Analysis of Variance 1 Flashcards
The outcome of a chi-squared test is ____
nominal
e.g. frequency tables
Chi-square goodness of fit test compares categorical data to a ________
theoretical standard
is it the same?
Chi-squared test of association compares categorical data (e.g. frequency table) to _______
another frequency table
are they the same?
In a t-test the outcome is _____
numeric
T-tests compare ______
means
One-sample t-tests compare a single mean to a ______
theoretical standard
Independent samples t-tests compare _________
two means to each other
Paired-samples t-tests compare
two means representing two time points to each other
What sort of test should you use if you have more than 2 means (variables)?
ANOVA
What does ANOVA stand for?
Analysis of Variance
What is a one-way ANOVA?
Groups are defined by a single variable
E.g. ‘treatment’ could be ‘placebo, ‘drug 1’ or ‘drug 2’
What is the test statistic for ANOVA?
F
What might H0 and H1 look like for an ANOVA?
H0 = all x are equally effective at y
H1 = Some x are more effective at y
What are the two types of variability, both captured with the sum of squares (SS)?
Between groups (SSb): how different are the group of means from one another
Within groups (SSw): how much do individuals within a group differ from the mean of that group
What is the ‘sum of squares’?
The sum, over all observations, of the squared differences of each observation from the overall mean.
Between groups variability (SSb) is low if…
SSb is low if the difference between group means and the global mean is low
Between groups variability (SSb) is high if…
SSb is high if the difference between group means and the global mean is high
What is within groups variability (SSw)?
How much individuals within a group differ from the group mean
If you add SSb + SSw together to look for total variability, is this the test statistic (F)?
No, you need to correct for DOF
What number should the F test statistic be if the means are different?
F is greater than 1
If the null hypothesis is true, the sampling distribution of the F statistic is what?
An F-distribution
With N (sample size) and G (groups) as the association degrees of freedom
If the null is true, the F statistic is typically?
Small
R command for ANOVA?
ANOVA is performed in stages
aov() calculates the SS values etc
Creates an ‘aov’ object (variable) which contains lots of quantities of interest relating to ANOVA
summary() runs the hypothesis tests
other functions to pull out other things of interest
e.g. model1 <- aov( formula = speed ~ species, data = undead)
summary(model1)
Explain the important outputs of an ANOVA table.
How do you write up the results of an ANOVA table?
What are the important values to include in the stat block?
Stat block:
sampling distribution = F
G-1 degrees of freedom for SSb
N-g degrees of freedom for SSw
The value of the F statistic
the p-value
In an ANOVA the test statistic reflects the total ______ of SStot
What is the formula for SStot?
variability
SStot = SSb + SSw
The F-statistic is the ratio of these: ____/____
F = MSb/MSw
MSb = between groups variability corrected for DOF (SSb/(g - 1))
(g = seperate group means)
MSw = within groups variability corrected for DOF (SSw/(N-G))
N = total observations
G = group means from which they deviate