Advanced Experimental Design

About this quiz

What this quiz asks

1. In a controlled lab experiment, you observe 40 successful outcomes out of 160 total trials. Calculate the success ratio (R) as a decimal to identify the baseline for your Causal Inference Framework analysis.
2. Given a treatment effect size of δ = 0.8 and a standard error of σ = 0.2, calculate the Z-score (Z = δ / σ) to determine if the result is significant within your Causal Inference Framework.
3. In a study using a Causal Inference Framework, the potential outcomes Y(1) and Y(0) are modeled as Y(1) = 15 and Y(0) = 10. Calculate the Average Treatment Effect (ATE = E[Y(1) - Y(0)]).
4. Given a propensity score weight w = 1/P(T=1|X) where P = 0.25, calculate the weight w required to adjust for selection bias in your Causal Inference Framework.
5. In a clinical trial with a significance level (α) of 0.05, a standard deviation (σ) of 10, and a sample size (n) of 25, what is the standard error of the mean (SEM)?
6. If a researcher requires a power (1-β) of 0.80 for a study with an effect size (Cohen's d) of 0.5, and the calculated sample size per group is 64, what is the total sample size (N) for a two-group design?
7. A study detects an effect size of 0.8 with a sample size of 20. If the researcher increases the sample size to 80, by what factor does the standard error of the mean decrease?
8. A power analysis calculation requires finding the non-centrality parameter (δ) where δ = d * √n. Given Cohen's d = 0.4 and n = 100, what is the value of δ?
9. In a clinical trial, the ratio of control subjects to experimental subjects is 3:5. If the total sample size is 1200 participants, how many experimental subjects are included?
10. A chemical concentration in a solution is scaled by a factor of 1.5. If the initial molarity was 0.4 M, what is the new molarity?
11. In a multi-stage experiment, the ratio of signal to noise is 4:1. If the noise level is reduced by 50%, what is the new signal-to-noise ratio?
12. An experiment requires a dilution ratio of 1:100. If you have 5 mL of concentrated solute, how much solvent is required to achieve this ratio?
13. In a Bayesian hypothesis test comparing two experimental models, the prior odds for Model A over Model B are 2:1. The Bayes Factor (BF) derived from new experimental data is 4. Calculate the posterior odds for Model A.
14. A laboratory test has a prior probability of success of 0.2. After observing data that yields a likelihood ratio of 10, what is the new posterior probability of success?
15. In a clinical trial, the null hypothesis H₀ has a prior belief of 0.9. If a test results in a Bayes Factor BF₀₁ = 0.1 (favoring the alternative), what is the posterior probability of the null hypothesis?
16. Given a Bayesian model where the marginal likelihood of the data under model H₀ is 0.05 and under H₁ is 0.20, calculate the Bayes Factor BF₁₀ and the evidence level for H₁.
17. In a 2x2 factorial experimental design, you are measuring the response variable Y based on two binary factors (A and B). If the main effect of factor A is 10 units and the interaction effect (A×B) is 4 units, calculate the difference in response between the two levels of factor A when factor B is at its high level (level 1).
18. A researcher conducts a 3-factor experiment (A, B, C) where each factor has 2 levels. How many distinct treatment combinations are required for a full factorial design, and if the experiment requires 3 replicates per combination, what is the total number of experimental runs?
19. In a fractional factorial design 2^(3-1), you define the generator as C = AB. If you have the following data for the main effects: A=5, B=3, and the interaction AB=2, what is the aliased effect of factor C in this design?
20. Given a response surface model Y = β₀ + β₁X₁ + β₂X₂ + β₁₂X₁X₂, where β₀=10, β₁=2, β₂=3, and β₁₂=1. Calculate the predicted response Y when X₁ = 2 and X₂ = -1.
21. In a controlled laboratory experiment, you observe a systematic bias in sensor readings where the raw output R is related to the true value T by R = 1.05T + 0.2. To mitigate this bias, calculate the corrected true value T for a raw reading R = 10.7 units.
22. To mitigate selection bias in a population sample, you must apply a weighting factor. If a subgroup represents 20% of the population but 40% of your sample, what is the weight w required for each member of this subgroup to restore representativeness?
23. In a multivariate experimental design, you calculate a sensitivity index S = (μ₁ - μ₂) / σ. If the difference between means is 5 and the pooled standard deviation σ is 2, what is the S value, and if you require S > 3 for significance, is this design biased toward Type II error?
24. A system exhibits a cascading bias where error E accumulates as E_n = E_0 * (1.1)^n. If E_0 = 10 and n = 3 steps, what is the total error E_3, and which of the following values are equivalent to the error magnitude?

Answer choices and explanations are shown when you take the quiz.

Topics

Quizzes on Remee

Remee quizzes come in six formats — including image questions, matching, drag-and-drop and branching — and can be played live with up to 35 people at once, which makes them work as easily in a classroom as they do on your own.