Flashcards in Statistics exam 3 Deck (64)
the symbol for level of significance
the probability of failing to reject (accepting) a false null 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", or "not equal to".
approximate two-sample t test
a test for comparing the means of two independent samples or two treatments where the test statistic has an approximate t distribution. The formula for computing degrees of freedom is complicated.
ANOVA (analysis of variance)
a statistical procedure for testing the equality of means using variances.
Central Limit Theorem:
the name of the statement telling us that when sampling from a non-normal population, the sampling distribution of x bar is approximately Normal whenever the sample is large and random.
Claimed parameter value
the value of the parameter given in the null hypothesis
the basic premises for inferential procedures. If the conditions are not met, the results may not be valid.
conditions necessary for a one-sample t procedure (using t* for C.I. or getting P value from t table):
normality of the original population and SRS
check data collection and if n40 apply CLT.
Conditions necessary for a two-sample t procedure (using t* for C.I. or getting P-value from t table)
normality of both populations and either stratified sample (independent SRS's) or random allocation. Check data collection and if n1+n240, apply CLT.
conditions necessary for matched pairs t procedure (using t* for C.I. or getting P-value from t table)
normality of population of differences and either SRS or random allocation. Check data collection and if number of pairs 40, apply CLT.
Conditions necessary for ANOVA
normality of all populations, equality of variances and either stratified sample (independent SRS's) or random allocation. check data collection if n1 + n2 + ... +nk40, apply CLT and largest standard deviation divided by smallest standard deviation <2.
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.
conservative two-sample t test
a test for comparing the means from two independent samples or two treatments where the degrees of freedom are taken to be the minimum of (n1-1) and (n2-1).
what happens to the width of a confidence interval when sample size is increased (or level of confidence is decreased)
degrees of freedom
a characteristic of the t-distribution; a measure of the amount of information available for estimating theta using s.
a condition for ANOVA; the condition is met when the largest standard deviation divided by the smallest standard deviation is less than 2.
estimated standard deviation of x bar.
called standard error of x bar and equals s/sq.rt.n; measures variability of sampling distribution of x bar.
Fail to reject H0
The appropriate statistical conclusion when the P-value is greater than alpha
results from statistical analysis performed on non-random samples or experimental data obtained without random allocation of treatments to individuals.
using results about sample statistics to draw conclusions about population parameters
laws of probability
the basis for hypothesis testing and confidence interval estimation
level of confidence
The percent of the time that the confidence interval estimation procedure will give you intervals containing the value of the parameter being estimated. 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.
level of significance (symbolized by alpha)
the probability of rejecting a true null hypothesis; equivalently, the largest risk a researcher is willing to take of rejecting a true null hypothesis
lower tailed test (also called a left-tailed test)
a test with " in the alternative hypothesis. This is a one-sided test
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.
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 or windows matched by installer when comparing installation time of two brands of windows.
matched pairs t test
the hypothesis testing method for matched pairs data. The typical null hypothesis is H0: mu=0 where mu.d 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 statistic.
the claimed value of the population mean given in H0.