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Stats Exam 3
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Terms in this set (40)
α
The symbol for level of significance (probability of a type I error).
Alternative hypothesis
The hypothesis that the researcher wants to
prove or verify; a statement about the value of a parameter that is either
"less than," "greater than," "not equal to."
β
The probability of failing to reject a false null hypothesis (probability
of a type II error).
Conditions
The basic premises for inferential procedures. If the
conditions are not met, the results may not be valid.
Confidence interval
An estimate of the value of a parameter in interval
form with an associated level of confidence; in other words, a list of
reasonable or plausible values for the parameter based on the value of a
statistic. E.g. a confidence interval for µ gives a list of possible values
that µ could be based on the sample mean.
Confidence level
The percent of the time that the confidence interval
estimation procedure will give you intervals containing the value of the
parameter being estimated. (Note: This can only be defined in terms of
probability as follows: ―The probability that the confidence interval to
be computed (before data are gathered) will contain the value of the
parameter. After data are collected, level of confidence is no longer a
probability because a calculated confidence interval either contains the
value of the parameter or it doesn't.)
Degrees of Freedom
A characteristic of the t-distribution (e.g. n - 1 for
a one-sample t); a measure of the amount of information available for
estimating σ using s.
Fail to reject H0
The appropriate statistical conclusion when the Pvalue
is greater than α.
Hypothesis testing (Test of significance)
assessing evidence provided
by the data in favor of or against some claim about the population
Inference
Using results about sample statistics to draw conclusions
about population parameters.
Interval estimation
estimate an unknown parameter using an interval
of values that is likely to contain the true value of that parameter
Level of significance (symbolized by α)
The probability of rejecting a
true null hypothesis; equivalently, the largest risk a researcher is willing
to take of rejecting a true null hypothesis.
Margin of error for 95% confidence
The maximum amount that a
statistic value will differ from the parameter value for the middle 95% of
the distribution of all possible statistics. (Note: 95% can be changed to
any other level of confidence.) This only accounts for sampling
variability.
Matched pairs
Either two measurements are taken on each individual
such as pre and post OR two individuals are matched by a third variable
(different from the explanatory variable and the response variable) such
as identical twins.
Matched pairs t test
The hypothesis testing method for matched pairs
data. The typical null hypothesis is H0:µd = 0 where µd is the mean
difference between treatments. For this test, a difference is computed
within every pair. The mean and standard deviation of these differences
are computed and used in computing the test statistics.
Multiple comparisons
Performing two or more tests of significance
on the same data set. This inflates the overall α (probability of making a
type I error) for the tests. (The more comparisons performed, the greater
the chances of falsely rejecting at least one true null hypothesis.)
Null hypothesis
The hypothesis of no difference or no change. This is
the hypothesis that the researcher assumes to be true until sample results
indicate otherwise. Generally it is the hypothesis that the researcher
wants to disprove. (Note: Interpretations of P-value and statistically
significant need to say something about ―if H0 is trueǁ in order to be
correct.)
One-sample t test
An inferential statistical procedure that uses the
mean for one sample of data for either estimating the mean of the
population or testing whether the mean of the population equals some
claimed value.
One sided or one-tailed test
A test where the alternative hypothesis
contains either "<" or ">". The left-tailed test will have a "<" in the
alternative hypothesis. The right-tailed test will have a ">" in the
alternative hypothesis.
p
population proportion
p̂
sample proportion
po
proportion under the null hypothesis
p*
proportion used in sample size calculations if you do not have a p̂
value, p*=.5
Point estimation
estimate an unknown parameter using a single
statistic (e.g. xˉ , p̂ )
Practical importance
A difference between the observed statistic and
the claimed parameter value that is large enough to be worth reporting.
To assess practical importance, look at the numerator of the test statistic
and ask ̳Is it worth anything?' If yes, then results are also of practical
importance. Note: Do not assess practical importance unless results are
statistically significant.
Power
The probability of rejecting a false null hypothesis; computed as
1 - β. Increase power by increasing sample size or increasing α.
p-value
The probability of getting data (summarized with the test
statistic) as extreme or more extreme than the one observed (in the
direction of the alternative hypothesis) assuming Ho is true
Reject H0
The appropriate statistical conclusion when P-value < α
Standard deviation of p̂ (√(p(1-p)/n))
A measure of the variability
(spread) of the sampling distribution of p̂ .
Standard error of p̂ (√(p̂ (1-p̂ )/n))
A measure of the variability
(spread) of the sampling distribution of p̂ .
Standard deviation of xˉ (σ /√n):
A measure of the variability (spread)
of the sampling distribution of xˉ .
Standard error of xˉ (s /√n)
An estimate of the variability of the
sampling distribution of xˉ ; estimates the standard deviation of the
sampling distribution of xˉ
Standard error of a statistic
An estimate of the standard deviation of
the sampling distribution of the statistic; in other words, it is a measure
of the variability of the statistic. Note: The denominators of most test
statistics are called standard errors.
Statistically significant
Results of a study that differ too much from
what we expected to attribute to chance variation alone.
Test statistic
A number that summarizes the data for a test of
significance; usually used to obtain P-value.
t distribution
A distribution specified by degrees of freedom used to
model test statistics for the one-sample t test, etc. where σ ('s) is (are)
unknown. Also used to obtain confidence intervals and p-values for tprocedures
Type I error
The error made when a true null hypothesis is rejected.
(i.e. you reject H0 when H0 is true.)
Type II error
The error made when a false null hypothesis is not
rejected. (i.e. you fail to reject H0 when H0 is false.)
t*
The multiplier of standard error in computing margin of error for
estimating a mean. The value for t* is found on the t table in the
intersection of the appropriate df row and level of confidence column
μ0
The claimed value of the population mean given in H0
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