Glossary
Alpha (a). The probability of rejecting a true null hypothesis. Alpha also refers to a measure of internal consistency—see Cronbach’s coefficient alpha.
Alternate forms reliability. A procedure for obtaining evidence of the reliability of test scores by calculating a reliability coefficient from scores produced by two or more forms of the same test. This is also known as equivalent forms reliability. When there are two forms, the term parallel forms is sometimes used.
ANOVA. An abbreviation for the statistical procedure known as the Analysis of Variance. The procedure analyzes the variance between the means of the groups in the study compared to the variance among the participants in a study. From the resulting ratio, an F statistic is calculated.
ANCOVA. Analysis of Covariance is a statistical procedure for analyzing results when there are one or more independent variables, one dependent variable, and one or more covariates.
Categorical variable. Categorical variables are those variables having two or more groups or levels such as sex, ethnicity, and religious group.
Chi-Square. A statistic that represents differences between obtained and expected values. The chi-square statistic can be used with frequency data.
Coefficient alpha. See Cronbach’s alpha.
Concurrent validity. A method of test score validity based on the correlation of two sets of scores obtained at the same time.
Confounding variable. A variable that produces unexpected changes in the dependent variable and therefore interferes with interpreting the capacity of an independent variable to produce or explain changes in a dependent variable.
Construct validity. A collection of evidence using different methods that support the existence of a particular construct, which can be recognized by many independent researchers.
Content validity. The extent to which experts judge the items in a test adequately sample the domain a test is supposed to measure.
Continuous variable. A variable having a wide range of numerical values, such as intelligence, achievement, and personality variables.
Correlation. The relationship between two variables. When two variables vary in a specific way with each other, they are said to covary. The covariation can be described in a graph of the relationship or in a summary statistic known as a correlation coefficient. There are a few common correlation coefficients.
Correlation coefficient. A statistic that summarizes a correlation between two variables. Correlations range from -1.0 to +1.0. Positive correlation values represent relationships such that as one variable increases, so does the other. Negative correlation values represent relationships that are inverse. In an inverse relationship, one value increases as the other value decreases. A common coefficient is the Pearson Product Moment Correlation Coefficient reported using a lower case, italicized letter r. See also correlation.
Covariate. A variable that is correlated with a dependent variable.
Cramer’s V. A correlation coefficient that may be used with nominal data.
Criterion related validity. Criterion-related validity compares a set of test scores on one test to scores on another test using a correlation procedure.
Cronbach’s coefficient alpha. A statistic indicating the internal consistency of test items based on an average of the interitem correlations in a sample.
Dependent variable (DV). The variable in a research study that is expected to change when a researcher varies the level of an independent variable.
df (degrees of freedom). When calculating a statistic, there is a limit on the number of values in a set of data that are free to vary.
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Effect sizes (ES). How much of the variance in the dependent variable is accounted for by the independent variable. There are different measures of effect size, such as Cohen’s d, r2, and η2.
Extraneous variable. A variable in a study that is not supposed to produce a change in a dependent variable. Variations in the temperature and humidity of a testing room are examples of extraneous variables.
F-statistic. The F statistic in this text is the value obtained from an ANOVA procedure. It is also called the F ratio. The letter F is taken from the surname of statistician and biologist, Sir Ronald Fisher.
Face validity. A term used to describe the way a test appears to a test taker or test purchaser. It is not a scientific term for a type of validity and it is sometimes confused with content validity.
Independent variable (IV). The variable in a research study that a researcher studies or manipulates to determine if another variable, the dependent variable, changes when the IV changes.
Item Response Theory (IRT). Item Response Theory (IRT). An analysis of information about each item in a test to see how well an item functions as a measure of the trait or ability being measured.
Kendall’s tau. A correlation coefficient that indicates the relationship between sets of ordinal data.
MANOVA (Multivariate Analysis of Variance). A statistical procedure for analyzing results when there are one or more independent variables and two or more dependent variables.
MANCOVA (Multivariate Analysis of Covariance). A statistical procedure for analyzing results when there are one or more independent variables, two or more dependent variables, and one or more covariates.
Mean. The arithmetic average for a set of scores or values.
Median. The number representing the mid-point in a set of scores or values. The median divides a distribution of scores in half. Half the scores are above the median and half the scores are below the median.
Mode. The number representing the most frequent score in a distribution of scores. A distribution may have more than one mode.
Null hypothesis. This is the assumption of no difference between the means stated in terms of population values on the dependent variable. Most researchers only report the research question or research hypothesis and rarely state the null hypothesis. Example: There is no difference between the population means of regular and special education teachers’ job satisfaction scores. The statistical null hypothesis is rarely written but is given as μ:1 = μ:2, where Greek letters represent the population means.
Observed Power (OP). The probability of finding an effect based on the sample size and effect size.
Parallel forms reliability. See alternate forms reliability.
Pearson Product Moment Correlation coefficient. See correlation coefficient.
Population. The entire set of data of interest to a researcher. In counseling research, the population is usually thought of in terms of people who have the characteristics relevant to the topic being studied. For example, if researchers are studying optimism in the elderly, they may define the population of interest as all North Americans above age 70.
Predictive validity. A type of criterion-related validity. A procedure that relies on knowledge about the correlation between two sets of score data to predict future scores or values from the results of a current set of scores or data. For example, predicting future college GPA from knowledge of the relationship between a high school aptitude test and college GPA in previous studies.
Probability (p). The probability of falsely rejecting the null hypothesis. The p value is commonly compared to an alpha level. Common values include .05, .01, and .001 depending on the nature of the variables and the research questions. Older articles typically reported p values as less than or greater than a specified alpha value such as .05. More recent articles report the actual p values.
Sample. A small set of data drawn from a large set of data called the population. A population is the entire set of data. In counseling research, data sets are created from the data produced by samples of people drawn from a population.
Spearman’s Rank Order Correlation Coefficient. The Spearman Rank Order Correlation Coefficient indicates the relationship between sets of ordinal data.
Standard deviation (SD). A statistic based on the deviation of scores from their group mean. The number reveals how much the scores in a distribution deviate from the mean. When the standard deviation is small relative to the mean, the scores are close to the mean, and when the standard deviation is large, the scores are considerably above and below the mean.
Standard Error of Estimate (SEE). A measure of error used to create a range above and below an estimated or predicted value or score. SEE is an indicator of precision in estimating values.
Standard Error of the Mean (SE). A measure of error used to create a range above and below an obtained sample mean suggesting where a mean might fall if means were calculated for repeated samples.
Standard Error of Measurement (SEM). A measure of error used to create a score range above and below an obtained test score suggesting where a person’s true score might fall if the test is taken again. SEM is related to the reliability of test scores.
Test reliability. An imprecise but commonly used term about test scores. Tests do not have a specific reliability value because reliability is a product of test scores, which vary with each administration. Reliability values also vary with the method used to obtain the scores in the calculation.
Test-retest reliability. A method of calculating the reliability of test scores based on giving the same test or alternate forms separated by a period of time.
Test validity. Technically, tests do not have a specific validity value because validity is a product of test scores, which vary with each administration. Validity values also vary with the method used to obtain the scores.
Type I error. A Type I error occurs when researchers find their data support their research hypothesis and conclude the null hypothesis is false when in fact the research hypothesis is false.
Type II error. A Type II error occurs when researchers conclude their data do not support their research hypothesis. They fail to reject the null hypothesis.
Variable. A characteristic that varies in two or more ways.
Variance (VAR). Variance is the average of the squared differences from the mean of a set of values. The variance of a set of scores is the square of the standard deviation. The variance is a measure of variability used in statistical analyses.
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