POLS1009 Lecture Notes - Lecture 7: Simple Random Sample, Sampling Bias, Pivot Table
L7 INFERENCE (AKA STATISTICS WITHOUT TEARS)
- Under methodology heading you need to explain why you recoded etc. Justify your literature. Find
some else who has done what you’ve done.
- DUE 4pm
INFERENCE
- Pivot tables are the most powerful features
- Make cross tabs
- Way to represent data
- Doggy tag, insert, pivot table, new tab, clock vote house, click gender (IDV),
- What is normal distribution?
- What is a sample (including confidence intervals)
Three Questions
- What is normal distribution?
- What is a sample (including confidence intervals)
What is the null hypothesis (and why do we care?)
Recall
- The research process involves identifying a problem and formulating a question and a hypothesis
- A hypothesis makes a statement about the direction of the relationship between two concepts
- The underlying relationship between the two concepts is a theory
- The be able to test the hypothesis or conduct empirical research we need to operationalize the
concepts
Normal Distribution
- Features:
oSymmetrical: mean, mode, and median are equal
oIf distribution is normal: a certain number of cases will fall within a certain distance form the
mean
- Empirical Rule tells us:
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o1SD (z value = 1) the probability is 0.68
o1.96 SD (z value =~2) probability is 0.95
o3 SD the probability is almost 1
o68-95-99 Rule
- The empirical rule tells us it is 68-95-99 RULE
Normal Distribution is a Common Distribution
- The standard deviation (σ) of the probability distribution measures the variability
oThe larger the σ the more spread the distribution
- Example:
oContinuous variable: hours spent by MP in constituency
oMean = 20, SD = 5
oCan assign probabilities to the intervals of
numbers
o0.0025 probability that you picked a MP at
random the work less than 10
hours/month
Populations and Samples
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- Population = Everyone (USA)
- Sample = Subset of everyone (East Coast)
Our statistics come from samples (and what do they tell us about the population)
oHow representative is the sample?
oWhat can we infer from the sample?
- The GOAL: we want to make probabilistic statement about the population based on our sample
Good Sampling
- Random
- Pull 1000 names from a that, and ask question
-Simple random sample
- What’s so good about random?
oProbability theory
oCan assess representativeness
oUse the normal curve to calculate probability
oConfidence interval. Errors. Above 3 is bad.
Recall: Hypotheses
- A theory based statement about what we would expect to observe (xy)
- Hypotheses are testable and falsifiable
Hypotheses Testing
- Two types:
oDescriptive Inference: old people are more religious than young people
oCausal inference: old people are more religious than young people because they think about
death more
-Significance testing
oCompare the data we have to the valued predicted by the hypothesis
Null and Alternative
- Want to choose between two conflicting statements:
- Null Hypothesis (H0) is directly tested
oHas a value similar to no effect
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