PSYC 2019H Lecture 3, Winter 2022 PDF

PSYC 2019H – Lecture 3 Sampling and Probability Samples and Popula.ons Probability Inferen.al Sta.s.cs Type I and II Errors  Samples and Popula.ons “The popula?on includes all possible observa.ons about which we would like to POPULATION know something (N...

PSYC 2019H – Lecture 3 Sampling and Probability Samples and Popula.ons Probability Inferen.al Sta.s.cs Type I and II Errors  Samples and Popula.ons “The popula?on includes all possible observa.ons about which we would like to POPULATION know something (N & H, 2021, p. 3).” A sample is a set of observa.ons drawn Sample from the popula.on of interest (N & H, 2021, p. 3).”  Samples and Popula.ons Random sample – “…is one in which every member of the popula.on has an equal chance of being selected into the study” (Nolan & Goedert, 2024, p. 122). Convenience sample – “…is one that uses par.cipants who are already available” (Nolan & Goedert, 2024, p. 122).  Samples and Popula.ons Convenience sample – Major disadvantage: Lower _____________ “…. refers to the researcher’s ability to apply Wndings from one sample or in one context to other samples or contexts; also called external validity (N & H, 2021, p. 114).” WEIRD samples: Western, Educated, Industrialized, Rich and Democra.c  Samples and Popula.ons Convenience sample – What can we do about threats to generalizability? – Replica?on “…refers to the duplica.on of scien.Wc results, ideally in a di_erent context or with a sample that has di_erent characteris.cs (N & H, 2021, p. 114).” – Constraints on generality (COG) statements “… a statement of the target popula.on to which the study’s results should generalize (N & H, 2021, p. 117).”  Probability Psychology, and other sciences, use probabilis.c reasoning  Probability Some Enemies of Reason! Anecdotal evidence ConWrma.on Bias – “…our usually uninten.onal tendency to pay acen.on to evidence that conWrms what we already believe and to ignore evidence that would disconWrm our beliefs” (Nolan & Goedert, 2024, p. 128). Illusory Correla.on – “…the phenomenon of believing one sees an associa.on between variables when no such associa.on exists” (Nolan & Goedert, 2024, p. 128).  Probability Personal Probability “…is a person’s own judgment about the likelihood that an event will occur” (Nolan & Goedert, 2024, p. 130). Probability “…is the likelihood that a par.cular outcome – out of all possible outcomes -- will occur” (Nolan & Goedert, 2024, p. 130). Expected Rela?ve-Frequency Probability “…the likelihood of an event occurring, based on the actual outcome of many, many trials” (Nolan & Goedert, 2024, p. 130).  Probability Example (Howell, 2017): New bag of M&Ms You want to know what is the probability of grabbing a red M&M at random 1. You reach in and grab one M&M, no.ng it’s colour (____________) 2. You then put it back (________________________) You then repeat steps 1 and 2 many many.mes (_________) and Wnd the following percentage of red M&Ms (______________): ____  Calcula.ng Probability Step 1 Determine the total number of trials. Step 2 Determine the number of these trials that are successful outcomes. Step 3 Divide the number of successful outcomes by the number of trials. 11  Probability, Propor.on, and Percentage The terms probability, propor.on, and percentage are oien confused. – ______________ is the propor.on that we expect to Wnd in the long run. – _______________ is the number of successes divided by the number of trials. – ______________ is simply probability or propor.on mul.plied by 100. Sta.s.cal probability requires that the individual trials be _______________. 12 Inferen.al Sta.s.cs POPULATION Inferen.al Sample Sta.s.cs POPULATION POPULATION Given Drug X Given Placebo Sample Sample  Developing Hypotheses Null hypothesis – Statement that usually postulates that ___________________ between popula.ons or that the di_erence is in a direc.on opposite to that an.cipated by the researcher. Research (alterna?ve) hypothesis – Statement that usually postulates ________________ a di_erence in a certain direc.on between popula.ons Groups – Control group Does not receive the treatment – Experimental group 15 Does receive the treatment  Making a Decision About Hypotheses Reject the null hypothesis. – When the data suggest that there is a mean di_erence, we reject the idea that there is no mean di_erence. – Conclude that _____________ is found Fail to reject the null hypothesis. – We fail to reject the null hypothesis; no mean di_erence – Conclude that _____________ found 16  Hypothesis Tes.ng: Hypotheses and Decisions Hypothesis Decision Null hypothesis No change or Fail to reject the null hypothesis difference (if research hypothesis is not supported) Research Change or Reject the null hypothesis (if hypothesis difference research hypothesis is supported) 17 Type I and Type II Errors: Sta.s.cal Inferences Can Be Wrong Type I error – Rejec.ng the null hypothesis when it is true Say that ______________________________ Type II error – Failing to reject the null hypothesis when it is false Say that ________________________________ 18  Inferen.al Sta.s.cs Type I Error “…involves rejec.ng the null hypothesis when the null hypothesis is correct (N & H, 2021, p. 127).”  Inferen.al Sta.s.cs Type II Error “…involves failing to reject the null hypothesis when the null hypothesis is false (N & H, 2021, p. 128).”  State of the World Null Hypothesis is Null Hypothesis Experimenter’s TRUE FALSE (Drug = Placebo) (Drug > Placebo) Decision Reject Null Hypothesis (Drug Group statistically significantly better than Placebo Group) Fail to Reject Null Hypothesis (Drug Group not statistically significantly better than Placebo Group)  Data Ethics: The Shocking Prevalence of Type I Errors Posi.ve outcomes are more likely to be reported than null results. Why does this happen? 22  IDENTIFYING TYPES OF SAMPLES AND PROBLEMS WITH GENERALIZING Direc.ons: For each example, iden.fy which sampling method was used (random or convenience). Which popula.on did the researcher likely have in mind? Then, think about how well the sample might represent the popula.on. Can you iden.fy reasons why the sample might not be a good representa.on of the popula.on? 23