answer 13

That there is no significant difference between the group means (𝐻0:𝜇1=𝜇2=𝜇3).

Question 15

What does a significant ANOVA result indicate?

Answer 15

At least one group mean is significantly different from the others.

Question 16

What is the F-ratio in ANOVA?

Answer 16

The ratio of variance between groups to variance within groups, used to determine statistical significance.

Question 17

What assumptions must be met for ANOVA?

Answer 17

The dependent variable is continuous.

The data are normally distributed.

Homogeneity of variance (equal variances across groups).

Observations are independent.

Question 18

What follow-up test is used if ANOVA is significant?

Answer 18

Post Hoc tests like Tukey’s HSD to identify specific group differences

Question 19

What is the formula for the F-statistic in ANOVA?

Answer 19

F=variancebetweengroups/variancewithingroups

Question 20

What is repeated measures ANOVA?

Answer 20

A test used when the same participants are measured multiple times under different conditions.

Question 21

How does ANOVA differ from t-tests?

Answer 21

ANOVA compares multiple groups, while t-tests compare only two groups.

Question 22

What is the assumption of homogeneity of variance in ANOVA?

Answer 22

The assumption that all groups have equal variances.

Question 23

What does a large F-statistic indicate?

Answer 23

A greater difference between group means relative to within-group variation.

Question 24

When should ANOVA not be used?

Answer 24

When data do not meet assumptions such as normality and homogeneity of variance.

Question 25

What are non-parametric alternatives to the t-test and ANOVA?

Answer 25

Mann-Whitney U test (for t-test alternative)

Kruskal-Wallis test (for ANOVA alternative)