# Shared Flashcard Set

## Details

ANOVA Test 1
Chapters 1-8
116
Other
02/15/2009

Term
 Designed Experiments
Definition
 Experiments consisting of two or more treatment conditions in which subjects are treated identically except one feature that is different where the performance of the subjects is measured and recorder. "Gold standard of science" = being able to say that one factor "caused" the distinguished differences in the groups' results.
Term
 Analysis of Variance
Definition
 statistical analysis involving the comparison of variances reflecting different sources of variability
Term
 Independent Variable/ Manipulated Variable/Treatment Variable/Factor
Definition
 critical difference bw 2 groups
Term
 Qualitative Independent Variable/Categorical Variable
Definition
 Used to classify variables into different types or kinds, descriptor variables
Term
 Quantitative Independent Variable/Continuous Independent Variable
Definition
 Variables representing variation in amount
Term
 Quasi-Experiments/ Nonrandomized experiments
Definition
 naturally occurring groups
Term
 Univariate Procedures
Definition
 Look at one dependent variable at a time
Term
 Multivariate Methods
Definition
 Look simultaneously at several different dependent variables
Term
 Floor effect
Definition
 Many subjects are receiving scores close to the minimum possible value.
Term
 Ceiling effect
Definition
 Many subjects are recieving scores close to the maximum possible value
Term
 Nuisance Variable
Definition
 A factor influencing the value of the dependent variable other than the treatment of interest.
Term
 Confounding Variable
Definition
 Nuisance variable that is systematically related to the treatment conditions
Term
 Counterbalanced
Definition
 Including all the values of a nuisance variable equally often in each condition
Term
 Randomization
Definition
 Randomly assigning each subject to a condtion to break any possibility of confounding.
Term
 Blocking
Definition
 Making groups more comparable by grouping the subjects into sets based on some nuisance variable and then assigning an equal # of members from each set to each of the experimental groups. 2 effects: 1) it renders the treatment groups more comparable by assuring that each has the same distribution of the nuisance variable and 2) it reduces the variability of the scores within a block
Term
 Population
Definition
 Larger group of individuals that the results are assumed to effect given the representative sample
Term
 sample
Definition
 smaller group of individuals actually used in an experiment
Term
 Random sample
Definition
 Each member of the population is equally likely to trun up inside the sample and equally likely to be assigned to anny of the treatment conditions
Term
 Between-subjects design
Definition
 subjects recieve only one of the different treatment conditions. Smallest # of statistical assumptions. Less sensitive than some of the other approaches = larger # of subjects to be used.
Term
 Within Subjects Design
Definition
 Each subject serves in every treatment condition. = groups are more comparable and tests are more sensitive and there are more assumptions that must be met
Term
 Factorial design
Definition
 Experimental design with 2 or more factors in which every level of one factor is combined with every level of the other.
Term
 Between subjects factorial design
Definition
 every treatment condition contains unique sample of subjects
Term
 Within-subjects factorial design
Definition
 a single sample of subjects serves in every condition
Term
 Mixed Factorial Design
Definition
 Experimental design in which some treatment conditions have unique sets of subjects and some in which the same subjects are used again.
Term
 Parameters
Definition
 Measures calculated from all the observations within the population
Term
 Null Hypothesis
Definition
 Specifies the values of a particular parameter in the different treatment populations...gives the parameters the same value in the different populations.
Term
 Experimental Error, Error variability, or error variance
Definition
 The influences of every nuisance variable in an experiment that one controls through random assignment of subjects to the treatment conditions is a potential contributor to the results.
Term
 Subject score minus the total (N) mean
Definition
 total deviation
Term
 Between Groups Deviation
Definition
 Group mean minus the Total mean
Term
 Within Groups Deviation
Definition
 Subject score minus the group mean
Term
 Sum of Squares (SS)
Definition
 sum of the squared deviations from the mean - degree to which the numbers in a set vary among themselves.
Term
 Degrees of freedom
Definition
 The number of ways that the deviations are able to vary from each other.
Term
 Pooling
Definition
 Adding together the separate within-group sums of squares
Term
 Treatment sums (A)
Definition
 sums of the scores in each of the treatment groups ("A" indicates the sums of the scores for the levels of factor A with a subscript to indicate the particular treatment condition)
Term
 Bracket terms
Definition
 Used to calculate the raw sums of squares: 1) Square all quantities in a given set. 2) Sum these squared quantities if more than one is present. 3) Divide this sum by the # of scores that went into each of its components.
Term
 Mean squares
Definition
 variance estimates found by dividing the sum of squares by its degrees of freedom
Term
 Confidence interval
Definition
 Plausible range for each population treatment mean (not guaranteed to always include the population mean) specified by the % of time we will be successful in bracketing the population treatment means
Term
 Error Term
Definition
 The denominator of the F ratio which reflects only error variability
Term
 Sampling Distribution
Definition
 Where F's are plotted to get an idea of the variability of the test statistic caused by the random sampling of scores.
