central limit theorem - relates the sampling distribution of the mean to the theoretical model of the distribution of scores. The central limit theorem comes in a variety of flavors, but generally stated says that the sampling distribution of the mean will be a normal distribution with a theoretical mean equal to mu and a theoretical standard deviation, called the standard error, equal to sigma of the model of scores divided by the square root of the sample size. In theory the central limit theorem requires that the sample size approach infinity, but in practice the results converge with relatively small sample sizes (N>10).

Central Limit Theorem - the mean of the sampling distribution of the mean equals the mean of the population model and that the standard error of the mean equals the standard deviation of the population model divided by the square root of N as the sample size gets infinitely larger (N-> ? ).

Central Limit Theorem - relates the sampling distribution of the mean to the theoretical model of the distribution of scores. The central limit theorem comes in a variety of flavors, but generally stated says that the sampling distribution of the mean will be a normal distribution with a theoretical mean equal to mu and a theoretical standard deviation, called the standard error, equal to sigma of the model of scores divided by the square root of the sample size. In theory the central limit theorem requires that the sample size approach infinity, but in practice the results converge with relatively small sample sizes (N>30).

central tendency - a typical or representative score; mean, median, and mode are measures of central tendency.

chi-square statistic - a measure of the difference between observed and expected values.

chi-squared distribution - a theoretical probability model, described by a single parameter, called degrees of freedom. In this model, scores are positively skewed and range from zero to infinity.

compound event - a combination of simple events joined with either "and" or "or."

compound probabilities - the probability of a compound event.

computational formula for the standard error of estimate - a formula to compute the standard error of estimate that includes the variance of Y and the correlation coefficient. It is easier to compute than the definitional formula because it does not require a table of squared residuals to be computed.

conditional distribution - a distribution of a variable given a particular value of another variable.

conditional probability - the probability of an event given that another event is true.

confidence interval - a pair of scores that describe a theoretical range of values of a score.

constant - a value that does not change with the different values for the counter variable (i).

control condition - in an experiment, a condition identical to the treatment condition except no treatment is given.

correlation - changes in one variable are related to changes in another variable, they "co-relate".

correlation coefficient - a measure of relationship between two variables. Conventionally this measure may take on value from minus one to one.

correlation coefficient - a measure of the degree of linear relationship between two variables.

correlation coefficients - numbers between minus one and one that measure the linear relationship between two variables.

correlation matrix - a table of all possible correlation coefficients between a set of variables.

crossed design - experimental design in which each subject sees each level of the treatment condition.

degrees of freedom - the number of scores that are free to vary.

df - see degrees of freedom.

effect - when a change in one thing is associated with a change in another; the changes may be either quantitative or qualitative.

effect - when a change in one thing is associated with a change in another the changes may be either quantitative or qualitative.

estimator - a statistic used to estimate a model parameter.

exact significance level - the probability of the results of the study given the null hypothesis model is true

exact significance level - the probability of finding an effect equal to or larger than the effect found in the study given that the null hypothesis is true.

expected utility theory - a mathematical theory combining cost and probabilities.

experimental condition - in an experiment, the level of treatment in which some treatment is given.

experimental design - the manner in which an experiment is set up; specifically, the way the treatments are administered to subjects.

experiment-wise error rate - the probability of committing at least one type I error somewhere in the analysis.

F-distribution - a theoretical probability distribution characterized by two parameters, df 1 and df 2 .

F-distribution - a theoretical probability distribution characterized by two parameters, df1 and df2, both of which affect the shape of the distribution; the distribution is nonsymmetrical, skewed in the positive direction.

form board test - one of the earliest Psychological tests where the score of the person being tested is the time it takes to place a number of pegs in a board of cut-out forms.

fractions - are an algebraic phrase involving two numbers connected by the operator "/".

F-ratio - the Mean Squares Between divided by the Mean Squares Within; a measure of how different the means are relative to the variability within each sample.

hypothesis tests - procedures for making rational decisions about the reality of effects.

intercept - another name for the additive component in a linear transformation. When a line is drawn on a plane, the line will cross the y-axis at the intercept.

intercept - the a value that defines where the line crosses the Y-axis in a regression model.

interval estimate - see confidence interval.

invariant - does not change.

inverse relationship - a relationship between two variables where in general, as one variable becomes larger, the other becomes smaller.

