POLS285 Test 2 Flashcards
What is the definition of probability?
Probability of an event occuring is the proportion of its occurrences over an infinite number of trials.
What is a random trial and random outcome?
-An action that produces a random outcome of interest (e.g, rolling a six-sided die).
-Random outcome: the result of a trial, e.g. rolling a one.
What is an event?
-A set of outcomes (could refer to any number of outcomes).
What are properties and rules of probability?
- All outcomes fall between 0 and 1.
-The sum of all possible outcomes (or the sample space) is always one.
-If event A and B are mutually exclivsive, the probability that either A or B occurs equals the probability that A occurs plus the probability that B occurs: P(A or B)=P (A) + P(B).
What is mutually exclusive?
-Probability of an action happening is mutual.
What is probability distribution and random variables?
-Random variable: Assigns a numeric value to each mutually exclusive event of a trial.
-Probability distribution: Identifies the possible events associated with a random variable along with their probabilities.
What are the properties of probability distribution?
1: Includes all possible events of a given random variable.
2:Identifies the probability of each event occuring.
3: Area under curve sums to 1.
What is the normal/Guassian distribution and what are its key properties?
-A probability distribution defined entirely by iys mean and standard deviation
-Key properties: Bell-shaped and Symmetrical.
-68-95-99 rule: 68% of observations within 1 standard deviation of the mean, 95% of observations within the second on e.
What is the significance of Gaussian distribution?
-Describes the distributions of some random variables in the natural and social worlds.
-But its real significance is its relationship with the central limit theorem.
-This relationship provides the foundation for inferential statistics,
and the subject of the next lecture.
What is statistical inference?
-Any descriptive or causal inference involves a target population: A group of units or cases we want to generalize to.
-But we’re usually stuck studying samples: a subset of population
units or cases selected for analysis and measurement.
-Statistical inference is the process of using information from samples to make probabilistic claims about target populations.
What is central limit theorem?
-Central limit theorem provides the mathmatical bridge to descriptive inference.
-States that if a random sample of n observations is drawn from a non-normal population, and if n is large enough, then the sampling distribution becomes approximately normal (bell shaped).
What does central limit theorum ask us to imagine and what is its relationship with sampling distribution?
- Have a target population (e.g. voting aged Canadians).
-Draw an infinite number of random samples from that population of the same size (or size n).
-Calculate the mean of a random variable for each sample e.g. Trudeaus mean thermometer score.
-Use those means to produce a sampling distribution or a distribution of the sample means.
What does the sampling distribution of central limit theorum look like and what is its central error?
- The means of the sampling distribution will be normally distributed.
- the mean of the sampling distribution will equal the true population mean μ.
- the standard deviation of the sampling distribution (or standard error) will equal the standard deviation of the variable divided by the square root of the sample size:
σ ̄y = σy√n
What are the different populations?
Target population: A group of units we want to generalize to.
Population parameter:
Sample statistics:
Census:
What is systematic sampling error?
-Affects the validity of our estimates.
-Occurs when sample statistics deviate from population parameters by chance.
-Key factors: sample size, population variance or heterogeneity.
-If non-systematic error is high, we say our estimates are unreliable
What does central limit implicate to statistical inference?
- The mean of any given sample is our best guess of μ
- The bigger the sample size, the more precise our estimate of μ/ We can see this in the denominator of the standard error:
σ ̄y = σy
√n - The more disperse the variable, the less precise our estimate of μ. We can see this in the numerator of the standard error:
σ ̄y = σy
√n
What is systematic sampling error?
-Systematic sampling error is different then non-systematic.
-Its when sample statistics deviate from population parameters BECAUSE OF BIASED sampling procedures.
-Sources of bias: coverage bias, non-response bias and non-probability or non-random sampling.
-If systematic error is present, our estimates are systematically too high or too low and we say our estimates are biased or invalid.
What is coverage bias?
-Caused by slippage between population and sampling frame.
Ex: Researcher samples from phone book. Phone book under-represents certain groups. Groups are less likely to be sampled as a result.
What is non-response bias?
-Caused by failure or refusal of certain subjects to participate in study.
-Ex: Pro-life students were less likely than pro-choice students to participate in a survey on attitudes toward abortion.
What are non-probability and non-random samples?
-Probability sample: all units of a population have some known non-zero probability of being sampled.
-Equal probability sample (what KW call a random sample): each unit has an equal chance of being sampled.
-Non-probability sample: Sample isn’t collected by ways suggested by probability theory. Convenience samples are an example.
What is relationship of systematic and non-systematic sampling errors with reliability and validity?
-The quality of our inferences depends upon on the (1) validity and (2) reliability of our sampling procedures.
