POLI 3000 Lecture Notes - Lecture 8: Simple Random Sample, Central Limit Theorem, Oversampling
22 May 2018
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I. Sampling
a. Golden standard= simple random sample
i. What makes it a SRS? Each individual has equal probability of getting chosen, and
each group has to have same probability to get chosen
b. Non SRS random samples
i. Stratification (break into groups)
1. Lowers chance of weird sample
ii. Oversampling
1. Exame: over-sampling minority groups
iii. Clustered random sample
1. Lowers cost
iv. Combinations of these
v. Sometimes you are forced to do non SRS
1. This is’t ideal, ut it is okay
c. Population, sample and inference
i. Have to be careful of defining population
II. Sampling error
a. A statistic from a simple random sample is an unbiased estimate for the paramenter in the
population
i. Unbiased= on average, it will be correct. In expectation, it will be correct
ii. Statistic= talking about sample
iii. Paremter: about population, and most likely a greek symbol
iv.
b. Sampling error: variance in our sample statistics
III. Statistical inference
a. Sampling distribution: distribution of estimates from many samples )of the same seize,
drawn from the same population). Distribution of sample statistsics
b. Standard error (SE)
i. The standard deviation of the sampling distribution
IV. Key theorem in inferential statistics
a. Central limit theorem (WILL BE ON THE FINAL)
b. The averages of samples will have approximately normal distribtuions
c. As the sample size gets larger, the less variance there will be (narrower bell curve) and will
be more normal
d. Does’t atter hat the distriutio of the ariale atually is
i. The sampling distribution of the average of the means will always be normal
V. Normal distributon
a. Perfectly symmetrical
b. Need to know 2 things:
i. Mean, median or mode (all same)
ii. Variance
c. 68% of data falls within 1 standard division of the mean
d. 95% will faill within 1.96 standard deviations
e. 99.7% will fall within 3 SDs
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