IQ scale - test scores have a mean of 100 and a standard deviation of either 15 or 16, depending upon the test selected.

least-squares criterion - a value the minimizes the sum of squared differences between the scores and the predicted values.

linear transformation - a transformation of the form X' = a + bX.

linear transformations - a transformation where each score multiplied by a constant and then a different constant is added to the resulting product.

mean - the sum of the scores divided by the number of scores.

mean - the sum of the scores divided by the number of scores; the most-often used measure of central tendency.

Mean Squares Between - the variance of the means times the number of scores within each group, an estimate of the theoretical variance of scores.

Mean Squares Within - the mean of the variances, an estimate of the theoretical variance of scores.

median - the score value which cuts the distribution in half.

median - the score value that cuts the distribution in half, such that half the scores fall above the median and half fall below it; a measure of central tendency.

mode - the most frequently occurring score value.

mode - the most frequently occurring score value; on a frequency distribution it is the score value that corresponds to the highest point; a measure of central tendency.

model - A model is a representation containing the essential structure of some object or event in the real world.

MSB - see Mean Squares Between.

MSW - see Mean Squares Within.

mu - one of two parameters of normal curves. Mu defines the center of the distribution.

multiple R - the correlation coefficient between the observed and predicted Y values.

multiple t-tests - hypothesis testing procedure when there are more than two groups that compares all possible pairs of means using a t-test.

multiplicative component - the b in the linear transformation equation X' = a + b X. The constant that is multiplied times the score in a linear transformation.

negative correlation coefficient - If one variable increases, the other variable decreases; and if one decreases, the other increases.

negatively skewed distribution - an asymmetrical distribution that points in the negative direction, with the mean being smaller than the median, which is smaller than the mode.

nested design - experimental design in which, each subject receives one, and only one, treatment condition.

nested t-test - an hypothesis testing procedure for nested designs with two levels.

non-optimal regression model - a regression model that does not meet the least squares criterion.

null hypothesis - the hypothesis that there were no effects.

null hypothesis - there are no effects. Chance or random variation is responsible for any differences discovered.

one-tailed t-test - a direction t test where alpha is placed in a single tail of the distribution under the null hypothesis.

optimal regression model - a regression model that meets the least squares criterion.

outlier - a score that falls outside the range of the rest of the scores on the scatter plot.

parameters - variables that change the shape of the probability model.

path analysis - a branch of correlational analysis that attempts to establish causation from correlational evidence.

percentile rank - the percentage of scores that fall below a given score.

percentile rank based on the normal curve - the percentage of scores that fall below a given score in a hypothetical distribution of scores based on the normal curve.

percentile rank based on the sample - the percentage of scores that fall below a given score within a sample of scores.

percentile ranks - the percentage of scores that fall below a given score.

point estimate - a single value that represents the best predicted value of Y.

population distribution - a theoretical probability model.

positive correlation coefficient - If one variable increases (or decreases), the other variable also increases (or decreases).

positively skewed distribution - an asymmetrical distribution that points in the positive direction, with the mode smaller than the median, which is smaller than the mean.

predicted variable - the variable being predicted, the dependent variable.

predictor variable - the variable used to predict, the independent variable.

probability - a theory of uncertainty.

probability models - a mathematical equation used to model a relative frequency distribution.

probability theory - defines probabilities of simple events in algebraic terms and then presents rules for combining the probabilities of simple events into probabilities of complex events given that certain conditions are present (assumptions are met); a mathematical model of uncertainty; defines probabilities of simple events in algebraic terms and then presents rules for combining the probabilities of simple events into probabilities of complex events given that certain conditions are present (assumptions are met).

probability theory - a mathematical model of uncertainty; defines probabilities of simple events in algebraic terms and then presents rules for combining the probabilities of simple events into probabilities of complex events given that certain conditions are present (assumptions are met).

range - is the largest score minus the smallest score.

range - a measure of variability the largest score minus the smallest score.

raw score - the score that is given.

regression - a movement backwards toward the mean.

