PSYC 202 Chapter Notes - Chapter 6: Statistical Population, Statistical Parameter, English Alphabet
15 Jun 2018
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WEEK 6 VIDEO NOTES-- Estimation
Population distribution and sample:
- Population distribution
o Histogram of all measurements in the entire statistical population
o Mean does not change
o Proportion of outcomes of a random variable after lots of random trials
- Sample
o Histogram of the data collected from the population
o Mean changes each time the sample is redone
▪ Variation is due to the random nature of sampling process
- Pop distribution remains same all the time and only the sample changes – will change if
you resample the population
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Estimation
- Population parameter
o True value of a characteristic of the population distribution
▪ Could be mean, variance etc
o Typically shown as a Greek letter
o Fixed
- Estimation
o Process of inferring a population parameter from sample data
o Use letters from English alphabet
o Use data in sample to estimate population parameter
- Sample estimate
o Estimate of the population parameter based on your sample
We do not know the population distribution?
Sampling distributions
- Imagining the process of sampling things
- Each time we take a sample, the observations are going to be different
- Plot distributions of the means
- Probability distribution of the estimate from sampling the population a large number of
times
- Mean of sampling distribution has the same mean as population distribution
- Variance is smaller in sampling distribution
- Increasing size of the sample will reduce the width of the sampling distribution
Standard error
- Specific term
- Meant to describe only the variation in a sampling distribution
Document Summary
Population distribution: histogram of all measurements in the entire statistical population, mean does not change, proportion of outcomes of a random variable after lots of random trials. Sample: histogram of the data collected from the population, mean changes each time the sample is redone, variation is due to the random nature of sampling process. Pop distribution remains same all the time and only the sample changes will change if you resample the population. Population parameter: true value of a characteristic of the population distribution, could be mean, variance etc, typically shown as a greek letter, fixed. Estimation: process of inferring a population parameter from sample data, use letters from english alphabet, use data in sample to estimate population parameter. Sample estimate: estimate of the population parameter based on your sample. Each time we take a sample, the observations are going to be different. Probability distribution of the estimate from sampling the population a large number of times.
