Masterclass 1-3 Flashcards
What is a variable?
A variable is a characteristic of things that may take more than one value. In probability, a random variable is an expression whose value is the outcome of an experiment.
What are the two components of Hume’s conception of causality?
- CONTIGUITY (contiguity in space and time of cause and effect) and
- CAUSE-EFFECT (cause occurs before effect), where there is a necessary connection if cause ad(?) effect.
What is a sufficient condition for an effect to occur?
if that condition occurs the effect will occur. It may be necessary or not.
What is a necessary condition for an effect to occur?
If and only if that condition occurs the effect will occur. It may be sufficient or not.
What are necessary and sufficient conditions?
With both necessary and sufficient conditions, they have to occur for the effect to occur and no other conditions will make the effect occur.
Why did David Lewis propose to take into account only the second part of Hume’s definition of causality?
There are situations in which the first rule occurs and there is no causality: night follows the day but the day is not the cause of night. The connection between cause and effect may not happen repeatedly (e.g. a person shoots and kills another person).
What does each rug of Pearl’s ladder of causation tell us about causality?
Observations: correlations;
Actions: causation by intervention;
Imagination: causation by modelling
What is a chain? And, why is it important?
In chain and mediation of X–>V–>Y,
The effect of X on Y is mediated by V.
What is a common cause? And why is it important?
In confounding U–>X–>Y, we are studying whether X causes Y. But U–>Y and so U is a common cause of X and Y.
U is confounding the link X–>Y (the confound is on the DV Y).
What is a collider? And, why is it important?
In Selection bias X–>Y–>Z, we study whether X causes Y (Z the collider is on BOTH the IV X & DV Y).
Z is a common effect of X and Y or a collider. If we control for Z we may find an association X–>Y that was absent if not controlling. Or we dilute an actual r/s.
In a study, the Bayes Factor (BF10) comparing an H1 to a H0 is 0.05…
Meaning: the data is 20x more likely under the H0 than under the H1.
The Bayes Factor (BF10) comparing the H1 and H0 is 0.10…
Meaning: the data is more likely under the H0 than under the H1.
The prior distribution in the model of the H0 used by JASP is:
A spike over the value 0.
In a study, the Bayes Factor (BF10) comparing an H1 to a H0 is 0.5…
Meaning: the data is 2x more likely under the H0 than under the H1.
The probability of the data under the H1 is 0.001 and that of the H0 is 0.0001. What is the value of the Bayes Factor (BF10)?
a. 1
b. 0.0001
c. 10.
d. 0.001.
The prior distribution in the model of the H1 used by JASP is:
A symmetrical distribution centered around the value 0 (or another H0).
In the H0 testing approach, if the value of the statistic calculated in the sample (e.g. b1), or a more extreme value, has a lower probability than that of a pre-established threshold, what is the correct decision?
To reject the H0.
In the Maximum likelihood estimation approach, why is the more complex model penalised?
To avoid overfitting.
Which component in the Bayesian approach is the most similar to an equivalent component in the Traditional approach?
Probability of the data given a parameter value.
The probability of the data under the H1 is 0.008 and that of the H0 is 0.8. What is the value of the Bayes Factor (BF01)?
a. 0.0001.
b. 100.
c. 1.
d. 0.001.
Consider two sampling distributions (A and B) from the sample population of values: A was constructed with samples of 10 values, B was constructed with samples of 100 values.
Ans: The standard error of A is larger than the standard error of B.
The sampling distribution of the mean is constructed by generating…
Thousands of samples of values and calculating their means.
Prior knowledge combined with likelihood allows to calculate…
A posterior distribution.
The mathematical formula that corresponds to the Linear model with one predictor variable:
Y ~ Normal (Beta0 + Beta1 X, sigma)
The standard deviation of a population and the standard error of the mean calculated from that population tells us that:
The standard deviation of the population is higher than the standard error of the mean.
If the prior distribution for a parameter value is a normal distribution…
the parameter values close to the mean of that distribution are more plausible than those far from the mean of that distribution.
The mathematical formula that corresponds to the Simplest linear model?
Y ~ Normal (Beta0, sigma)
If the prior distribution for a parameter value is a uniform continuous distribution…
All the possible values of that parameter are equally plausible.
In a linear model with B0=70 and B1=2.5, what is the expected value for Y for X=0?
a. 95.
b. 0.
c. 72.5.
d. 70.
In a linear model in which the expected value for Y is 92, an actual observation of Y is expected to…
be 92 or a value close to 92.
A psychologist uses the normal distribution as a model for her experiment. How would you best classify this model?
a) A model of reality
b) A statistical model.
c) A causal model.
d) A probability model.
Which of the following options provides a correct classification of the following variables:
a) Interest in intellectual tasks (possible values: Low, Medium, High)
b) Reaction Time (measured in ms.)
Ordinal and Continuous
What are the two components of DAG (directed acyclic graphs)?
- Nodes (represent variables)
- Edges (represent causal relationships)
- They are directed, meaning - they are arrows that indicates that one variable causes the other variable.
In DAG (directed acyclic graphs), which of the following paths is allowed?
A path from variable A to variable B, with no path from variable B to variable A.
A cognitive scientist develops a computational model of the mind. How would you best classify this model
a) A model of reality
b) A statistical model.
c) A causal model.
d) A probability model.
Counterfactual thinking forces us to…
Consider what would have been the effect had the cause did not occur.
