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Biostat Moule 4
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Graduate
07/15/2017

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Term

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

Definition

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

Term

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

Definition

Factors = variables  = gender, dosage, ect

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

 

levels = different values of the factors(variables)

Term

What are the four assumptions of ANOVA?

Definition
  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 
Term

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

Definition

Hull is all means are ewual

 

alternate is not all means are equal

Term

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

Definition

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

 

Term

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

Definition

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 

Term

What is the equation for calculating the F statistic?

 

Definition

 

 

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

 

If no difference F = 1

 

If differences we expect F > 1

Term

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

Definition

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.

Term

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

Definition

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 

Term

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

 

Definition

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

Term

Ducan's Multiple Range Test

Definition

Review that reading module it is a beast

 

Term

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

Definition

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

Term
When do we use the Turkey-Kramer test? Basically how does it work? What effect does a balanced distend have on it?
Definition

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

 

 

Term

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

 

Definition

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

 

Sub type of one-way ANOVA

Term

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

Definition

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.

Term

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

Definition

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

Term
What factors and levels are involved in a mixed variable anova
Definition
At least 2 factors which 2 or more levels where one factor is dependent and one is independent.
Term
What factors, levels, and their relationships to each other are involved in a Repeated-Measure ANOVA??????
Definition

One factor with at least two variables which are dependent 

Term
The Kruskal-Wallis test is the nonparametric alternative to what type of ANOVA? What other kinds of data can it be used for?
Definition

When you have one nominal variable and one measurement variable 

 

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

Term
When should you use the Kruskal-Wallis test?
Definition

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

Term

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

Definition

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 

 

Term

Duncan's Multiple Range test

Definition
Term
Welch's ANOVA
Definition

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

Term

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

Definition

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.

Term

Names the variables and use of a repeated-Measures ANOVA

 

Definition

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.

Term
When do you use a nested ANOVA
Definition

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

Term

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?

Definition

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.

Term

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

Definition
In a two-level anova the null is that the groups have the same mean. and all subgroups within each group have the same mean.
Term
What is the equation to calculate the number of observations per subgroup.
Definition

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; 

Term
Which test relies heavily on a balanced design?
Definition

NESTED ANOVA

If not P values are conservative 

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

Term

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

Definition

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

Term

The null and alternate Hypothesis for the Kruskal-Wallis test 

 

Definition

The samples come from populations with the same distributions.

 

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

Term
What does the Friedman test do. what are null and alt hypothesis
Definition

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

Term
Between the two post-hoc tests for a one-way ANOVA (Tukey HSD and Scheffe) which one is more conservative?
Definition

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

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