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.