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How to Design and Evaluate Research in Education Book Cover
How to Design and Evaluate Research in Education, 5/e
Jack R. Fraenkel, San Francisco State University
Norman E. Wallen, San Francisco State University

Inferential Statistics


Analysis of covariance (ANCOVA)   A statistical technique for equating groups on one or more variables when testing for statistical significance; it adjust scores on a dependent variable for initial differences on other variables, such as pretest performance or IQ.
Analysis of variance (ANOVA)   A statistical technique for determining the statistical significance of differences among means; it can be used with two or more groups.
Chi-square test   A non parametric test of statistical significance appropriate when the data are in the form of frequency counts; it compares frequencies actually observed in a study with expected frequencies to see if they are significantly different.
Confidence interval   An interval used to estimate a parameter that is constructed in such a way that the interval has a predetermined probability of including the parameter.
Degrees of freedom   A number indicating how many instances out of a given number of instance are "free to vary" – that is, not predetermined.
Friedman two-way analysis of variance   A nonparametric inferential statistic used to compare two or more groups that are not independent.
Inferential statistics   Data analysis techniques for determining how likely it is that results based on a sample or samples are similar to results that would have been obtained for the entire population.
Kruska-Wallis one-way analysis of variance   A nonparametric inferential statistic used to compare two or more independent groups for statistical significance of differences.
Level of significance   The probability associated with a confidence interval; the probability that the interval will contain the corresponding parameter. Commonly used confidence levels in educational research are the 95 and 99 percent confidence levels.
Mann-Whitney U test   A nonparametric inferential statistic used to determine whether two uncorrelated groups differ significantly.
Multivariate analysis of covariance (MANCOVA)   An extension of analysis of covariance that incorporates two or more dependent variables in the same analysis.
Multivariate analysis of variance (MANOVA)  
Nonparametric technique  A test of statistical significance appropriate when the data represent an ordinal or nominal scale, or when assumptions required for parametric tests cannot be met.
Null hypothesis   A statement that any difference between obtained sample statistics and specified population parameters is due to sampling error, or "chance."
One-tailed test   The use of only one tail of the sampling distribution of statistic – used when a directional hypothesis is stated.
Parametric technique   A test of significance appropriate when the data represent an interval or ratio scale of measurement and other specific assumptions have been met.
Power of a statistical test   The probability that the null hypothesis will be rejected when there is a difference in the populations; the ability of a test to avoid a Type II error.
Practical significance   A difference large enough to have some practical effect. Contrast with statistical significance, which may be so small as to have no practical consequences.
Probability   The relative frequency with which a particular event occurs among all events of interest.
Research hypothesis   A prediction of study outcomes. Often a statement of the expected relationship between two or more variables.
Sampling distribution   The theoretical distribution of all possible values of a statistic from all possible samples of a given size selected from a population.
Sampling error   Expected, chance variation in sample statistics that occurs when successive samples are selected for the sample in systematic sampling.
Sign test   A nonparametric inferential statistic used to compare two groups that are not independent.
Standard error of the mean   The standard deviation of sample means that indicates by how much the sample means can be expected to differ if other samples from the same population are used.
Statistically significant   The conclusion that results are unlikely to have occurred due to sampling error or "chance;" an observed correlation or difference probably exists in the population.
t-test for means   A parametric technique for comparing two means.
t-test for r   A parametric technique for determining if there is a non-zero correlation among two variables in the population.
Two-tailed test   Use of both tails of the sampling distribution of a statistic – when a nondirectional hypothesis is stated.
Type I error   The rejection by the researcher of a null hypothesis that is actually true. Also called alpha error.
Type II error   The failure of a researcher to reject a null hypothesis that is really false. Also called beta error.
Wilk's lambda   The numerical index calculated when carrying out MANOVA or MANCOVA.