Probabilities and Research Statistics
Sampling a Population Interviewed 83 out of 616 (13.5%) initial victims Generalizability: Ability to apply findings from one sample or in one context to other samples or contexts (external validity)
Risks and Rewards of Sampling Almost everything worth studying requires a sample Risks 1. The sample might not represent the larger population 2. We might not know that the sample is misleading 3. We might reach inaccurate conclusions 4. We might make decisions based on this bad information First day of class Making soup
Risks and Rewards of Sampling Almost everything worth studying requires a sample Rewards 1. The sample represents the larger population 2. We increase our level of confidence in our own findings 3. We reach accurate conclusions at a very low cost 4. We remain open-minded because we know samples can mislead us 5. We make wiser decisions based on the available evidence
Types of Sampling Random Sampling Every member of the population has an equal chance of being selected into the study Very rare, still the ideal Convenience Sampling Uses participants who are readily available as opposed to Uses participants who are readily available, as opposed to randomly selecting participants from the entire population of interest.
Random Does Not Always Look Random Make a plan for the random numbers before you begin to use them. Example. Assigning to two conditions
Variations on Random Sampling Cluster sampling All of the clusters in a population are identified and a certain number of these clusters are selected randomly; everyone in the selected clusters would then be recruited to participate in the study. Stratified sampling Strata, usually levels of a nominal variable, are identified, and then a random sample of the same size is taken from each stratum
Convenience Sampling Volunteer sample Special kind of convenience sampling in which participants Special kind of convenience sampling in which participants actively choose to participate in a study (self-select).
Random Assignment Equal chance of being assigned to a condition Randomized Block Design Creates equivalent groups by matching the participants with regard to important characteristics and then using randomization only within blocks, or groups, of participants who are similar on one or more of these characteristics. Replication Refers to the duplication of scientific results, ideally in a different context or with a sample that has different characteristics.
Randomized Block Design
Neither Random Selection nor Random Assignment: Torture Survivors & PTSD Some things are still worth studying!
Random Assignment but Not Random Selection: Eyewitness Testimony
Random Selection but Not Random Assignment: Children s Literature
Coincidence and Probability 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. If it is raining, the grass is wet Raining Dry Grass Not Raining Wet Grass
Coincidence and Probability Illusory Correlation Believing one sees an association between two variables when Believing one sees an association between two variables when no such association exists
Groupthink The overconfident, biased decision making when a group of people confirm one another s beliefs rather than relying on objective evidence.
Probability Theory Subjective Probability An individual s opinion or judgment about the likelihood that an event will occur. Amos Tversky s 60% probability Expected Relative Frequency Probability Expected outcome if a trial were repeated many, many times Trial: Each occasion that a given procedure is carried out
Independence and Probability Example Flip your coin 9 times
Independence and Probability Gambler s Fallacy A type of biased thinking in which an individual believes a previous A type of biased thinking in which an individual believes a previous occurrence has an effect on an ensuing occurrence, when in fact the two are unrelated
Logic of Inferential Statistics Grandmothers Suggestions Eliminate exams entirely Allow only orphans to enroll in your classes Have students lie to families
Hypothesis Testing: New Terms Control Group Level of IV designed to match experimental group in all ways except the manipulation Experimental Group Level of IV that receives the treatment or intervention of interest in the experiment Null Hypothesis Statement that postulates there is no mean difference between populations or that the mean difference is in a direction opposite from that anticipated by the researcher Alternative (Researcher/Experimental) Hypothesis Statement that postulates there is a mean difference between populations (sometimes directional)
Hypothesis Testing: Decision Making
Errors Type I Error (Sins of Commission) Occurs when we reject the null hypothesis, but the null hypothesis is correct. Type II Error (Sins of Omission) O h f il t j t th ll h th i b t th ll Occurs when we fail to reject the null hypothesis, but the null hypothesis is false
Errors
Errors Example: Pregnancy Testing