Topcis

  1. Designing Studies
    • A sample survey selects a sample from the population of which we desire information.
    • A census collects data from every individual in the population
    • Bias is when the results consistently underestimate or overestimate the value you want to know
      • Convenience samples, in which individuals who are easiest to reach are chosen, is one cause of bias
      • Volunary response samples, in which individuals chose weather to be in the sample, also lead to bias
    • Random Sampling avoids bias by using a chance process to select the sample
      • A simple random sample (SRS) is when every individual has an equal chance of being selected
    • A stratified random sample is when the population is divided into strata
      • The strata are similar within, different between
    • A cluster sample divides the population into clusters
      • The clusters are different within, similar between
    • Even with random sampling, bias can still occur
      • Undercoverage happens when some members of the population can't be choosen
      • Nonresponse happens when people can't be contacted or refuse to answer
      • Response bias can occur when people give false answers
      • Wording of a question can effect a persons answer
  2. Experiments
    • Observational studies gather data on individuals as they are. Experiments activley do something in order to measure the response to those changes
    • Variables are confounded when their effects on a response variable can't be distinguished from each other
      • If you are testing two different studying techniques but don't assign a constant time limit, the varying lengths people spent studying could interfear with what is being measured
    • In experiments, one or more treatments are applied to experimental units (or subjects if they are human)
    • The basic principles for experimental design are
      • Comparison: Use a design that compares two or more treatments
      • Random assignment: Use chance to assign experimental units to treatments to create roughly equivalent groups
      • Control: Keep as many other variables as possible the same for all groups (to avoid confounding)
      • Replication: Impose each treatment on enough experimental units so the effects of the treatments can be distinguished from chance differences
    • A completely randomized design has all of the experimental units assigned to treatments by chance
      • Groups are usually not the same size if truely random
    • Some experiments give a pacebo (fake treatment) to a control group to help prevent confounding through the placebo effect (people think they are better since they expect the treatment to work)
    • Some experiments are double-blind in which neither subjects nor those interacting with them know which treatment the subject is receiving
    • The results are statistically significant if the difference between responses is large enough to not be due to chance
    • A randomized block design forms groups (blocks) that are similar within but different between. The experiment is then carried within each block

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randInt(min, max, trials) generates random integers in the range [min, max]

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  1. A polling team wants to gather data on peoples voting habits in different counties within St. Louis. To save time, what sampling method should be used?
    • A) Simple random sample
    • B) Convenience sample
    • C) Stratified random sample
    • D) Cluster sample
  2. An experiment is designed to determine if a new medication prevents migranes. A sample of 25 subjects was randomly selected from a population of 50. The experiment was double blind and there were no confounding variables. What principle of experiment design wasn't followed?
    • A) Comparison
    • B) Random assignment
    • C) Control
    • D) Replication
  3. A survey was sent to a household, but the families five year old managed to find it and put in false responses. What form of bias could this create?
    • A) Undercoverage
    • B) Response bias
    • C) Nonresponse
    • D) Wording of a question
  4. In order to successfully destory the Death Star and save the galaxy, you must avoid the turrets in order to reach the surface (60% chance of success), navigate your ship through the narrow corridors inside (40% chance of success), and then fire a torpedo at the stations core (80% chance of success). Design a simulation on your calculate to estimate the probability of successfuly destroying the Death Star.
  5. The forcast for the following day states that there is a 60% chance of rain. If it rains, there is a 20% chance of the temperature being low enough to snow. Weather or not it rains or snows, there is also a 15% chance of a volcano erupting. If it only rains, your crops will grow. If there is snow and/or the volcano erupts, your crops will not grow. Design a simulation to determine the probability that your crops will grow.