regression analysis - application of linear regression procedures, including parameter and error estimation techniques.

regression coefficients - the values of the regression weights.

regression line - the representation of the regression model on a scatter plot.

regression model - used to predict one variable from one or more other variables.

relational database - a number of flat tables linked together with index variables. Complex queries and tables can be constructed with relational databases

relative measure - a measure of a variable relative to some other measure. The ratio of weight to height would be a relative measure of weight.

residuals - deviations of observed and predicted values.

sample distribution - the distribution resulting from the collection of actual data.

sample statistics - mathematical equation used to measure properties of samples. Sample statistics are used as estimators of parameters in the probability models.

sampling distribution - a theoretical distribution of a sample statistic.

scatter plot - a visual representation of the relationship between the X and Y variables.

sig. - the probability of the results of the study given the null hypothesis model is true

sigma - one of two parameters of normal curves. Sigma defines the spread or dispersion of the distribution.

significance level - see alpha

simple linear regression - a prediction model of the form Y' = a + bX.

skewed distribution - a distribution that is asymmetrical, and in which the mean, median, and mode do not all fall at the same point.

slope - another name for the multiplicative component in a linear transformation. When a line is drawn on a plane, the steepness of the line will be determined by the slope.

slope - the value of b in the regression equation Y' = a + bX.

squared correlation coefficient - the proportion of variance in Y.

standard deviation - a measure of variability; the positive square root of the variance.

standard error - the theoretical standard deviation of a sampling distribution.

standard error of estimate - a measure of error in prediction.

standard normal curve - a member of the family of normal curves with ? = 0.0 and ? = 1.0.

standard score transformation - is a linear transformation such that the transformed mean and standard deviation are 0 and 1 respectively.

standard scores - a linear transformation such that the transformed mean and standard deviation are 0 and 1 respectively; also called z-scores.

stanine transformation - scores are linearly transformed to a distribution with a mean of 5 and a standard deviation of 2 and the decimals are dropped, so that the numbers are integers between one and nine.

subjective probabilities - probabilities obtained by procedures designed to extract "degree of belief" from individuals.

subscripted variables - a method by which large numbers of variables can easily be represented; its form is X i , where the X is the variable name and the subscript (i) is a counter variable that can take on values from 1 to N.

sum of squared deviations - the sum of the squared differences between the observed and predicted values of Y.

summation notation - a scheme that provides a means of representing both a large number of variables and the summation of an algebraic expression.

summation sign - used to represent summation in an expression.

symmetrical distribution - a distribution in which the mean, median, and mode all fall at the same point. If drawn, cut out, and folded the two sides would be identical.

t distribution - a theoretical probability distribution.

t distribution - a theoretical distribution that is symmetrical, bell-shaped, has tails approaching the x-axis but never touching, and total area under the curve equal to one. The t distribution has three parameters, degrees of freedom, mu, and sigma. The fewer the degrees of freedom, the flatter the t distribution is relative to the normal distribution.

T score - score that has been transformed into a scale with a mean of 50 and a standard deviation of 10.

transformations - are rules for rewriting sentences in the language of algebra without changing their meaning, or truth value.

transformations - a procedure that converts a number into another number.

transformed scores - raw scores that have been converted into another number. Generally transformed scores can be more easily interpreted than raw scores.

treatment - quantitatively or qualitatively different levels of experience.

treatment condition - any of the levels of treatment in an experiment.

t-test - an hypothesis test employing the t distribution.

two-tailed t-test - alpha is divided in half and placed in both tails of the distribution under the null hypothesis

Type I error - the null hypothesis is rejected when in fact it is true. The hypothesis testing procedure decides that the effects are real when if fact the results were due to chance.

Type II error - the null hypothesis is retained when in fact the alternative hypothesis is true. The hypothesis testing procedure decides that the no effects model could explain the results when in fact the effects were real.

utility - the gain or loss experienced by a player depending upon the outcome of the game.

variability - the spread or dispersion of scores; three measures of variability are the range, the variance, and the standard deviation.

variance - a measure of variability.

variance - a measure of score dispersion.

vectors - lines from the origin to a point on a graph, sometimes represented as points on a graph.