Intro to Randomness& Probability
What is a random variable?
A variable whose numeric value depends on chance.
When it comes to the mean, standard deviation, proportion, and correlation, what are the symbols for statistic and parameter?
Name Statistic Parameter
Mean ȳ μ
Std. Dev s σ
Proportion p̂ p
Correlation r ρ
What is the difference between observational study and an experiment?
Observational study: do not assign treatments. Researchers play a passive role, simply observing experimental units. They can show association but NOT causation.
Experiments: assign treatments and control the experimental conditions. Researchers play a active role. Experiments can show causation.
What equation would you use to standardize variables on different scales and compare z-scores?
z = (y-ȳ)/s
What is placebo effect?
Giving a person a treatment can affect the response regardless if treatment has an effect.
What is the Law of Large Numbers?
For repeated trials of an event the long run frequency of the event and the empirical probability gets closer to the theoretical probability of the outcome.
What are the issues of taking a census of a population?
- populations are typically very large
- too time consuming to work with
- too expensive to work with
- populations may be ever-changing
What is the difference between a retrospective and prospective study?
Retrospective study: data is gathered on past behavior, looking for relationships, etc.
Prospective study: record data as events unfolds, look for relationships on current/future behavior.
To find area values for any given observation from a normal distribution, what equation would you use to calculate a z-score?
z = (y-μ)/σ
What is blinding?
EUs is not aware of which treatment they got
What is the simple theoretical probability model?
If all outcomes of a random event are equally likely, then the probability of a collection of outcomes is:
probability = # of outcomes in collection of interest/total # of outcomes possible
What are the three main ideas of sampling?
1. Select a sample from the population
2. The sample should be selected randomly
3. The sample size n matters. Larger samples do provide more information.
What is difference between random selection and random assignment in an experiment?
Random selection: randomly selecting units from the population for the study.
Random assignment: randomly assigning the units to the treatment groups. Important use of randomization.
What is the 68-95-99.7% rule?
i. 68% of observations are within +- 1 standard deviation of mean
ii. 95% of observations are within +- 2 standard deviations of mean
iii. 99.7% of observations are within +- 3 standard deviations of mean
What is double-blinding?
Both the researcher and EUs are blind to treatments administered.
What are the characteristics of a random event?
i. The outcome you get cannot be predicted perfectly every time.
ii. No short-term structure. Unpredictable/random from trial to trial.
iii. There is a long-term structure/pattern
What are the types of problems or bias that come with survey sampling?
Voluntary response sample, Convenience sample, Response Bias, Non-response Bias, Undercoverage, Wording of questions
What is the difference between replication and repeatability?
Replication: refers to having more than one EU per treatment.
Repeatability: repeating the entire experiment to see if you can obtain similar results to validate experiment.
What are the characteristics of a z-table?
- Rows contain the ones and tenths place
- Columns contain the hundredths place
- Total area under the curve is 1
- The values range from -3.46 to 3.46
How is notation represented?
N(μ,σ)
What are the types of interpretations of probability?
Subjective, Empirical, Theoretical
What are the different types of random sampling plans?
Simple Random Sample, Stratified Sample, Cluster Sampling, Multi-stage Sampling
What are the key components of experiments?Provide main ideas for the components.
- EU: who or what the experiment is performed on.
- Factors: variables we manipulate to see how the EUs respond. Need at least one factor to manipulate.
- Levels: specific values we choose for the factors. Need at least two levels for every factor.
- Treatment: combos of levels of the factors that we assign to EUs.
- Response variable: the EUs "response" to the treatment applied.
How do you find a value of an observation when given a percentile or area?
1. Find the closet percentile value inside z-table
2. Obtain corresponding z-score from the margins
3. Reverse standardization formula to: y= μ + zσ
Why was the normal distribution chosen?
Based on its shape, center, and spread.