| Inferential statistics | Statistical procedures used to infer a characteristic of a population based on certain properties of a sample drawn from that population.
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| Standard error of the mean | An estimate of the amount of variability in expected sample means across a series of samples. It provides an estimate of the deviation between a sample mean and the underlying population mean.
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| Degrees of freedom (df) | The number of scores that are free to vary in a distribution of a given size having a known mean.
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| Type I error | Deciding to reject the null hypothesis when, in fact, the null hypothesis is true. Also referred to as an alpha error.
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| Type II error | Deciding not to reject the null hypothesis when, in fact, the null hypothesis is false. Also referred to as a beta error.
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| Alpha level | The probability of obtaining a difference at least as large as the one actually obtained, given that the difference occurred purely as a result of chance factors. By convention, the maximum acceptable alpha level of .05 (5 chances in 100 or 1 change in 20).
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| Critical region | Portion of the sample distribution of a statistic within which observed values of the statistic are considered to be statistically significant. Usually the 5 percent of cases found in the upper and/or lower tail(s) of the distribution.
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| t test | An inferential statistic used to evaluate the reliability of a difference between two means. Versions exist for between-subjects and within-subjects designs and for evaluating a difference between a sample mean and a population mean.
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| t test for independent samples | A parametric inferential statistic used to compare the means of two independent, random samples in order to assess the probability that the two samples came from populations having the same mean.
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| t test for correlated samples | A parametric inferential statistic used to compare the means of two samples in a matched-pairs or within-subjects design in order to assess the probability that the two samples came from populations having the same mean.
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| z test for the difference between two proportions | A parametric inferential statistic used to determine the probability that two independent, random samples came from populations having the same proportion of “successes” (for example, persons favoring a particular candidate).
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| Analysis of variance (ANOVA) | An inferential statistic used to evaluate data from experiments with more than two levels of an independent variable or data from multifactor experiments. Versions are available for between-subjects and within-subjects designs.
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| F ratio | The test statistic computed when using an analysis of variance. It is the ratio of the between-groups variance and within-groups variance.
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| p value | In a statistical test, the probability, estimated from the data, that an observed difference in sample values arose through sampling error. p must be less than or equal to the chosen alpha level for the difference to be statistically significant/
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| Planned comparisons | Hypothesis-directed statistical tests made after finding statistical significance with an overall statistical test (such as ANOVA).
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| Unplanned comparisons | Comparison between means that is not directed by your hypothesis and is made after finding statistical significance with an overall statistical test (such as ANOVA).
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| Per-comparison error | The alpha level for each of any multiple comparisons made among means.
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| Familywise error | The likelihood of making at least one Type I error across a number of comparisons.
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| Analysis of covariance (ANCOVA) | Variant of the analysis of variance used to analyze data from experiments that include a correlational variable (covariate).
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| Chi-square | Nonparametric inferential statistic used to evaluate the relationship between variables measured on a nominal scale.
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| Mann—Whitney U test | Nonparametric inferential statistic used to evaluate data from a two-group experiment in which the dependent variable was measured along at least an ordinal scale. It can also be used on interval or ratio data if the data do not meet the assumptions of the t test for independent samples.
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| Wilcoxon signed ranks test | A nonparametric statistical test that can be used when the assumptions of the t test for correlated samples are seriously violated.
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| Power | The ability of an experimental design or inferential statistic to detect an effect of a variable when one is present.
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| Effect size | The amount by which a given experimental manipulation changes the value of the dependent variable in the population, expressed in standard deviation units.
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| Data transformation | Mathematical operation applied to raw data, such as taking the square root or arcsine of the original scores in a distribution. Often applied to data that violate the assumptions of parametric statistical tests, to help them meet those assumptions.
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