Term
 Monte Carlo Simulation
Definition
 producing a sampling distribution by repeated random draws
Term
 F ( df numerator, df denominator)
Definition
 formula for finding the proportion of area to the right of an ordinate in an F table.
Term
 Decision Rule
Definition
 Reject the null hypothesis when the observed F falls within the region of incompatibility
Term
 Type I Error
Definition
 Occcurs when the null hypothesis is true but we reject it anyway. (alpha = probability of error given that null is true)
Term
 Type II Error
Definition
 Occurs when the alternative hypothesis is true but we retain the null hypothesis anyway. (Beta = probability of error given that null is false)
Term
 Power
Definition
 Probability of rejecting the null when a specific alternative to the hypothesis is true. It is the compliment of making a type II error (____ = 1 - beta)
Term
 analytic comparison
Definition
 comparison made between 2 or more treatment groups that are componetns of a larger experimental design
Term
 Planned comparisons
Definition
 Comparisons between 2 or more groups that are performed instead of an overall F test
Term
 Pairwise Comparisons
Definition
 Comparisons that pit one group mean against another
Term
 Complex comparison
Definition
 Any comparison that involves an average of the group of means
Term
 Standard Form
Definition
 Contrast in which the sum of the positive coefficients equals 1 and the sum of the negative coefficients equals -1
Term
 Nondirectional hypothesis/Omnidirectional hypothesis
Definition
 Alternative hypothesis in which the difference between two means in either positive or negative direction are incompatible with the null hypothesis (two-tailed test)
Term
 one-tailed test
Definition
 t-test with a directional hypothesis
Term
 orthoginality
Definition
 Contrasts without overlapping information. (when the sums of products of the two sets of coefficients is zero)
Term
 mutually orthogonal
Definition
 when all contrasts in a set are orthogonal to one another (Helmert contrasts).
Term
 Trend Analysis
Definition
 The approach used when a quantitative independent variable that is manipulated
Term
 Concave up
Definition
 A quadratic function that has an opening facing up
Term
 Concave down
Definition
 A quadratic function that has an opening facing down
Term
Definition
 A function with a single concavity or bend
Term
 Coefficients of orthogonal polynomials
Definition
 Specialized coefficients for quadratic trend that is sensitive to the presence of curvature, but not influenced by linear trend; constructed so that each one is orthogonal to the others.
Term
 Cubic function
Definition
 The function tested when Ffailure remains significant after including the quadratic term. ...can rise, level out (or even reverse), then rise again
Term
 Quartic function
Definition
 The function tested when Ffailure remains significant after including the cubic term.
Term
 Nonlinear regression
Definition
 procedures used for complicated trend analyses when none of the other prescribed analyses are able to capture the pattern of a data set
Term
 Monotonic hypothesis
Definition
 A prediction concerning only the rank order of the conditions - asserting that the relationship between the independent and dependent variables is a monotonic function
Term
 Linear 2-4 Rule
Definition
 Quadruple the 2 extreme linear trend coefficients, and leave the remaining coefficients unchanged.
Term
 Simultaneous testing/simultaneous comparisons
Definition
 The process of controlling the errors that may occur during a process of multiple testing ...the more tests that are performed, the greater the probability that at least one error is taking place
Term
 Family of Tests
Definition
 A set of analyses performed to test a set of related hypotheses or research questions
Term
 Familywise Type I error rate
Definition
 The probability of making at least one Type I error in the family of tests when all the null hypotheses are true.
Term
 Experimentwise Error Rate
Definition
 The error rate for very large (infinite) families of all possible tests that could be made while analyzing an experiment
Term
 Per-comparison error rate
Definition
 Type I error rate for an individual test that is a part of a family of tests (alpha)
Term
 Bonferroni correction
Definition
 Most widely applicable familywise control procedure for small families; very general and applies to any sort of test including statistical procedures other than ANOVA; Relationship between the per-comparison and the familywise error rates for a family of "c" independent tests; can't be applied directly because tests are rarely mutually orthogonal (ie: the same control group is used for several experimental groups)
Term
 Bonferroni inequality
Definition
 The familywise error rate is always less than the sum of the per-comparison error rates of the individual tests.
Term
 Nominal value
Definition
 The actual familywise error rate is always less than the value of
Term
 Sidak - Bonferroni correction
Definition
Term
 Dunnett's Test
Definition
Term
 Tukey's procedure
Definition
 honestly significant difference (HSD) the simplest way to control the familywise error rate over the entire set of pairwise comparisons
Term
 honestly significant difference (HSD)
Definition
 Tukey's procedure, the simplest way to control the familywise error rate over the entire set of pairwise comparisons
Term
 Studentized range statistic
Definition
 found by using the # of groups, in the study, the value of dferror, and the desired level of error control (alpha familywise). Any pair of groups whose means differ by more than this amount is significantly different.
