One-way ANOVA Flashcards
Why do you use ANOVA rather than doing lots of t-tests?
ANOVA reduces the amount of type 1 error
What is a type 1 error?
A type 1 error is when you reject a true null hypothesis.
What is alpha?
Alpha is the probability of a type one error
What is a type 2 error?
Accepting a false null hypothesis
What is MS error?
MS error is an estimate of the population variance
How do you calculate MS error?
We calculate MS error by pooling (averaging) the variance in each of te groups
What is MS treatment?
An estimate of the population variance (different from MS error)
What is the central limit theorem?
The central limit theorem states that the variance of means drawn from the same population equals the variance of the population divided by the sample size.
When do you use a One-way ANOVA?
You use a one-way ANOVA when you have 1 independent variable with more than 2 levels
How many degrees of freedom are there in a one way ANOVA?
2
What is the formula for an ANOVA? What do the symbols mean?
Xij = μ + τj + eij
X = the persons score μ = the overall mean τ = the effect of which group they're in (the treatment) e = the difference between that persons score and the mean of that group (also called the error)
What is another way of writing τ?
μj - μ
What is another way if writing eij?
Xij - μj
Put into the formula:
Average weight is 65kgs
Average weight for women is 60kgs
Your weight is 80kgs
You = average + effect for women + special to you 80 = 65 - 5 + 20
What is the effect of treatment?
The difference between the groups
What is an assumption of MS treatment?
That the null hypothesis is true
If the null hypothesis is true what does f equal?
F = 1
If the null hypothesis is false what should f equal?
F > 1
F should be more than 1
What are the 3 types of df?
df total
df treatment
df error
How do you calculate df treatment?
Number of people in the treatment - 1
How do you calculate df error?
df total - df treatment
What does MS mean?
Mean squares
What does SS mean?
Sum of squares
What is the sum of squares?
Sum of squares represents deviation from the mean.
What is eta-squared η2?
Eta-squares is the measure for effect size for a one-way ANOVA.
How do you calculate effect size?
SS treatment / SS total
Or
Cohens f
F= the square root of η2 / 1-η2
What do you need to calculate power?
Effect size
Sample size
Alpha (α)
State whether or not the analysis is priori or post hoc
What do you need to calculate an effective sample size?
Effect size
Power
Alpha (α)
Priori or post hoc
What do you do when you find that p is significant after running an ANOVA?
Do follow up tests. Find where the significant difference is
What is family wise error rate?
The probability that a family of comparisons (multiple comparisons) will contain at least one type 1 error
How do you calculate family wise error rate?
α x number of comparisons
What are the 2 post hoc tests we were taught and when do you use each?
SNK (Newman keuls test)
Or when there are differences in group sizes us the
Scheffe test
