GLOSSARY

Alternative hypothesis: the prediction that is not tentatively held to be true; it states that a relationship will be found between two variables, or that the means of multiple groups are not equal.

Appropriate sample size: Too large a sample tends to yield statistical significance even in the presence of a small effect; i.e., statistical significance overrides the practical significance of your results. Such a situation leads to inflated Type I error. On the other hand, too small a sample size tends to suggest that there is no reasonable effect in your study; but, even a large effect can be difficult to detect if the sample size is inadequate. This situation leads to increased chance of Type II error. An appropriate sample size is one that can detect a statistical difference or effect that you feel represents a meaningful practical result, given that such an effect truly exists within the data, without wastefully oversampling.

Categorical variable: a characteristic that has been measured on the nominal scale.

Cohen's d: An effect size measure representing the standardized difference between two means.

Condition (Group) mean: the average of the scores of all individuals in a group.

Confidence interval: range of values that is formed to contain within its boundaries, with a predetermined level of confidence, the population value being estimated.

Continuous variable: a variable that theoretically can assume an infinite number of values (something that is measurable and ongoing).

Contrast(s): Specific question(s) regarding the differences between two or more means. A method for comparing two or more means.

Critical value: a value that a statistic must surpass in order to have a hypothesis test result in rejection of the null hypothesis

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Dependent groups t-test: A statistical technique to compare the means of two related samples, such as pre-post differences, or analyses comparing the means of dependent pairs such as husbands and wives, sibling pairs, twins, etc. Also called a paired or correlated t-test.

Effect size: An index measuring the magnitude of a specific result. Effect sizes can be standardized comparisons of means, or they can be correlation coefficients or squared correlation coefficients. Effect sizes are used to assess the degree to which the research hypothesis under study is actually observed via the sample data.

Factorial analysis of variance: a procedure for comparing the mean scores of two or more groups based on two or more (categorical) independent variables; it also tests for interactions among the IVs.

F-distribution: a theoretical relative frequency distribution of the ratio of two independent sample variances.

Greek letters and symbols

Independent groups t-test: procedure for comparing the mean scores of two independent groups on a given quantitative variable.

Multiple regression: a procedure for determining the relationship between a criterion variable and several predictor variables

Null hypothesis: the prediction that is tentatively held to be true; it states that no relationship will be found between two variables, or that the means of multiple groups are equal.

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One-tailed test: a statistical test in which the critical region for rejecting the null hypothesis falls in one direction of the probability distribution

One-way analysis of variance: a procedure for comparing the mean scores of two or more groups based on one categorical independent variable

Paired t-test: procedure for comparing the mean scores of two variables for each case. Also see dependent groups t-test.

Partial-R²: In multiple regression, the partial-R² for X_p indicates the strength of the relationship between an independent variable and the outcome, adjusting or controlling for the presence of any other previously entered independent variables in the model. The partial-R² for X_p represents the proportion of residual variance explained by the addition of X_p.

Part-R² (also called semipartial-R²): In a multiple regression model, the semi-partial or part-R² for X_p represents the proportion of variance of the outcome that is uniquely attributed to X_p, controlling for the contribution of all other variables in the model.

Pooled variance: Also called "within-groups" variability. Under the assumption of equal population variances, the pooled variance represents the best estimate of this equal but unknown population variance. It is a weighted average of the variance within each group.

Population: The group or collection of individuals from which a sample was drawn, and/or to which one hopes to generalize based on sample results.

Power: In hypothesis testing, the power refers to the probability of making a correct decision to reject the null hypothesis. Power tells us the likelihood of detecting a difference between groups, or a hypothesized relationship within the population of interest.

p-value: obtained significance level for a statistical test. The p-value represents the likelihood, under the assumption that the null hypothesis is true, that the data would yield the obtained results.

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R²: Represents the overall proportion of variance in an outcome that's accounted for by a (regression) model.

Sample: Collection of observations selected in a such a way to offer a model of the population of interest.

Semipartial-R²: see part-R²

Significance level: In hypothesis testing, the significance level refers to the probability of making a Type I error, or rejecting the null hypothesis when it is actually true. The researcher decides on the level of significance for each test.

Standard deviation: For a collection of observations, the standard deviation (S) represents "average" deviation from the mean. It is the square root of the variance.

Standard error: In multiple regression, the standard error represents "average" deviation between actual and predicted observations. Graphically, it represents the spread or variability around the predication line. Standard errors are also found for statistics, such as standard error of the mean, standard error for a proportion, etc. In this context, the standard error refers to the standard deviation of the sampling distribution for that statistic.

Standard error of the difference: Refers to the standard deviation of the sampling distribution for the difference of two means; it is the denominator used when calculating the observed t-statistic for a two-sample t-test.

t-distribution: a theoretical relative frequency distribution in which the standard error of the mean is estimated from sample values. Similar to a normal distribution but used when population variances are unknown.

Two-tailed test: a statistical test in which the critical region for rejecting the null hypothesis falls in both directions of the probability distribution.

Variance: The variance (S²) represents "average" squared deviations from the mean for a set of observations. Variances may be determined for linear combinations of observations as well.

Z-distribution: Standard normal distribution. Theoretical distribution of population scores where the mean always equals zero and the standard deviation equals one.

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