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Data analysis 1 lecture 1 SE (standard error) is related to smaller sample sizes SD (standard deviation) is related to larger sample sizes Df = degrees of freedom = n-1
Sampling distribution of the mean is normal if:
- Population distribution is a normal distribution (lets say a country)
- AND/OR the sample size is large enough > 50 (Central Limit Theorem)
5 examples:
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The larger the sample you have, the more certainty you have about the mean.
Sampling distributions: behave predictably for most population distributions
- Mean of the sampling distribution is the population mean
- Shape of sampling distribution is approximately normal for large sample sizes
- The spread of the sampling distribution depends on the spread of the population
distribution and the sample size
Standard error (SE):
Show:
◼ That standard deviation of the sampling distribution (=sampling error) represents uncertainty ◼ Is computed in the following way ◼ The larger the samples, the closer the sample means are to the population mean → sample size is important!
The t-distribution
When s is used to estimate the SE, the distribution is no longer a normal distribution.
There are different t-distributions for different sample sizes. 2 / 4
The shape of the t-distribution depends on the degrees of freedom (n-1)
The t-statistic t-values are like z-values In a t-distribution you can find t-values
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Confidence intervals:
To show how this works:
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