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31 Cards in this Set
- Front
- Back
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Sampling Error
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- amount of error beween a sample statistic and its corresponding population
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Sampling Distribution
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- a distribution of statistics obtained by selecting all possible samples of a specific size from a population
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Distribution of Sample Means
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- collection of sample means form all possible random samples of paricular size (n) that can be obtained from a population
both a ampling distribution and population set of scores |
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What is the mean of distribution of sample means?
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- expected value of M
- = population mean |
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What is the standard deviation of the distribution of sample means?
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- the standard deviation of the distribution of sample means is called the standard error of M
- Qm = deviation / sqrt(sample pop) |
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What is the standard error of M
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- standard deviation of the DSM
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What is the variance of he distribution of sample means?
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- the variance if he distribution of sample means is called the standard error of M squared
- Qm^2 = deviation^2/ sample pop |
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DSM(mean, standard deviation, variance)
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DSM(expected value of M, standard error of M, standard error of M squared)
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Central Limit Theorem
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- mean = population mean
- standard deviation = deviation / squrt(sample pop) - shape = norm distr |
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Law of Large Numbers
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- as sample (n) increases, the error between the sample mean and population mean decreases
- thus, a very large sample will have a mean that approximately equal to the population mean |
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two problems with samples
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- limited in size (parts of population are left out)
- each sample has its own mean; some samples will ahve means that do not reflect the population mean - samples are variable |
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The ability to predict the sample characteristics of a sample from a population of samples with some accuracy is based on
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- the distribution of sample means
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What is neccesary to compute probability?
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numerator : likely hood of a specific outcome
denominator : all possible outcomes |
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Sampling Distribution
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- is a distribution of statisitcs obtained by selecting all the possible samples of a specific size from a population
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Sample means obtained with a large sample size should
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- cluster around popoulation mean
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sample means obtaiend with a small sample size should
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- be more widely scattered
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Central Limit Theorem
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- percise description of the distribution that would be obtained if you selected every possible sample, calculated every sample mean and constructed a distribution of sample means
- at n = 30 almost perfectly normal shape, central tendency and variability |
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Central Limit Theorem states:
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- For any population with mean u and the standard deviation o~, the distribution of sample means for sample size n will ahve a mean of u and a standard deviation of o~/ sqrt(n) and will approach a normal distribution as n approaches infinity
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Shape of DSM
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almost perfectly normal if:
- if taken from a normal distribution - n = 30+ (regaurdless of the population) |
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Expected Value of M
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- the sample mean is an unbiased statistic, which means that on average the sample statisic produces a value that is exacly equal to the corresponding population parameter
- average value of all sample means is equal to the population mean |
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Expected Value of M
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- the sample mean is an unbiased statistic, which means that on average the sample statisic produces a value that is exacly equal to the corresponding population parameter
- average value of all sample means is equal to the population mean |
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Two Purposes of Measuring Variability (standard deviation)
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- help distinguish the spread or cluster of scores
- describe how one individual score represents the population |
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Two Purposes of Measuring Variability (standard deviation)
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- help distinguish the spread or cluster of scores
- describe how one individual score represents the population |
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Two Purposes of Standard Error
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- describes DSM (sample spread)
- how much distance to expect between sample and population mean; how much difference should be expected on average betwen M and u |
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Two Purposes of Standard Error
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- describes DSM (sample spread)
- how much distance to expect between sample and population mean; how much difference should be expected on average betwen M and u |
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Standard Error of M
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- standard deviation of a DSM
- how much distance to be expected between population mean and sample mean |
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Standard Error of M
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- standard deviation of a DSM
- how much distance to be expected between population mean and sample mean |
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Factors Influencing Magnitude of Standard Error
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- size of the sample
- standard deviation of the population form which the sample is selected |
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Factors Influencing Magnitude of Standard Error
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- size of the sample
- standard deviation of the population form which the sample is selected |
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Law of Large Numbers
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- the larger the (n) the more probable it is that the sample mean will be close to the population mean
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Law of Large Numbers
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- the larger the (n) the more probable it is that the sample mean will be close to the population mean
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