What is does ANOVA stand for and what is it used for?

Analysis of variance 

It is used to compare 2 or more groups 

If it is comparing 2 groups then it is mathematically equivalent to t-test

In the context of an ANOVA what are "factors" and "levels" and how do they relate to each to each other. list examples.

Factors = variables  = gender, dosage, ect

Levels= male/female, 50mg 100mg, ect

levels = different values of the factors(variables)

What are the four assumptions of ANOVA?

1. The distribution of sample means are normally distributed
2. Independence of errors
3. Absence of outliers
4. homogeneity of variance- everything has equal variance 

What are the null and alternate hypothesis for ANOVA with one factor

Hull is all means are ewual

alternate is not all means are equal

State the null and alternative hypothesis for an ANOVA with two factors.

All means of variable A are equal = null

All means of variable A are not equal = alt

All means of variable B are equal = null

All means of variable B are not equal = alt

Interaction between A & B is not present = null

Interaction between A & B is present = alt

What does it mean if there is an interaction effect present in your ANOVA

An interaction effect means that the variable A is affected by variable B different for a given categorical variable.

Basically it means that the slope of cause an effect for a different nominal variables are not equal??? maybe something like that 

What is the equation for calculating the F statistic?

F = (Treatment Differences + random differences)/ Random Differences 

If no difference F = 1

If differences we expect F > 1

Why do we use analysis of variance instead of multiple T-tests?

Well the more t-test you preform the higher your type 1( false positive) error rate is. ANOVAS help reduce it by condensing everything down to one test.

State the equations to calculate the total number of degrees of freedom, degrees of freedom between groups, and degrees of freedom within groups 

Total numbers of degrees of freedom = Total number of samples -1

Degrees of freedom between groups = groups - 1

Degrees of freedom within groups = total df - df between groups 

Why do we preform post-hoc tests after and ANOVA and what are some examples of post-hoc tests?

The ANOVA tells us that there is a difference between some or all of the groups but it doesn't tell us which ones. Post hoc tests tell us which ones.

The bonnferroni correction might be used but most consider B error rate too high 

Tukey's test

and Ducans test have lower Type I error rate

Ducan's Multiple Range Test

Review that reading module it is a beast

If your experiment has an unbalanced design what does that mean? How does/could this affect homoscedasticity?

An unbalanced design means the number of samples in each group are unequal.

Depending who if the larger or smaller group has a larger standard deviation this can increase alpha error rate or reduce power

We use it after we reject the null with a ANOVA.

It works by calculating the minimum significant difference for each pair of means. if a difference is great than MSD then it is significant 

unbalanced studies mean groups with smaller n have greater MSD

What is a "fixed effect" or "model one" ANOVA used for? What does it compare?

You want to compare different groups to determine which are significantly different from each other.

Sub type of one-way ANOVA

What is the "random effect" or Model II ANOVA used for? What is the goal of this ANOVA?q

The different groups are random samples from a larger set of groups, and you're not interested in which groups are different from each other

ou'd be interested in how the variation among families compared to the variation within families; in other words, you'd want to partition the variance.

How many factors and levels of those factors does a factorial ANOVA have?

A factorial ANOVA has at least 2 factors (variables) with at least 2 or more values. 

factors can be independ, depended or both (mixed)

It is like the one-way ANOVA but with more than one independent variable

One factor with at least two variables which are dependent 

When you have one nominal variable and one measurement variable 

It is similar to the independent measures (one-way) ANOVA

When you have one nominal variable and one ranked variable 

OR

When you would use a one-way (indepdennt samples) ANOVA but your data is severely not normal

Some people say use if sample size is small

What is the equation and use of a pairwise type I error rate.

1-(1-alpha)^N = alpha = p value

N= the number of comparisons

and alpha is the chance of correctly rejecting the null hypothesis = .95

This is attributed to the Bonnferroni Correction 

Duncan's Multiple Range test

Use weclch's ANOVA when design is balanced, small sample sizes (less than 10) and very large standard deviations. Unless the large standard deviations are ver similar.

I think it is less powerful verison of one-way anova

Tukey-Kramer test when do you use it? What is it good for?

Post-Hoc test for ANOVA's. The minimum significant difference (MSD) is calculated for each pair of means and MSD will be the same for all pairs if it is a balanced design.  If the differerence between means is greater than the MSD then it is significant.

Names the variables and use of a repeated-Measures ANOVA

One factor with atleast two levels and the levels are dependent.

EX Factor = time anxiety was measured

before, week 1, week 2 = dependent 

almost ID to one-way ANOVA except for one additional calculation.

Use when you have one measurement variable and more than one nominal variable and the nominalvaribables are nesed (from subgroups with groups)

AKA hierarchical ANOVA

Measurements are not indpendent because they come from the same rat which would violate assumption of independence and be pseudoreplication. so gotta do nested

What is the advantage of using a nested ANOVA over taking the average of the subgroups and doing a one-way ANOVA is the study is balanced?

The advantage is you can compare variation within subgroups. Which is useful for resource allocation.

aka what is better few samples from more rats or more samples from fewer rats.

Explain how the alt and null hypothesis are set in a nested ANOVA.

n=√(Csubgroup×Vwithin)/(Cwithin×Vsubgroup)

If we estimate that each rat costs $200 to raise, and each measurement of protein uptake costs $10, then the optimal number of observations per rat is √(200×77)/(10×23), which equals 8 rats per subgroup. The total cost per subgroup will then be $200 to raise the rat and 8×$10=$80 for the observations, for a total of $280; 

NESTED ANOVA

If not P values are conservative 

Satterthwaite approximation can correct for this but makes P values less accurate  

The Kruskal-Wallis test is best used when...

One nominal variable and one measurement variable that you would do a one-way ANOVA on but the data violates normality 

Or one measurement variable which is ranked and one nominal variable with 2 or more values

assumes different groups have the same distribution but doesn ot assume normality

The null and alternate Hypothesis for the Kruskal-Wallis test 

The samples come from populations with the same distributions.

Some differences slip through if they are similar and opposite side of mean

Non paramentric for analyzing randomized complete block designs equivalent to the repeated measures ANOVA.

ordinal aka ranked data

Null treatments have ID effects

At treatment effects no D

ID

in the case of ties take the average

The Tukey test is more liberal than the Scheffe which means higher change of a type I error 

The Scheffe test is more conservation. less chance of rejecting null hypothesis