Stats Lecture 12

One-way ANOVA

used to test the claim that three or more population means are equal

One-way ANOVA example

how different seating in a classroom (front, middle, back) effects exam scores

Assumptions

data is normally distributed, variances of each sample are assumed equal, all samples were taken independently of each other and are randomly taken from their respective populations

Response variable

the variable you are comparing (dependent variable)

Factor variable

a variable that the experimenter manipulates or controls in an experiment to see its effect on the response variable (independent variable)

Continuous variable

a variable that can take on an infinite number of values within a given range, often used for measurements such as height, weight, and temperature (typically measured rather than counted)

Categorical variable

a variable that can take on a limited, fixed number of possible values, often representing groups or categories, such as gender, race, or blood type

Null hypothesis

the means are equal

Alternative hypothesis

at least one of the means is different

Variation

the sum of squares (SS) of the deviations between a value and the group mean of the value

Two scores of variation

SS(B) and SS(W)

SS(B)

the variation due to the factor

SS(W)

the variation that can’t be explained by the factor so it’s called the error variation

Variance

also called the mean of squares (MS); average squared deviation from the mean and are found by dividing the variation by the df (SS/df)