Lecture 20: ANOVA and T-tests in Statistics

What is the purpose of statistics in data analysis?

To understand data, identify patterns, draw conclusions, inform decisions, and expand knowledge.

What is Multiple Regression?

A statistical method for making predictions using two or more independent variables.

How does adding more variables affect variance explained in Multiple Regression?

As more variables are added, more variance is explained due to pooled correlation of variables.

What does the Multiple correlation coefficient (R) indicate?

The relationship between the criterion and the weighted sum of the predictor variables.

What does R² represent in Multiple Regression?

The amount of variance explained by the combined predictors.

What is the formula for degrees of freedom (df) in a one sample t-test?

df = n - 1.

What is the formula for degrees of freedom (df) in independent samples t-test?

df = n1 + n2 - 2.

What is the formula for degrees of freedom (df) in dependent samples t-test?

df = n - 1.

What is the formula for degrees of freedom (df) in simple linear regression?

df = n - 2.

What is the formula for degrees of freedom (df) in a Chi-square goodness of fit test?

df = k - 1.

What is the formula for degrees of freedom (df) in a one-way ANOVA?

df = N - 1.

What are the steps in testing differences using statistics?

Define independent and dependent variables, set significance level, evaluate null hypothesis, and establish calculated and critical values.

What is the purpose of a one sample t-test?

To compare the sample mean against a population mean.

What does an independent t-test compare?

The means of two independent groups to determine if they are significantly different.

What is the goal of a dependent t-test?

To compare two mean scores that are related, such as pre/post data in one group.

What is the difference between one-tailed and two-tailed tests?

Two-tailed tests assume differences could favor either group, while one-tailed tests assume differences lie in one direction.

What does a significant t ratio indicate?

That the true variance exceeds the error variance to a significant degree.

What does statistical significance at p<0.05 imply?

The null hypothesis is rejected, indicating a 95% chance of a difference between conditions.

What is ANOVA used for?

To determine differences among two or more groups.

What is the F-ratio in ANOVA?

A statistic calculated as the ratio of true variance over error variance.

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

To identify where the differences exist between groups after finding a statistical difference.

What is a two-way ANOVA?

A factorial analysis with two independent variables, resulting in three F-ratios.

What does ANCOVA do?

Compares treatment effectiveness while adjusting for covariates like age and health status.

What is the simplest form of repeated measures ANOVA?

The dependent t-test.

What is the overall summary of t-tests and ANOVA methods?

One sample t-test tests against a known mean, independent and paired t-tests compare two groups, and ANOVA/ANCOVA determine differences among several groups.