Biostats Two Way ANOVA

Front

central limit theorem

Back

you take many large random samples from any population the distribution of those sample means will approximate a normal distribution, allowing you to use t-test + Z-scores

Front

Example of the central limit theorem

Back

Imagine studying the average recovery time from an illness. The population data might be skewed (most recover quickly, a few take ages). But if you take many groups (samples) of patients, calculate the average recovery time for each group, and plot those averages, the plot will be normal, allowing you to confidently say if a new drug changes the true average recovery time. 

Front

Two Factor ANOVA assumptions

Back

random sampling

normal dist variable

equal variance

Front

No Effect two factor outcome on graph

Back

slope is 0

no change from A1 to A2

no change from B1 to B2

ALL 4 DOTS HAVE THE SAME y-value

THE LINES OVERLAP (on top of e/o)

graph appearance

two horizontal lines, close together

Front

Main Effects of A two factor outcome on graph

Back

A is significant

• - A1 has a higher mean than A2

• (A1 mean and A2 mean r significantly diff)

B has no effect

• - does not explain sig amount of variance

• - B1 and B2 have the same mean

(same avg from B1 to B2)

graph appearance

two dec lines, close together

Front

Main Effects of B two factor outcomes on graph

Back

B is significant

the mean of B1 is diff from the mean of B2

A is not sig

A1 and A2 have the same mean (y-value)

graph appearance

two horizontal lines, further apart

Front

Main Effects of A and B two factor outcomes on graph

Back

B is significant

B1 and B2 have different y-values

A is significant

A1 and A2 have diff means (diff y-vals)

graph appearance

lines are dec and r further apart

B1 + B2 lines shift in the same direction when move frm A1 to A2 so "A" has a main effect

Parallel slopes = no interaction

Front

Main Effects of B, Interactions of A + B ANOVA two factor outcomes on graph

Back

B is significant

• B1 and B2 have significant difference

A is not significant (has no effect)

A1 and A2 have the same mean

Interaction present

move frm A1 to A2 in B1 slope inc

as move from A1 to A2 in B2 slope dec

(diff pattern in B1 n B2)

graph appearance

B1 line is pos

B2 line is neg

(B lines r in diff direction )

Front

Interactions of A + B ANOVA two factor outcomes on graph

Back

A is not significant

A1 and A2 have the same mean

B is not significant

B1 and B2 have the same mean (in middle)

Interaction

From A1 to A2, B1 starts low + ends high

From A1 to A2, B2 starts high + ends low

graph appearance

B1 and B2 lines cross ("x")

B1 line is pos

B2 line is neg

Front

How to know if there is an interaction between A and B

Back

Ask urself this

does pattern changes from A1 to A2 while in Bi and B2?

if pattern changes = interaction

pattern stays the same = no interaction