MATH 10051 Lecture Notes - Lecture 5: Type I And Type Ii Errors, Analysis Of Variance, Null Hypothesis

• School: Kent State University
• Department: Mathematics
• Course: MATH 10051
• Professor: Mary Theresa Sharp

Document Summary

The one-way analysis of variance is used to test the claim that three or more population means are equal. This is an extension of the two independent samples t-test. The response variable is the variable you"re comparing, i. e. , dependent variable. The factor variable is the categorical variable being used to define the groups, i. e. , independent variable. The one-way is because each value is classified in exactly one way. Examples include comparisons by gender, race, political party, color, etc. The variances of each sample are assumed equal. Equal variances is called homoscedastic (same + scatter) rule of thumb: ratio of largest to smallest sample st. dev. must be less than 2:1. The residuals are normally distributed (not skewed or partial) The null hypothesis is that the means are all equal. The alternative hypothesis is that at least one of the means is different.