Chapter 17- Inferential Statistics

Type I error (p.408)

a error created by rejecting the null hypothesis when it is true (i.e., the researcher concludes that a relationship exists when in fact it does not-- a false positive)

null hypothesis (p.408)

a hypothesis predicting no relationship between the variables under study; used primarily in statistical testing as the hypothesis to be rejected

Friedman test (p.420)

a nonparametric analog ANOVA, used with paired-groups or repeated measures situations

Mann-Whitney U test (p.416)

a nonparametric statistic used to test the difference between two independent groups, based on ranked scores

McNemar test (p.421)

a statistical test for comparing differences in proportions when values are derived from parked (nonindependent groups)

one-tailed test (p.410)

a statistical test in which only values in one tail of a distribution are considered in determining significance; sometimes used when the researcher states a directional hypothesis

effect size (p.423)

a statistical expression of the magnitude of the relationship between two variables, or the magnitude of the difference between groups on an attribute of interest; also used in metasynthesis to characterize the salience of a theme or category

phi coefficient (p.422)

a statistical index describing the magnitude of relationship between two dichotomous variables

analysis of variance (ANOVA) (p.416)

a statistical procedure for testing mean differences among three or more groups by comparing variability between groups to variability within groups, yielding an F-ratio statistic

statistically significant (p.410)

a term indicating that the results from an analysis of sample data are unlikely to have been caused by chance, at a specified level of probability

F-ratio (p.416)

the statistic obtained in several statistical tests (e.g., ANOVA) in which variation attributable to different sources (e.g., between-group variation and within-group variation) is contrasted

confidence limits (p.406)

the upper (or lower) boundary of a confidence interval

beta (p.422)

1) in multiple regression, the standardized coefficients indicating the relative weights of the predicator variables in the equation 2) in statistical testing, the probability of Type II error

alpha (p.409)

1) in tests of statistical significance, the significance criterion-the risk the researcher is willing to accept of making a Type I error 2) in assessments of internal consistency reliability, a reliability coefficient, Cronbach's alpha

statistical tests (p.408)

a analytic tool that estimates the probability that results obtained from a sample reflect true population values

nonparametric tests (p.411)

a class of statistical tests that do not involve stringent assumptions about the distribution of critical variables

parametric tests (p.411)

a class of statistical tests that involve assumptions about the distribution of the variables and the estimation of a parameter

sampling distribution of the mean (p.404)

a theoretical distribution of a statistic, using the values of the statistic, using the values of the statistic (e.g., the means) computed from an infinite number of samples as the data points in the distribution

Bonferroni correction (p.414)

an adjustment made to establish a more conservative alpha level when multiple statistical tests are being run from the same data set; the correction is computed by dividing the desired alpha by the number of tests--for example, .05/3=.017

repeated-measures ANOVA (p.418)

an analysis of variance used when there are multiple measures of the dependent variable over time (e.g., in a crossover design)

paired t-test (p.415)

t-test for dependent groups when the means for two sets of scores are not independent groups

power (p.422)

the ability of a design or analysis strategy to detect true relationship that exist among variables

critical region (p.409)

the area in the sampling distribution representing values that are "improbably" if the null hypothesis is true

expected frequencies (p.420)

the cell frequencies that would be found if there was no relationship between the two variables

two-tailed tests (p.410)

statistical tests in which both ends of the sampling distribution are used to determine improbable values

Cramer's V (p.422)

an index describing the magnitude of relationship between nominal-level data, used when the contingency table to which it is applied is larger than 2 x 2

multifactor ANOVA (p.418)

analysis of data from studies with multiple factors

eta-squared (p.425

in ANOVA, a statistic calculated to indicate the proportion of variance in the dependent variable explained by the independent variables, analogous to R2 in multiple regression

main effects (p.418)

in a study with multiple independent variables, the effects of a single independent variable on the dependent variable

alternative research (HA) (p.408)

in hypothesis testing, a hypothesis different from the one actually being tested-- usually, different from the null hypothesis

Spearman's rank-order correlation (rho) (p.422)

a correlation coefficient indicating the magnitude of a relationship between variables measured on the ordinal scale

Kendall's tau (p.422)

a correlation coefficient used to indicate the magnitude of a relationship between ordinal-level variables

Wilcoxon signed-rank test (p.416)

a nonparametric statistical test for comparing two parked groups, based on the relative ranking of values between the pairs

Kruskal-Wallis test (p.420)

a nonparametric test used to test the difference between three or more independent groups, based on ranked scores

t-test (p.413)

a parametric statistical test for analyzing the difference between two means

power analysis (p.422)

a procedure used to estimate 1) sample size requirements prior to undertaking a study, or 2) the likelihood of committing a Type II error

test statistics (p.410)

a statistic used to test for the statistical reliability of relationships between variables (e.g., chi-squared, t); the sampling distributions of test statistics are known for circumstances in which the null hypothesis is true

degrees of freedom (p.412)

a statistical concept referring to the number of sample values free to vary (e.g., with a given sample mean, all but one value would be free to vary).

binomial distribution (p.407)

a statistical distribution with known properties describing the number of occurrences of an event in a series of observations; forms the basis for analyzing dichotomous data

Fisher's exact test (p.421)

a statistical procedure for testing the significance of differences in proportions, used when the sample size is small or cells in the contingency table have no observations

chi-square test (p.420)

a statistical test used in various contexts, often to assess differences in proportions; symbolized as X2

Cohen's d (p.423)

an effect size for comparing two group means, computed by subtracting one mean from the other and dividing by the pooled standard deviation; also called standardized mean difference or SMD

Type II error (p.409)

an error created by accepting the null hypothesis when it is false (i.e., the researcher concludes that no relationship exists when in fact it does-- a false negative)

Levene's test (p.427)

results show the equality of variances

separate variance t-test (p.427)

second row;

multiple comparison procedures (post hoc tests) (p.417)

statistical test, normally applied after an ANOVA indicated statistically significant group differences, that compare different pairs of groups; also called post hoc tests

inferential statistics (p.404)

statistics that permit inferences about whether results observed in a sample are likely to be found in the larger population

interaction effects (p.418)

the effect of two or more independent variables acting in combination (interactively) on a dependent variable

sampling error (p.404)

the fluctuation of the value of a statistic form on sample to another drawn from the same population

confidence interval (CI) (p.406)

the range of values within which a population parameter is estimated to lie, at a specified probability (e.g., 95% CI)

nonsignificant result (p.410)

the result of a statistical test indicating that group differences or an observed relationship could have occurred by chance, at a given probability level; sometimes abbreviated as NS

level of significance (p.409)

the risk of making a Type I error in a statistical analysis, with the criterion (alpha) established by the researcher beforehand (e.g., a= .05)

standard error of the mean (SEM) (p.405)

the standard deviation of a sampling distribution, such as the sampling distribution of the mean

pooled variance t-test (p.427)

top row; used when the equality of variances can be assumed

observed frequencies (p.420)

values observed in the data