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Lecture 6

Lecture 6 - Random Sampling Probability - October 25.docx

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Kristie Dukewich

October 25, 2012. Lecture 6 - Random Sampling & Probability (Binomial Distribution) Why Probability?  Avoid errors and bias in everyday life  Never sure we’re right o Allows us to see if we’re probably right  Rely on it for statistics Categories of Statistical Tools  Descriptive Statistics o Tools we use to describe our data in our study o E.g., frequencies, z-scores, mean, standard deviation, correlation, regression o Chapters 2-7  Inferential Statistics o Tools we use to help us make judgments about the population based on what we found in our study o E.g., t-test o Chapters 8-14+  8-10, 12 are foundations for understanding  13-14+ are commonly used statistical tests Ways to Use Inferential Statistics  To test hypotheses o Use sample to infer whether an effect exists in the population o People are prejudiced against atheists because they don’t trust them  To estimate population parameters o Use sample to infer magnitude of characteristics in the population o Ex: what percent of people in Canada identify as atheists  Random Sample o Everyone in the population has an equal chance of being in the study  Random Assignment o Everyone in the experiment has an equal chance of being in each of the experimental conditions Canadian Long-Form Census  Optional “because some Canadians found the mandatory process coercive and the detailed questions intrusive”  Government programs/businesses/city planners/transit… no longer have accurate representative sample of Canadians Random Sampling  Define population o 120 Hershey Kisses o What’s the distribution of pink, silver, red?  Sampling WITHOUT replacement o What we’re using in most experiments o Each participant has one chance to participate  Sample WITH replacement o What we use to build sampling distributions What’s the probability I’ll randomly select you?  If N = 500 o 1/500 = .0020 OR .20%  Boundaries o 1.0000 certain to occur o 0.0000 certain NOT to occur  Four decimal places so can convert to % with two decimal places What you already know about probability  Area under the curve! o With normally distributed, continuous variables  Ex: What’s the probability of someone speaking English 60% or more of the time that day? o Step 1: Convert to z-score o Step 2: Place score on curve o Step 3: Answer is column C o Can only use this method with continuous variables Approaches to probability  A priori o How likely will this happen? o Before collecting data o Deduce from reason  A posteriori o How often did this happen? o Collect data (empirical) o As gather more data, comes close to a priori levels How man RED kisses?  A posteriori o p(A) = number of times A has occurred/total number of possible events  p(A) = 3/12 = 0.25 Distinguishing Key Terms  Mutually Exclusive o Events cannot occur together o E.g., being dead and being alive are mutually exclusive, etc.  Exhaustive o All possible events are included o E.g. world religions by percentage, 6 sides of a die  Independent o If one happens, it has no effect on if other happens; events are un-correlated; no predictive c
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