Stat quiz notes
Robust implies the value of the statistic or the outcome of the procedure will be relatively unaffected by
the presence of a small number of unusual or incorrect data values
The ANOVA F test is more robust with regard to its assumptions if the largest sample standard deviation
is not more than twice the size of the smallest.
F test assumes population standard deviations are equal,
and is more accurate if no standard deviation is much larger than another.
In an ANOVA F test, the null hypothesis is most strongly rejected when the F value is strongly positive.
Essentially the F test is the ratio of the variation in sample means to the variation within the samples.
The
null is rejected more strongly when sample means differ greatly and the F value is large.
Chi squared statistics counts the number in each category
Differenceinproportions z statistic has 2 categories and the data is categorized by success or failure
ANOVA F test compares the means in different categories
To find the confidence interval for the binomial success probability: plus or minus z*the square root of
(((x/n)(1x/n))/n)
Confidence interval depends on sample size. So if the sample size quadruples, then the confidence
interval will be half of its original width
In the model y = a + bx, x is the explanatory variable because changes in x explain changes in y
(according to this model)
In a differenceinmeans t test using a pooled variance, the number of degrees of freedom is the sum of
the sample sizes minus 2. This can be explained as the total number of observations, minus the two
sample means that must be estimated to calculate the pooled variance.
In medical experiments comparing the benefits in a treatment group (pT) and a control group (pC), use
pT=pC as the null hypothesis. The value of the treatment is demonstrated by rejecting the null that is
worthless.
When constructing a confidence interval on the population mean and using an estimate of the population
standard deviation, use a t value instead of a z value. The t distribution takes into account the increased
uncertainty caused by the fact that the standard deviation must be estimated.
The central limit theorem implies that the sampling distribution of the mean of a sufficiently large sample
is approximately the symmetrical normal distribution, no matter what the population is.
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 Spring '07
 Storer
 Normal Distribution, Standard Deviation, Variance, Null hypothesis

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