Lecture 11: Bayesian Inference (Alt 3) Flashcards
(25 cards)
What is the primary goal of hypothesis testing in psychological research?
To explain variation in behavioural data, which can come from:
- systematic variation (e.g., due to manipulated or measured variables),
- random variation (e.g., due to unmeasured variables or chance),
- or a combination of both.
What does hypothesis testing aim to determine in an experimental context?
Whether observed effects are plausibly due to the experimental manipulation, or merely due to random noise.
What is the standard approach to hypothesis testing in psychology?
Null Hypothesis Significance Testing (NHST).
What does NHST assess?
The probability of obtaining the observed data (or more extreme data), assuming the null hypothesis (H₀) is true.
What is the p-value in NHST?
The probability of obtaining the observed data (or more extreme data), assuming the null hypothesis (H₀) is true.
What is the common decision threshold for rejecting H₀ in NHST?
p < .05.
On what logical foundation is NHST based?
Modus Tollens:
- frequentist probability theory
- logical reasoning from indirect inference
What logical limitation does NHST contain?
It assumes that a p-value < .05 implies H₀ is false, which is logically invalid.
For example:
- Under Modus Tollens the conclusion ALWAYS follows when the premises are true
- However this is not ALWAYS true or reflected in reality due to false alarms and misses etc.
What form of logical reasoning does NHST rely on, and why is it problematic?
NHST relies on modus tollens (If P, then Q; Not Q → Not P), which is not valid in probabilistic reasoning.
What key question does NHST fail to answer?
P(H₀|D), the probability that the null hypothesis is true given the data.
What probability does NHST provide instead of P(H₀|D)?
P(D|H₀), the probability of the data assuming the null hypothesis is true.
What is a common misinterpretation of a low p-value in NHST?
Treating a low p-value as evidence that the null is false, and thus wrongly accepting the alternative hypothesis (H₁).
Does NHST formally test the alternative hypothesis (H₁)?
No, the likelihood of the data under H₁ is not considered at all.
How does the HIV testing analogy illustrate a key Bayesian insight?
It shows that even highly accurate tests can yield misleading results in populations with low base rates of the condition, highlighting that base rates (prior probabilities) matter in interpreting evidence.
What flawed logic does the HIV testing analogy expose in NHST?
The flawed logic of assuming that p-values reflect the probability a hypothesis is true (e.g., false positive HIV test)
What is introduced as a solution to the limitations of NHST?
Bayesian inference.
What does Bayes’ Theorem calculate in Bayesian inference?
The posterior probability of a hypothesis given the data by combining prior beliefs (base rates) with the likelihood of the observed data under each hypothesis.
What does Bayesian analysis involve in the coin toss example?
It begins with prior probabilities, incorporates the data (coin toss outcomes), and updates prior probabilities in light of new evidence, producing posterior probabilities that directly answer the question: “How likely is each hypothesis given the data?”
What do Bayes Factors allow researchers to do?
- Compare hypotheses (H₀ vs. H₁),
- quantify relative support for each,
- provide graded evidence (e.g., anecdotal, moderate, strong),
- avoid binary decision rules and arbitrary cut-offs (like p < .05).
What are credible intervals in Bayesian inference?
A Bayesian alternative to confidence intervals that represent the range of parameter values most plausible given the data and reflect posterior belief, not hypothetical long-run frequency.
What flexibility does Bayesian inference offer researchers regarding alternative hypotheses?
It allows researchers to specify a range of possible alternative hypotheses, such as a distribution of effect sizes, rather than committing to a single precise value for the effect.
What form of subjectivity does Bayesian inference introduce?
Researchers must justify their chosen priors, which may differ across studies; these priors influence conclusions, making transparency and theoretical justification essential.
What is the consequence of subjectivity in Bayesian inference?
While it increases the transparency of assumptions, it also demands more care and responsibility from researchers.
Why has Bayesian inference only recently become practically viable in psychological research?
Due to advances in computational power and development of analytic tools and techniques.