In DAG, variable A affects variable C, and variable B also affects variable C. How is variable C called?
A collider.
A psychologist is interested in investigating the effect of variable A on B. She knows that there is a variable she cannot measure that affects both A and B. What is the effect of that unmeasured variable?
Confounding
A health psychologist develops a model including the variables therapy and depression. How would you best classify this model?
a) A model of reality
b) A statistical model.
c) A causal model.
d) A probability model.
How is the following structure of a DAG called?
A–>B–>C
Chain.
What is the difference between the concept of variable in science and research and that in probability?
In science and research a variable refers to…
a characteristic or a feature of a thing.
What is an event in probability theory?
A subset of the sample space.
Which of the following statements is true regarding a probability density?
It integrates to 1.
Consider an experiment in which the sample space contains the following outcomes ω1, ω2, ω3, ω4. Event A is defined as the set containing ω1, ω2, ω3, and event B is defined as containing ω3, ω4. What is the true statement in this situation?
The sum of the probabilities of events A and B does not necessarily add to 1.
What is the concept that best describes the Bayesian view of probability?
Probability is a degree of credence on an event.
A psychologist is interested in investigating the effect of variable A on B. She knows that there is a variable she cannot measure that affects both A and B. What is the effect of that unmeasured variable?
a) Selection bias
b) Confounding.
c) Collider
d) Chain
In a Binomial distribution with parameters pi=.60 and n=10, which of the following values is more plausible?
a) One successful trial.
b) Seven successful trials.
c) Three successful trials.
d) Ten successful trials.
In a normal distribution with parameters mu = 15 and sigma =5, which of the following values is more plausible?
a) Eighteen.
b) Seventeen
c) Ten
d) Five
What is a sample space?
The set of possible outcomes of an experiment.
What does the following expression denote: P (X=0 | Y=1)?
The conditional probability of X being 0, given that we know Y=1.
In a Beta distribution with parameters a=20 and b=80, which of the following values is more plausible?
a) 0.
b) 0.50.
c) 0.30
d) 0.80
Where do the values of a random variable come from?
From a random process.
What is probability?
Frequentist view: p is the long run expected frequency of occurrence of an event… e.g. the probability of heads or tails from a toss of a coin several times.
Bayesian view: p is the degree of credence of the occurrence of an event or basically, probability can be assigned to many events and do not need repeated events.
What is a random variable?
from research view: it is a variable in research with characteristics of something that can take many values.
from probability theory: the variable is an outcome of an experiment but the word “experiment” is not strictly an experiment as in science/research but any experiment, a random process of any event.
possible events in sample space…
e.g.
As in the events of A, B, C, and D in a sample space of the experiment, the possible events are A, B, C, or D.
We can also create a combo event say, X=A/B or Y=C/D.
Therefore, the possible events can be the events or events based on the combo of the outcomes (e.g. A/B , C/D)
What is the sample space of this experiment;
Let’s say event A has 4000 people, B has 3000 people, C has 2000, and D has 100.
e.g.
A sample space of this experiment is the set of all the possible outcomes-events A,B, C, and D.
What are probabilities;
probabilities are the likelihood of events or simply stated as the probabilities of events.
e.g.
the probability of X is 0 and it is written as “P(X=0) =” or the probability of X is 0 or 1 and it is written as “P(X=0 or 1) =”
Define a random variable for this experiment;
The random variable X is 0 if lands in A, 1 if lands in B, 2 if C, and 3 is D.
The random variable takes these four possible values.
Or
Random variable Q is 0 if the drone lands in A or B, P if the drone lands in C or D.
If we define random variable, we can go beyond the possible outcomes) or just outcomes.
What is a conditional probability;
For two random variables X and Y, X=0 if lands in A, =1 if lands in B, =2 if lands in C, and =3 if lands in D.
And Y=0 if inland or Y=1 if coastal.
The CP is the probability of an event (Y) given that another event (X) has occurred. It is the combine event of X and Y such that X happens then Y.
Name three discrete distributions
Bernoulli: Parameter pi. Values of random variable: Success (1) and Failure (0).
Binomial: parameters pi and n. Values of random variable: Number of success in n number of trials.
Categorical: parameters => one pi per category. Values of random variable: categories.
What is the r/s of the likelihood and the prior distribution?
They are not related.
A prior distribution with a spike on zero, is a typical model of…
The null hypothesis.
If the BF01 is 0.001, what does this mean regarding the null hypothesis?
The data is much more likely under the model of the H0 than under the model of the H1.
The BF10 comparing the H1 and the H0 is 0.05, meaning that…
The data is more likely under the H0 than under the H1.
In a normal distribution where is the value most probable?
The central values of the distribution.
The probability of the data under the H1 is 0.002 and that of the H0 is 0.0002. What is the value of the BF10?
a. 10.
b. 0.001.
c. 0.0001.
d. 1.
What is the true statement regarding the sampling distribution in relation to the H0 and the H1, respectively?
There is one sampling distribution in the model of the null and infinite number of sampling distributions in the model of the alternative.
If the BF10 is 125, what is the decision to make regarding the H0?
Decisions are not made in the Bayesian approach.
What is the product of the prior probability and the likelihood proportional to?
The posterior distribution.
What effect size is used in the Bayesian alternative to the t test?
Difference between means in a population.
In a study, the BF10 comparing an H1 to a H0 is 0.5. What is the correct statement?
The data is 2x more likely under the H0 than under the H1.
