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These are 10 questions from the practice exam from my free Coursera Course "Improving Your Statistical Inferences". If you had a 100% score, there's no need to do this free course. If you didn't score too well, no worries! We can all improve our statistical inferences - check out 21 free lectures, and 10 assignments, here: https://www.coursera.org/learn/statistical-inferences
After finding a single statistically significant p-value we can conclude that _____, but it would be incorrect to conclude that ______.
Answer
The data is surprising if we assume there is effect; the null hypothesis is likely to be false.
The null hypothesis is likely to be false; the alternative hypothesis is true.
The data favors the the alternative hypothesis; the null hypothesis is likely to be false.
The data is surprising assuming the alternative hypothesis is true; there is a true effect.
Question 2
Question
You analyze your data in two ways. With Frequentist statistics you find an mean effect size of 3, with a 95% confidence interval of 1 to 5. With Bayesian methods you find a mean of 2.75, with a 95% credible interval of 1.5 to 4. Which conclusions can you draw?
Answer
Both intervals give you estimates for the most probable values of the true mean.
The confidence interval gives you the values you believe are most likely based only on the data, the credible interval gives you the most probable values given the data and your prior.
Both procedures give intervals which contain the true value 95% of the time, but credible intervals are more accurate.
The confidence interval contains the true value 95% of the time, the credible interval contains the 95% most plausible values.
Question 3
Question
What are the benefits of performing a study with a larger sample size, compared to doing the same study with a smaller sample size?
Answer
Lower Type 1 error rates, lower Type II error rates, same accuracy of estimates.
Lower Type 1 error rates, lower Type II error rates, higher accuracy of estimates.
Same Type 1 error rates, lower Type II error rates, higher accuracy of estimates.
Same Type 1 error rates, lower Type II error rates, same accuracy of estimates.
Question 4
Question
You performed a p-curve analysis and found a skewed distribution of p-values with many more small p-values (around 0.01) than high p-values (around 0.04). What does this mean?
Answer
This distribution is typical for when there is no true effect.
This distribution is typical for when there is a true effect.
This distribution suggests the presence of p-hacking.
This distribution indicates there is publication bias.
Question 5
Question
How do we know there is publication bias in favor of significant results? Why is it unreasonable to expect articles with 4 experiments that aim for 80% power to exclusively show significant results?
Answer
We can’t be sure there is publication bias; because of the Type 1 error rate we will eventually get a non-significant result.
It’s impossible that 91.5% of findings in psychology confirm the hypothesis; the type 1 error rate makes that unlikely in the long run.
Researchers have admitted to not submitting all their results for publication; it is impossible that all hypotheses a researcher examines are true.
It’s unlikely that the observed drop in the p-value distribution for p-values higher than 0.05 in the published literature occurs by chance; If all four studies examine a true effect the probability of only significant results is power*power*power*power.
Question 6
Question
You predict that your intervention will significantly increase participants' performance on a test, this is an example of _____. You find a significant result and conclude your theory is true, this is an example of ______.
Answer
A progressive research line; affirming the consequent
A falsifiable prediction; denying the consequent
A degenerative research line; denying the consequent
A falsifiable prediction; affirming the consequent
Question 7
Question
A researcher reports two significant findings testing the same hypothesis, using an alpha of 5%. The researcher predicted one finding before doing the study, but the other finding was observed during exploratory analyses where many tests were performed. Which statement is correct?
Answer
Because the researcher performed two analyses, the alpha level should be divided by two for each test to bring the overall error rate back to 5%.
Because the second hypothesis was not predicted, the overall error rate is inflated by an unknown amount.
The predicted finding is confirmatory, the unexpected finding is exploratory. The error rate for each finding is maintained at 5%.
The exploratory finding has increased the Type 1 error rate to 10%.
Question 8
Question
We compare model A (the effect is 0) to model B (the effect is 1) and find a Bayes Factor of 10 in favor of model A which means _____.
Answer
The prior probability of model A is 10 times larger than that of model B
Model A is 10 times more likely to be true than model B
The data favor model A 10 times more than model B, given the prior
We can have a strong personal belief in the absence of a true effect.
Question 9
Question
You performed 6 studies, only 4 of them had a significant result. The likelihood ratio of this happening assuming H0 (no effect) is true versus assuming H1 (a true effect) is true tells you ______. If you assume the study had around 80% power to detect a true effect, this likelihood ratio will probably show that _____.
Answer
The likelihood of H0 being true, and the likelihood of H1 being true; it is not unlikely to have some significant effects, even if H0 is false
The likelihood of the data, assuming H0 is true; it is unlikely to get 4 significant results out of 6
How much more or less likely H0 is, compared to H1; it is likely to have some non-significant effects, even if H1 is true
If 4 significant studies out of 6 is likely to happen if H0 is true; it is unlikely to get 4 significant results out of 6, assuming H0 is false
Question 10
Question
An example of a standardized effect size is ______; these should always be reported because the are useful for _____.
Answer
Minutes; a-priori power analysis
Cohen's d; comparing the effect size across studies using different measures
Meters; calculating less biased effect size estimates