Exam 3 Review Session PDF

Exam 3 Review Session Chapter 17 Frequentism ○ Observing outcomes and patterns if events are repeated over and over again. ○ Truths of probability Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. Random ○ Indivi...

Exam 3 Review Session Chapter 17 Frequentism ○ Observing outcomes and patterns if events are repeated over and over again. ○ Truths of probability Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. Random ○ Individual outcomes are uncertain but regular distribution of outcomes in a large number of repetitions Probability ○ A number between 0 and 1 ○ Describes the proportion of times the outcome would occur in a very long series of repetitions Long-term regularity of random behavior ○ 0 = never occurs, 1 = always occurs; 0.5 = happens half the time in a very long series of trials. Chapter 17 Myth of Short Run regularity ○ The idea of probability is that randomness is regular in the long run, not random in the short run. Long-term probability in the coin example Half heads/half tails- in the long run Myth of Law of Averages ○ Assumption that independent events are related and more likely to occur depending on each other Ex- gamblers ‘due’ for a win after 5 losses Law of large numbers ○ In large number of independent repetitions of a random phenomenon, averages or proportions are likely to become more stable as the number of trials increases The sums/counts are likely to become more variable The outcome of one trial does not change the probabilities for the outcomes of any other trials. The trials have no memory. Personal Probability ○ A number between 0 and 1 that expresses an individual's judgement of how likely a particular outcome is. Chapter 18 Probability Model ○All the possible outcomes for a random phenomenon. ○A statistical model for a random phenomenon that describes all the possible outcomes and says how to assign probabilities to any collection of outcomes. Rules of Probability (BE ABLE TO APPLY THEM) ○Rule A Any probability is a number between 0 and 1. ○Rule B All possible outcomes must sum to 1. ○Rule C The probability that an event does not occur is 1 minus the probability that the even does occur. ○Rule D If two events have no outcomes in common, the probability that Chapter 18 Sampling Distribution ○What values the statistic takes in repeated samples from the sample population. ○Assigns probabilities to the values the statistic can take. Density Curve- when it should be used ○Density curve - graphical representation of a numerical distribution of a histogram. (This should be review from last exam) ○Because there are usually many possible values, sampling distributions are often described by a density curve such as Normal curve. Chapter 18 Probability of events ○ Add the probabilities of the outcomes that make up the event. Odds of events ○ The odds of “Y to Z” that an event occurs corresponds to a probability of ○ Youse lose Y times, and win Z times. Odds of an event vs. probability of an event ○ The probability that an event will occur is the fraction of time you expect to see that event in many trials, will always range from 0 to 1. ○ The odds are defined as the probability that the event will occur divided by the probability that the event will not occur. Finding Probabilities Examples What is the probability that Taylor Swift and Travis Kelce ARE dating? ○ Probability that they are NOT dating = 0.20 Which Probability Rule does this follow? What is the probability that TAMU or Mississippi wins the SEC West title? ○ Alabama =.30 ○ Mississippi =.25 ○ LSU =.20 ○ TAMU =.15 ○ Auburn =.10 Which Probability rule does this follow? Chapter 19 Simulation ○ Allows us to imitate repeated trials of chance events. ○ Using random digits from a table or from computer software to imitate chance behavior. When would we want to use simulation? ○ For Convenience!! ○ Easier than doing math yourself! (because be honest who likes doing math?) ○ Faster than actually running many repetitions in the real world. ○ Gives good estimates of probabilities. 3 broad steps of doing simulation ○ 1. Give a probability model ○ 2. Assign digits to represent outcomes. ○ 3. Simulate many repetitions. Chapter 19 Assumptions of independence ○ Knowing the outcomes of phenomenon does not change the probabilities of outcome of another. Each trial does not have a memory from one trial to another trial. ○ One of the most basic assumptions of statistics. ○ Approaches 1- Apply the definition Coin toss- probability of a heads landing after a heads should be 0.5 2- Correlation Should be = 0 ○ Limited to linear relationships 3- Visualization Scatterplots should show no patterns 4- Know your study thoroughly (most commonly used by researchers) Chapter 19 Simple random phenomena ○ Several independent trials with the same possible outcomes and probabilities for each trial. Tree diagrams ○ A probability model in graphical form that shows stages and the possible outcomes and probabilities at each stage. ○ Helpful by giving the probability model in graphical form. More complex random phenomenon ○ To simulate more complicated random phenomena, string together simulations of each stage. May require varying numbers of trials or different probabilities at each stage or stages that are not independent. Chapter 20 Expected Values ○ an average of the possible outcomes ○ outcomes with higher probability count more How to calculate expected values? ○ Determine all the possible outcomes ○ Determine the probability each outcome ○ Multiply them together, respectively ○ Add all the products Can be used in and out of gambling settings Chapter 20 How does the law of large numbers apply to expected values? ○ The mean of the observed outcomes approaches the expected value ○ Probability- the proportion of each possible outcome will be close to its probability ○ Average outcome- will be close to the expected value ○ Together the long-run regularity of chance events “Pari-mutuel” system ○ Payouts depend on amount wagered ○ No fixed amounts → can’t calculate expected value ○ Constants- The state keeps half the money bet Less risky for the state ○ Ex- casinos Chapter 7 IRB ○ Stands for Institutional Review Board. ○ Reviews all studies in advance to protect participants from possible harm. ○ Questions surrounding their workload and their effectiveness in the past few few years. Informed Consent ○ For each psychology research participants must be informed about the nature of the study and any physical or psychological harm that it may bring. ○ Participants consent via their signature and this can be retracted at any time during or after the study. ○ Children & prison inmates- CANNOT Consent Chapter 7 Confidentiality ○ All individual data from a study must be kept private. ○ Only statistical summaries for groups of subjects may be made public. Anonymity ○ Individual’s names are unknown, impossible to identify which participant produced the data. ○ Prevents follow-ups Clinical Trials Ethics ○ Experiments that study the effectiveness of medical treatments on actual patients Ethical problems- Tuskegee Study ○ Produce benefits- most go to future patients ○ Balance future benefits against present risks Placebo Ethics ○ Placebo- gives a true baseline for the effectiveness of the new drug ○ Ethical except for life-threatening conditions, or if a better drug already exists Any Questions?