40 terms

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."

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).

of a type II error).

Conditions

The basic premises for inferential procedures. If the

conditions are not met, the results may not be valid.

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.

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.)

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.

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.

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

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.

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

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.

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.

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.

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.

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.)

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.)

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.

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.

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

value, p*=.5

Point estimation

estimate an unknown parameter using a single

statistic (e.g. xˉ , p̂ )

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.

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.

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

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 .

(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 .

(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 .

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

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.

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.

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.

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

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.)

(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.)

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

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