Psych Exam 3 10/12/2012
Population: the parameter is represented by Greek letters
Sample: the statistic is represented by normal letters
You cannot get data from the entire population.
It is cheaper and easier.
Logic of Sampling
Sampling error: variability of sampling statistic from sample to sample due to error
“error” = random variability
Sampling distribution: distribution of statistic drawn from many samples
expected value: (ev) mean of sampling distribution
standard error : (se) standard deviation of sampling distribution
Sampling distribution of mean: sampling distribution of sample means over repeated sampling of a
Over many samples, expected value = u (mu) the population mean
Approximately normally distributed (if n is sufficiently large), regardless of the shape of the original
distribution. N needs to be at least 30 samples to be large and near a normal distribution.
There can be sampling distribution for any type of statistic.
Central limit theorem: (sampling distribution of mean) for any population, regardless of form, sampling
distribution of mean will approach normal distributNon as gets large. Furthermore, sampling distribution of
mean will have a mean (expected value =mu x ) equal μo & SD (standard error = sigma x) eqσ N to /√
Standard Error of Mean:
Measure of dispersion
Will SD of sampling distribution be smaller, larger, or equal to SD of population?
The SD of sampling distribution of the mean will always be smaller than the SD of the population.
Do we want a small or large SE?
Small because there is less variability and therefore more precision on estimating a true value for a
SD of population (reflected in sample values)
bigger population sample distribution will lead to bigger sampling error •Sample size
The larger the sample, the closer the means of such samples will be to the u (mu). More accurate
representation if the population.
Estimating population mean:
Sampling distribution of mean is normal
zscores play role
Allows us to make probability statements about whether or not sample mean = population mean
Confidence intervals: a good way to see if sample mean is a good estimate of the population mean.
Intervals: values that will contain mean
Confidence: degree of certainty you have that intervals will contain true mean
95% or 99% confidence
LL = x − zσ
UL = x + zσ x
z : valuefrom normal curve corresponding toconfidence
σ x , whereσ isSDof population& N =samplesize
Hypothesis Testing x −μ
x −μ 600−500
zx= = = 6.00
σ x 16.67
σ x = =16.67
Important aspect of research is to examine data to see if it supports research hypotheses
With statistics, hypothesis is theorybased prediction of parameters
Sample ▯ populations
Logic of Hypothesis Testing:
No two samples will ever be alike
Does sample differ by chance fluctuations, or is it really different?
Use of inferential statistics
Statistical significance: based on statistics, effect is not due to chance
Statistical Hypotheses: statement about population expressed in terms of parameter
Using Greek letters sigma and mu instead of normal letters x and s
Different than, but related to, research hypotheses
H : no difference, no change, no effect, no relationship: Null Hypothesis, nothing going on