October 25, 2012.
Lecture 6 - Random Sampling & Probability (Binomial Distribution)
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
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
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
o Everyone in the population has an equal chance of being in the study
o Everyone in the experiment has an equal chance of being in each of the
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
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%
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
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
o How likely will this happen?
o Before collecting data
o Deduce from reason
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?
o p(A) = number of times A has occurred/total number of possible events
p(A) = 3/12 = 0.25
Distinguishing Key Terms
o Events cannot occur together
o E.g., being dead and being alive are mutually exclusive, etc.
o All possible events are included
o E.g. world religions by percentage, 6 sides of a die
o If one happens, it has no effect on if other happens; events are un-correlated; no