Advanced research methods and statistics (202200104)
Class notes
ARMS - extra lecture notes
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Course
Advanced research methods and statistics (202200104)
Institution
Universiteit Utrecht (UU)
This summary includes additional lecture notes that are not explicitly mentioned in the slides - it mainly includes examples of how to do certain things in JASP.
With this summary, I got a clearer picture of all the material and got an 8.9 for the exam!
Lecture 1
First prior is called a uniform distribution.
This one is not specific. It has no
expectation. It says that any value is
equally likely.
Second prior is called a bounded uniform.
This one is a bit more specific than 1, but
not very specific. In this range (40-160) all
values are equally likely. Outside the
range the probability is 0.
Third prior: middle values are most likely. Values that are very low are unlikely. The
probability for values outside the range are 0. We have more prior knowledge. Not a very
peaked distribution, we are not making very strong predictions.
Fourth prior: more extreme prior than 3. We have a really strong assumption that the
average will be in the middle. Drops off really quickly. Values outside the range unlikely. Very
strong informed prior, we are very certain that the prior is in the middle.
Fifth prior: similar to 4, but this one is not centered in the middle. Expects that average is
quite low. For example, a population where you are certain that IQ is very low.
In this example, the posterior is accurate to
the data, because we didn’t have any
expectations about the prior. This happens
in frequentists statistics.
The posterior will be more certain (higher)
when you add a prior.
,Output frequentist analysis:
R2: measure of how much variance the total model explains (in the sample)
R: multiple correlation coefficient, correlation between the observed Y and the Y in
our model
Adjusted R2: estimate of how much variance our model can explain outside our
sample (in the population).
Simpler models are simpler to generalize.
P-value: see if model is significant.
Unstandardized coefficients: B-values of regression lines, B0 = intercept. Other factors
are intercept of other B-values.
o If we increase a value with 1, with how many does the factor
increase/decrease?
o Difficult to compare, because of different scales.
o Can’t use this to see which factors has more influence.
Standardized coefficients: to see which of the factors has more influence. Show on
the same scale, can be compared. You want the biggest absolute number for the
factor with the most influence.
Output Bayesian analysis:
Test all combinations of predictors in the models.
BF10: support H1 10x stronger than for H0.
Coefficients: p-value based on the model, for example adding a new model can
overlap with the other factor. P-value is not significant anymore.
Regression models always depend on what you put in them. If you miss certain variables, you
can miss information.
Lecture 2
Example on the left: relatively
small within-group variation
Example on the right: relatively
large within-group variation.
More spread of the data.
The means of the right and on
the left are the same, so
between-group variation is the
same.
ANOVA compares between-group variation with within-group variation.
, On the left weight data, on
the right height data.
On the left, orange dots are
quite close together and blue
dots are quite close together.
They are apart from each
other.
On the right, there is a lot
more overlap between the
groups.
On the left, the groups have less variation, they are more together. On the right, there is
bigger spread in each group. In height, there is more overlap. In weight, there is less overlap.
In weight-data position explains more of the variances.
In weight, the within-group variation is smaller than in height.
Deciding whether there are
significant main effects and
an interaction effect: looking
at the p-value.
Only person condition is
significant, so there is a main
effect of person.
Partial eta-squared (effect
size): we use this because it
can tell us for each of the effects what the influence is of this factor while we are controlling
for the other factors. Isolates the effect of interest.
Simple Main Effects are follow-
up tests when an interaction-
effect is significant.
Which of the groups are
different from each other?
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