Statistics
Terms
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- What are two assumptions of the Bayesian paradigm?
- 1. defines probability as a selective belief 2. looks at parameters as random quantities because we can never know them for certain
- What is the formula for Bayes rule?
- P(A1|B) =P(B|A1)xP(A1)/ sum of P(B|Ai)xP(Ai)
- How do we calculate predictive probability?
- Sum the products of all of the model probabilities x posterior
- Do frequentist methods allow for the calculation of predictive probability?
- No!
- Controlled experiments
- experimenters get to decide who receives treatment and who does not
- Randomization
- Control group and treatment chosen at random
- Double-blind
- Neither subjects nor the scientists know who is assigned to which group until after the data are collected
- Confounding
- Occurs when the control and treatment group are different with respect to other factors besides the response A confounder must be 1. a factor that differs between the tx. and control groups 2. associated with the response
- What eliminates the impact of confounders?
- Randomization
- Observational Study
- Researchers do NOT get to decide who is in each group
- What is Simpson\'s Paradox?
- Simpson\'s paradox is the apparent reversal that happens when the effect of the confounder if so big that it actually reverses the true relationship between two variables.
- What are the three measure of central tendency?
- Mean Median Mode
- Mean
- the average of the data
- Median
- the middle value of n observations, if n is odd if n is even, average the 2 middle numbers
- Mode
- the value that occurs most frequently in the sample
- What is an outlier?
- an incorrect or unrepresentative observation that is very different from others in the sample
- What effect can an outlier have?
- A single outlier can have a BIG impact on the mean, but little impact on the median
- What is the range?
- the largest observation minus the smallest
- Is range influenced by outliers?
- Yes, range is strongly influenced by outliers
- What is the interquartile range?
- 1. 75th percentile - 25th percentile
- How to find the 25th percentile?
- A number, x, such that 25% of the sample is less than or equal to x and at least 75% of the sample is greater than or equal to x
- 75th percentile
- The number y such that at least 75% of the sample is less than y and 25% is greater than or equal to y
- Are percentiles and IQs affected by outliers?
- No, they are not strongly influenced
- Normal distribution is also known as...
- Gaussian distribution
- A standard normal distribution has sd (sigma)...
- 1
- Why can we use the standard normal distribution to calculate other normal distributions?
- Because in a normal distribution with any mean and sd, the same percentage lies within x standard deviations of the mean
- What is a p-value?
- A p-value is the probability of observing data that is as or more supportive of the alternative hypothesis when the null hypothesis is correct.
- What is a confidence interval?
- A CI is an interval such that C% of the time, the population value will be greater than L but less than U