PROBABILITY

• Probability


  Central to inferential statistics because we are basing a conclusion about a population on data collected from a sample

  
• Confirmation bias


  Our usually unintentional tendency to pay attention to evidence that confirms what we already believe and to ignore evidence that would disconfirm our beliefs
• Illusory correlation


  The phenomenon of believing one sees an association between variables when no such association exists
• Confirmation bias and illusory correlation


  Play a role in conspiracy theories
• How conspiracy theories develop

  1. Illusory correlation (belief that there is an association where none exists)

  2. Confirmation bias (increased attention to evidence that confirms what we already believe, combined with a failure to notice evidence that contradicts our beliefs)
• Illusory correlation and confirmation bias explain why developing the habit of statistical reasoning can help save us from ourselves
• Personal probability


  The likelihood of an event occurring based on an individual's opinion or judgment; also called subjective probability
• Probability


  The likelihood that a particular outcome will occur out of all possible outcomes
• Expected relative-frequency probability


  The likelihood of an event occurring based on the actual outcome of many, many trials

  
• Expected relative-frequency probability


  • When flipping a coin, the expected relative-frequency probability of heads, in the long run, is 0.50

  
• Trial


  Each occasion that a given procedure is carried out
• Outcome


  The result of a trial
• Success


  The outcome for which we're trying to determine the probability
• Determining probabilities


  Conduct many trials, record the outcomes, and determine the proportion of successes
• Probability


  The proportion that we expect to see in the long run
• Proportion

  The number of successes divided by the number of trials
• The proportion might not reflect the underlying probability

  
• Percentage


  Probability or proportion multiplied by 100
• Independence


  The outcome of each trial must not depend in any way on the outcome of previous trials
• In research, each participant must be independent of every other participant, or our sample might be biased