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Summary Advanced Research Methods and Research Ethics

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Technische Universiteit Eindhoven (TUE)

Clear summary of the content of the course Advanced Research Methods and Research Ethics that contains all the important concepts, theories, and commands you need to know for good study results.

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Summary BRM3
DL week 1
1.0 Intro
So the goal of data collection is to first draw statistical inferences and then to draw theoretical
inferences.

We want to improve statistical inferences. First reason was precognition experiment, gave positive
results, but it is unlikely that it exists.

Problems in scientific literature at the moment, these make it difficult to conclude whether
published findings are reliable:

- Studies have too small sample sizes, so underpowered studies
- Flexibility in data analyses leads to random things that are not true, but are interpreted as
true effects
- Publication bias; people share studies showing effects and not studies that do not show an
effect

1.1 Frequentism likelihoods Byesian
3 ways to draw statistical inferences from data:

- Path of action/Neyman-Pearson: search for rules to govern our behavior such that, in the
long run, we will not be wrong too often. p<alpha reject H0, p>alpha accept H0. Only relies
of relative evidence of data not on priors. It does not tell you anything about the single test,
only about the behavior in the long run
- Path of knowledge/likelihood: compares the likelihood of different hypothesis, given the
data, uses likelihood functiontop is the most likely outcome, and likelihood ratio1 if
there is no difference between different hypotheses (fair coin vs unfair coin).
- Path of belief/Bayesian statistics: no use of p values, allows you to express evidence in
terms of ‘degrees of belief’, relies on priors

Main difference between likelihood and Bayesian, both use relative evidence of data, but likelihood
does not rely on priors. You can use them both to answer your questions.

1.2 What is a p-value
P-values help in preventing to fool yourself and following your prior beliefs. P-values tell you how
surprising the data is, assuming there is no effect. The difference between the
two means of two groups is never exactly zero, the difference can be either
random noise or a real difference. A normal distribution centered at 0 is used.
If alpha level is 0,05, P>0.05 data is not surprising (95%), p<0.05 data is
surprising assuming the H0 is true (5%)

Real definition of p value: the probability of getting the observed or more
extreme data, assuming the null hypothesis is true. It is the probability of the data not the
probability of a theory (after p<0.05, an effect is not 95% to be true)! You can’t get the probability
the null hypothesis is true from a p value!! If you want to now the probability that a theory is true
you need to use Bayesian statistics.

p>0.05 is not surprising, but it doesn’t mean there is not true effect, you need large samples to
detect small effects. p<alpha, act as if data is not noise, p>alpha remain uncertain or act as if data is
noise (“mu”)

,Alpha: confidence interval 95% gives an alpha of 0.05, significance level, the probability of rejecting
the H0/observing a significant result when H0 is true (type 1 error rate). When you act as if there is
an effect when p<0.05, in the long run you won’t be wrong more than 5% of the time (making type
one error). When there is no effect there is a 5% chance of getting a p value below 0.05.

P-values are a starting point, but also look at size effects of other studies.

When there is an effect the p-values depend on the statistical power (The chance of observing a p-
value smaller than 0.05, given that there is a true effect). Here the chance of observing low p-values
is higher than high p-values. When power increases the number of p-values below 0.05 increases.

When there is no effect, every p-value is equally likely. So 5% of the p-values when there is no effect
fall below 0.05. That’s why there is a 5% probability of making a type 1 error when there is no effect.

Conclusion form null hypothesis significance test can be we can reject H0 or an inconclusive
outcome

1.3 Type 1 and type 2 errors
You want you control the Type I&II errors to prevent making a fool out of yourself too often in the
long run.

H0=there is no difference between two conditions (difference never exactly 0)

H1=there is a difference

Type 1 error/false positive: the probability of a significant result/rejecting H0
when H0 is true (alpha), so finding an effect when there is no effect

Type 2 error/false negative: the probability of a non-significant result/rejecting
H1 when H1 is true (beta), so finding no effect when there is an effect

Statistical power (1-beta): the probability of a significant result when H1 is true,
often 80%. So high power means low type II error rate.

True negative: correctly saying that something is not true, true positive: correctly saying that
something is true

So when H0 is true you can only make true negatives or false positives. When H1 is true you can only
make true positives or false negatives. The probability of making false negatives (Type II) is bigger
than false positives (type I). The probability that you find a true negative is the biggest in a study
with H0/H1 50%, alpha 5% and power 80%. How to improve the probability of true positive?

- Increase power (does help a bit)
- Lower alpha level (does not help much)
- Change prior probability of H0 and H1, when H1 is very likely the true positive probability
will increase a lot

There are recommendations for the error rates (alpha 5%, power 80%), but depending on the
research you can chose them yourselves. When you increase your power, you decrease your type II
error rate, this is what you want.

, Assignments
Graph p-value distribution when there is a difference between the two samples (an true effect)

Power=total number of p<0.05/total number of simulations.
When the sample size increases the power increases too, the p-
value distribution is steeper. So when there is an effect, the p-
value distribution depends on the power, the higher the power
the more p-values fall below 0.05 and the steeper the distribution

Graph p-value distribution when there is no difference between the two samples (0 power). The p-
values are uniformly distributed under the null, every p-value is equally likely when the null
hypothesis is true. The leftmost bar shows a type 1 error.

When the alpha decreases, the power decreases too. Given that with a very high power and an alpha
level of 0.05 you are more likely to observe p-values between 0.04 and 0.05 when the null
hypothesis is true, than when the alternative hypothesis is trueLindley’s paradox. So a significant
p-value is not always evidence for the alternative hypothesis. This means that p-values just below
0.05 are the very best weak support for the alternative hypothesis, replicate study!

Null model for the means differences is the model of data we should expect
when the H0 is true. The peak in the graph is the most likely mean
difference in the population, this is zero. The two red areas together form
5% of the most extreme mean differences we would expect. When a mean
difference in the red area/tails is observed it is ‘surprising’, the statistical
test will be statistically significant at a 5% alpha level (not more than 5% will be considered as
surprising, in this case red areas are a type 1 error because H0 is true).

When the sample size increases, the red ‘surprising’ area is closer to 0, but it is still centered on 0, so
narrower distribution. So when you observe 0.5 mean difference in a big sample compared to a
small sample it is more surprising.

Null model and alternative model, when the null model is not true (0.5 mean difference)

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