Psych Test 4 10/31/2012
One Sample Ttests
one sample test one sample compared to the rest of the population
two sample test comparing two samples to determine if they come from the same population
With ztest, you have to know population mean & *standard deviation*
Why not just substitute sample statistics as estimateszin formula? Because of sampling error!
Sampling Distribution: smaller samples will be even more skewed, most samples will underestimate true
Sampling distribution references variance (sigma^2)
skew refers to the tail
the mean of a sampling distribution is the excepted value
Logic of a ttest: How good an estimate sample statistics are of population values depends on sample size;
a ztest cannot do this!
Must adjust z formula for estimates oparameters & sample size information
as you increase sample size your estimate of the parameter gets better
each N value is associated with a different sample size – degrees of freedom takes care of the fact that
different sample sizes have different degrees of goodness
N refers to sample size not population size!!!!! You cannot use a pop size.
–Each nassociated with different distribution
–Family of t distributions
symmetric about the mean equal on both sides
“S” in the ttest
s as an estimate ofσ is likely to be an underestimate
Smaller estimate of standard error of mean
Inflated test statistic
Solution? Gosset created t
Wider than z so we don’t falsely reject null Degrees of Freedom
Statistics as estimates are a function of N
Separate tto go with each N
Degrees of freedom determine which distribution
Degrees of freedom: number of independent pieces of info remaining after estimating one or more
df = N 1
Steps for Hypothesis Testing
State in terms of parameters
Set up H 0
Set up H 1
Directional or nondirectional
Specify decision criteria
Specify alpha level
One (directional) or twotailed (nondirectional) test?
Compute test statistic
Reject or fail to rejHct?
Conclusions about research question?
Intervals: values that will contain mean
Confidence: degree of certainty you have that intervals will contain true mean
95% or 99% confidence LL = x −ts x UL = x +ts x
t :value that corresponds tocertain conf idence
s = , where sisSDof sample& N =samplesize
Confidence Intervals will be twotailed; upper and lower
Independent Samples ttest
Onesample: is sample statistic significantly different from population parameter?
Twosample: are these two sample statistics different, therefore indicating different populations?
Overlap of two distributions
If null is true? –virtually identi