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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. 


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statistical analysis involving the comparison of variances reflecting different sources of variability 


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Independent Variable/ Manipulated Variable/Treatment Variable/Factor 

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critical difference bw 2 groups 


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Qualitative Independent Variable/Categorical Variable 

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Used to classify variables into different types or kinds, descriptor variables 


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Quantitative Independent Variable/Continuous Independent Variable 

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Variables representing variation in amount 


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QuasiExperiments/ Nonrandomized experiments 

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naturally occurring groups 


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Look at one dependent variable at a time 


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Look simultaneously at several different dependent variables 


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Many subjects are receiving scores close to the minimum possible value. 


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Many subjects are recieving scores close to the maximum possible value 


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A factor influencing the value of the dependent variable other than the treatment of interest. 


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Nuisance variable that is systematically related to the treatment conditions 


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Including all the values of a nuisance variable equally often in each condition 


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Randomly assigning each subject to a condtion to break any possibility of confounding. 


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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 


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Larger group of individuals that the results are assumed to effect given the representative sample 


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smaller group of individuals actually used in an experiment 


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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 


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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. 


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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 


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Experimental design with 2 or more factors in which every level of one factor is combined with every level of the other. 


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Between subjects factorial design 

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every treatment condition contains unique sample of subjects 


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Withinsubjects factorial design 

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a single sample of subjects serves in every condition 


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Experimental design in which some treatment conditions have unique sets of subjects and some in which the same subjects are used again. 


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Measures calculated from all the observations within the population 


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Specifies the values of a particular parameter in the different treatment populations...gives the parameters the same value in the different populations. 


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Experimental Error, Error variability, or error variance 

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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. 


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Subject score minus the total (N) mean 

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Group mean minus the Total mean 


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Subject score minus the group mean 


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sum of the squared deviations from the mean  degree to which the numbers in a set vary among themselves. 


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The number of ways that the deviations are able to vary from each other. 


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Adding together the separate withingroup sums of squares 


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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) 


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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. 


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variance estimates found by dividing the sum of squares by its degrees of freedom 


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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 


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The denominator of the F ratio which reflects only error variability 


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Where F's are plotted to get an idea of the variability of the test statistic caused by the random sampling of scores. 


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producing a sampling distribution by repeated random draws 


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F ( df numerator, df denominator) 

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formula for finding the proportion of area to the right of an ordinate in an F table. 


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Reject the null hypothesis when the observed F falls within the region of incompatibility 


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Occcurs when the null hypothesis is true but we reject it anyway. (alpha = probability of error given that null is true) 


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Occurs when the alternative hypothesis is true but we retain the null hypothesis anyway. (Beta = probability of error given that null is false) 


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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) 


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comparison made between 2 or more treatment groups that are componetns of a larger experimental design 


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Comparisons between 2 or more groups that are performed instead of an overall F test 


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Comparisons that pit one group mean against another 


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Any comparison that involves an average of the group of means 


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Contrast in which the sum of the positive coefficients equals 1 and the sum of the negative coefficients equals 1 


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Nondirectional hypothesis/Omnidirectional hypothesis 

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Alternative hypothesis in which the difference between two means in either positive or negative direction are incompatible with the null hypothesis (twotailed test) 


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ttest with a directional hypothesis 


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Contrasts without overlapping information. (when the sums of products of the two sets of coefficients is zero) 


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when all contrasts in a set are orthogonal to one another (Helmert contrasts). 


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The approach used when a quantitative independent variable that is manipulated 


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A quadratic function that has an opening facing up 


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A quadratic function that has an opening facing down 


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A function with a single concavity or bend 


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Coefficients of orthogonal polynomials 

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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. 


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The function tested when Ffailure remains significant after including the quadratic term. ...can rise, level out (or even reverse), then rise again 


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The function tested when Ffailure remains significant after including the cubic term. 


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procedures used for complicated trend analyses when none of the other prescribed analyses are able to capture the pattern of a data set 


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A prediction concerning only the rank order of the conditions  asserting that the relationship between the independent and dependent variables is a monotonic function 


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Quadruple the 2 extreme linear trend coefficients, and leave the remaining coefficients unchanged. 


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Simultaneous testing/simultaneous comparisons 

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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 


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A set of analyses performed to test a set of related hypotheses or research questions 


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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. 


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Experimentwise Error Rate 

Definition
The error rate for very large (infinite) families of all possible tests that could be made while analyzing an experiment 


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Percomparison error rate 

Definition
Type I error rate for an individual test that is a part of a family of tests (alpha) 


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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 percomparison 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) 


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The familywise error rate is always less than the sum of the percomparison error rates of the individual tests. 


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The actual familywise error rate is always less than the value of 


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Sidak  Bonferroni correction 

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honestly significant difference (HSD) the simplest way to control the familywise error rate over the entire set of pairwise comparisons 


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honestly significant difference (HSD) 

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Tukey's procedure, the simplest way to control the familywise error rate over the entire set of pairwise comparisons 


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Studentized range statistic 

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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. 


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Groupings containing means that are not statistically differnt from one another 


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A special average of individual sample sizes when the samples sizes vary by group. 


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A pairwise comparison that uses a sequential approach to testing 


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NewmanKeuls procedure/Student NewmanKeuls 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 


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RyanEinotGabrielWelsch (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. 


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Mathematical device used to represent a numerical quantity whose value is uncertain and that may differ each time we observe it. 


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density function shown by a smooth theoretical function 


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Definition


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Deviation of the treatment mean from the grand mean 


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Sum of the quantities of the grand mean and its treatment populations, the treatment effect, and the experimental error 


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Random sampling assumptions 

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Independence and Identical Distribution  The 2 most fundamental assumptions of the experimental error 


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The theoretical mean of a random variable (longterm average of quantities) 


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If the F test is insensitive to certain violations of assumptions, it is said to be ____ to those violations. 


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Studies in which the groups constitue natural populations to which random assignment is impossible. (ANOVA only tells us that groups differ, but not why.) 


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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. 


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Missing at random/ ignorable 

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A missing value that does not disturb the random formation of the groups 


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Missing not at random/nonignorable 

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A missing value that does disturb the random formation of the groups 


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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. 


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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. 


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medium bulging  moderate spread; normal distribution with a bellcurve 


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asymmetry of the spread of a distribution 


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a deviation from normality (observed score  observed group mean) 


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As the size of the sample increases, the mean comes to ahve a normal distribution 


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Excess scatter caused by real data rather than a normal distribution including some extreme scores 


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Procedures that examine null hypotheses about location under weaker distributional assumptions. 


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James's secondorder method 

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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. 


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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. 


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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. 


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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 withingroups variability 


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1% of the variance is captured (d=.25) 


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captures 6% of the variance (d=.5) 


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captures at least 15% of the variability (d=.8+) 


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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 


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expresses the variability of the contrast relative to itself and the error, rather than tto all the variability in the study 


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measures the extent to which the experiment gives evidence for differences among the population means 

