Unit 1.5: f-Test & Analysis of Variance (ANOVA)

F-Test is used to __. Can be used in a variety of statistics, but most commonly in (2)

Test equality of two variances, analysis of variance (ANOVA), regression analysis

F-Tests are used in conjunction with __tests, tests if __ of populations with equal SD's are equal, tests if __ model fits data well, etc.

Additional, means, regression

ANOVA null hypothesis: __ (means are not significantly different)

All groups are random samples from same population

ANOVA is __ __ __, in it's simplest form it compares __ of more than __ groups.

Analysis of variance, means, two

F-test null hypothesis: __

Assumes two variances are equal to 1

F-test alternative hypothesis __

Assumes two variances are not equal to 1

F-Tests are never performed __, and are rarely done.

By themselves

__ also called "factor variables", these are variables with discrete groups (sex - male or female)

Categorical variables

Random-effects models have __variables - that is they can have a __ of possible values. Factors are not fixed when sampled from larger population (everyone having different glucose values)

Continuous, range

__the outcome you are measuring during an experiment. Responds to the __ variable

Dependent variable, independent

ANOVA can tell us that groups are from __ __, but not which groups exactly. For that we use __comparisons by t-Tests, then check the __ of those tests

Different populations, pairwise, p-values

ANOVA: when variances are unequal, it means the groups are __

Different.

ANOVA table: Residuals are __ __

Distances squared

Homoscedasticity means __

Equality of variances

ANOVA comprises a variety of low to high complexity procedures (5).Other types are (3)

Fixed, random, mixed, one-way, two-way, MANOVA, ANCOVA, MANCOVA

A __ __model - one or more factor variables are applied to subjects and response is measured (drug treatment across groups - can only be in one group at a time)

Fixed-effects

F-Test assumptions (2)

Independence, normality

ANOVA assumptions (4)

Independence, normality, homescedasticity, equal n

1-way ANOVA: when one __variable (treatment) is measured with one __variable (response) This is what we usually do.

Independent, dependent

__ a variable you choose to manipulate. Often is something you think will have an effect on an outcome (__ variable)

Independent, dependent

2-way ANOVA: multiple __ variables tested against single __ variable (like glucose tests considering age, diabetes status, weight, gender, etc.)

Independent, dependent,

__ models have variables of both __and __ effects types

Mixed-effects, fixed, random

ANOVA is useful because problems arise when there are >2 groups and __ __ __ are carried out, by performing multiple statistical tests, the likelihood of __ rejecting null is increased (type I error)

Multiple pairwise comparisons, falsely

ANOVA compares __groups to another group, but makes no __assumptions

Multiple, individual

Fixed-effect model: can only be in __ at a time.

One group

As more comparisons are performed, it becomes more likely to find one that differs purely due to __ __

Random chance

__ __ models: used when factors are not fixed, sampled from larger population and thus are __. (More than one measurement is taken from an individual - that individual is a group, but is taken from a larger random population of individuals)

Random effects, random

ANOVA tests if all groups are __from same population - determining if variance between groups is __ to variance within groups

Random samples, equal

The f-test is a __ test. Increases in __ affect it like the t-test (data gets more centered, which increases statistical __

Ratio, degrees of freedom, power

ANOVA is one of, if not the MOST used statistical tools - is __ to violations in assumptions, can compare __ groups at once, and __to many experimental designs

Resistant, multiple, flexible

Biological significance does not always correlate to __ significance

Statistical

ANOVA is so useful because it can test many groups at once without raising __ error (an omnibus test)

Type I

When F value is very high, groups are __ - null is __.

Unequal, rejected

F = __/__

V1/V2

F-test = __/__. ANOVA f-test = __/__

V1/V2, Variance between groups/Variance within groups

Mean squared are __ to calculate test.

Variances

F-Tests are used to see if __ of groups differ.

Variances.

Bonferroni test: __. It's overly corrective, but simple, makes it harder to __ __ __. Controls for __ __

alpha/n, reject the null, false positives.