Term
 Equivalent subsets
Definition
 Groupings containing means that are not statistically differnt from one another
Term
 Harmonic mean
Definition
 A special average of individual sample sizes when the samples sizes vary by group.
Term
 Fisher- Hayter procedure
Definition
 A pairwise comparison that uses a sequential approach to testing
Term
 Newman-Keuls procedure/Student Newman-Keuls procedure (SNK)
Definition
 Involves a whole series of gatekeeper tests; has greater power than other pairwise comparisons but is much more complicated and has less accurate error control
Term
 Ryan-Einot-Gabriel-Welsch (REGW)
Definition
 Pairwise comparison that holds the error rate close to its nominal level even when some of the population means differ and some do not.
Term
 Random variable
Definition
 Mathematical device used to represent a numerical quantity whose value is uncertain and that may differ each time we observe it.
Term
 Probability function
Definition
 density function shown by a smooth theoretical function
Term
 Experimental error
Definition
Term
 Treatment effect
Definition
 Deviation of the treatment mean from the grand mean
Term
 Linear Model
Definition
 Sum of the quantities of the grand mean and its treatment populations, the treatment effect, and the experimental error
Term
 Random sampling assumptions
Definition
 Independence and Identical Distribution - The 2 most fundamental assumptions of the experimental error
Term
 E (Expected Value)
Definition
 The theoretical mean of a random variable (long-term average of quantities)
Term
 Robust
Definition
 If the F test is insensitive to certain violations of assumptions, it is said to be ____ to those violations.
Term
 Nonexperimental designs
Definition
 Studies in which the groups constitue natural populations to which random assignment is impossible. (ANOVA only tells us that groups differ, but not why.)
Term
 Unbalanced design
Definition
 experimental design resulting in unequal sample sizes = 2 problems... 1) Analyses are more complex 2) Loss of subjects potentially damages the equivalence of groups that were originally created randomly.
Term
 Missing at random/ ignorable
Definition
 A missing value that does not disturb the random formation of the groups
Term
 Missing not at random/nonignorable
Definition
 A missing value that does disturb the random formation of the groups
Term
 Positive Bias ; liberal
Definition
 When the observed proportion exceeds the nominal alpha level, the violation of the assumption has given the test a ________ and that is ______ with regard to a Type I error.
Term
 Negative bias ; conservative
Definition
 When the observed proportion is less than the nominal alpha level, the violation of the assumption has given the test a ________ and that is ______ with regard to a Type I error.
Term
 Mesokurtic
Definition
 medium bulging - moderate spread; normal distribution with a bell-curve
Term
 skew
Definition
 asymmetry of the spread of a distribution
Term
 kurtosis
Definition
Term
 residual
Definition
 a deviation from normality (observed score - observed group mean)
Term
 Central Limit Theorem
Definition
 As the size of the sample increases, the mean comes to ahve a normal distribution
Term
 Overdispersed
Definition
 Excess scatter caused by real data rather than a normal distribution including some extreme scores
Term
 Nonparametric tests
Definition
 Procedures that examine null hypotheses about location under weaker distributional assumptions.
Term
 Kruskal-Wallis Test
Definition
Term
 Mann-Whitney U Test
Definition
Term
 Wilcoxon rank sum test
Definition
Term
 James's second-order method
Definition
 The best, though quite complicated method, used to accommodate unequal variances with less power than the standard hypothesis, even though the variances may be equal.
Term
 Effect-size
Definition
 A quantity that measures the size of an effect as it exists in the population in a way that is independent of certain details of the experiment such as the sizes of the samples used.
Term
 Standardized difference between means
Definition
 a measure of the effect that takes variability of subjects in a group into account: divide the difference of group means by the standard deviation of the scores.
Term
 Correlation ratio
Definition
 Overall measure of the effect: the ratio of the size of SSA to the total amount of variability (SStotal). it is 0 when there are no differences among groups and approaches one as the group differences come to dominate the within-groups variability
Term
 Small effect
Definition
 1% of the variance is captured (d=.25)
Term
 medium difference
Definition
 captures 6% of the variance(d=.5)
Term
 large effect
Definition
 captures at least 15% of the variability (d=.8+)
Term
 omega-squared
Definition
 A measure of effect size used when group membership is known and the variability is reduced to the variance around the individual group means; uses parameters of the linear model
Term
 Partial Omega Squared
Definition
 expresses the variability of the contrast relative to itself and the error, rather than tto all the variability in the study
Term
 Noncentrality parameter
Definition
 measures the extent to which the experiment gives evidence for differences among the population means
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