PSYC1111 Study Guide - Final Guide: Sampling Distribution, Statistic, Central Limit Theorem

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28 May 2018
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Inferential Statistics
Standard Normal Distributions
Transforming any distribution of raw scores into Z-scores results in a distribution
with a MEAN of 0 and a STANDARD DEVIATION of 1
Z-Score quantifies the original score in terms of the number of standard deviations
that that score is from mean of the distribution
A negative z-score means that the original score was below the mean. A positive z
score means that the original score was above the mean
Population and Samples
Population (Universe, All items of interest)
summary properties or measures about population values are called parameters and
are usually expressed by using Greek letters
e.g. population mean
Sample (A portion of population that is actually measured)
summary properties or measures of sample values called statistics and are usually
expressed by using Latin (normal) letters
e.g. sample mean
Symbols
Aim
Aim of inferential statistics is to make inferences about population parameters
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Researchers use a sample statistic to estimate the corresponding population
parameter
you would not expect that means drawn from different samples are equal nor do
you expect them to be equal to the population mean
M1 != M2 != M3 … != μ
So it would be useful to know how far sample statistics are likely to vary from the
population (parameter) and from each other
How sample means behave in repeated sampling when the sample size increases?
Based on the IQ data (the population mean = 100, sd = 15)
Overall mean values are all close
The SDs are decreasing
Shape of distribution?
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Document Summary

A positive z score means that the original score was above the mean. Population (universe, all items of interest: summary properties or measures about population values are called parameters and are usually expressed by using greek letters, e. g. population mean. Sample (a portion of population that is actually measured: summary properties or measures of sample values called statistics and are usually expressed by using latin (normal) letters, e. g. sample mean. The sampling distribution: frequency distribution of sample means. Central limit theorem: distribution of sample means is always normal. Shape of distribution of sample means: the distribution of sample means is perfectly normal if, the population from which the samples are selected is a normal distribution, the number of scores in each sample is 30 or more. How much more accurate is an average (compared to single measurement): we use the standard deviation of the averages (standard error of the mean; Steps to reduce sem: random sampling, large sample, reliable measures.

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