PYB210 Lecture Notes – Week 7
In simplified terms, the purpose of conducting an ANOVA is to determine whether
we should reject or retain the null hypothesis (H0).
What is Sampling Error?
Sampling error occurs when samples of the population may have different means
even though the null hypothesis is true.
Monte Carlo Study
A Monte Carlo Study helps us obtain a ‘safe’ value for which we can determine
whether the IV has actually had an effect on the DV.
Monte Carlo Studies work by drawing thousands of samples from a population and
performing an F test on each one. These F scores are then presented in an F
F Distribution Table
F tells us the likelihood that something has occurred by chance.
Remember that if the null hypothesis is true then F should always equal 1.
The F distribution table will tell us how big F has to be before we can say that
something has occurred by chance.
If we were to run a Monte Carlo Study where our samples are drawn from different
means (in other words, the H 1s true) then we get a second distribution which we
call the noncentral F-distribution.
This noncentral distribution lies to the right of the F-distribution because, on
average, we get a larger value of F when there is a real difference between the
Similarly to the F-distribution, the noncentral F varies as a function of the number of
samples (dfA) and the number of scores (df S/A
In addition, noncentral F also varies as a function of the size of the difference
between means (called the effect size).
In summary, noncentral F is the distribution of F values we get when H i0 false.
From the F distribution we can determine the probability of obtaining an F-value
greater than any given value.
Our decision when determining whether H or 0 is t1ue will be based on the
probability of getting an F as large asobservedhen H 0s true.
Alpha Level The probability le