20 Glossary – Key Terms
Terms are organized by sections of the textbook
Research & Variable Terminology
| A collection of measurements or observations. | |
| datum | A single measurement or observation and is commonly called a score or raw score. |
| dependent variable | In an experiment, the variable that is observed for changes. (the scores) |
| descriptive statistics | Techniques that organize and summarize a set of data |
| discrete variable | A variable that exists in indivisible units. |
| experimental condition | A condition where the treatment is administered. |
| experimental method | A research method that manipulates one variable, observes a second variable for changes, and controls all other variables. The goal is to establish a cause-and-effect relationship. |
| independent variable | In an experiment, the variable that is manipulated by the researcher. (the treatment conditions) |
| inferential statistics | Techniques that use sample data to draw general conclusions about populations. |
| integer | whole numbers (no decimal or fraction) |
| interval scale | An ordinal scale where all the categories are intervals with exactly the same width. |
| lower real limit | The boundary that separates an interval from the next lower interval. |
| nominal scale | A measurement scale where the categories are differentiated only by qualitative names. |
| nonequivalent groups study | A research study in which the different groups of participants are formed under circumstances that do not permit the researcher to control the assignment of individuals to groups and the groups of participants are, therefore, considered nonequivalent. |
| operational definition | A procedure for measuring and defining a construct. |
| ordinal scale | A measurement scale consisting of a series of ordered categories. |
| parameter | A characteristic that describes a population. |
| population | The entire group of individuals that a researcher wishes to study. |
| pre–post study | Quasi-experimental and nonexperimental designs consisting of a series of observations made over time. The goal is to evaluate the effect of an intervening treatment or event by comparing observations made before versus after the treatment. |
| quasi-independent variable | In a quasi-experimental or nonexperimental research study, the variable that differentiates the groups or conditions being compared. Similar to the independent variable in an experiment. |
| ratio scale | An interval scale where a value of zero corresponds to none. |
| raw score | An original, unaltered measurement. |
| real limits | The boundaries separating the intervals that define the scores for a continuous variable. |
| real number | Using real data, data can be written in fraction/decimal form |
| reliability | Consistency of measure |
| sample | A group selected from a population to participate in a research study. |
| sampling error | The discrepancy between a statistic and a parameter. |
| statistic | A characteristic that describes a sample. |
| statistics | A value, usually a numerical value, that describes a sample. A statistic is usually derived from measurements of the individuals in the sample. |
| upper real limit | The boundary that separates an interval from the next higher interval. |
| validity | Authenticity of measure (face validity, construct validity, predictive validity) |
| variable | A characteristic that can change or take on different values. |
Graph, Tables, & Distribution Vocabulary
| apparent limits | The score values that appear as the lowest score and the highest score in an interval. |
| axes | The two perpendicular lines that form a bar graph. |
| bar graph | A graph showing a bar above each score or interval so that the height of the bar corresponds to the frequency. A space is left between adjacent bars. Typically used for nominal and ordinal data |
| class interval/class limit | A group of scores in a grouped frequency distribution. Groups of scores have same range (e.g., grouped by 10s) |
| cumulative frequency | Percentage of individuals with scores at or below a particular point in the distribution |
| frequency distribution | A tabulation of the number of individuals in each category on the scale of measurement. |
| grouped frequency distribution | A frequency distribution where scores are grouped into intervals rather than listed as individual values. Uses class intervals. |
| hinges | The 25% and 75% in a box plot, the top and bottom of the “box” |
| histogram | A graph showing a bar above each score or interval so that the height of the bar corresponds to the frequency and width extends to the real limits. |
| negatively skewed distribution | A distribution where the scores pile up on the right side and taper off to the left. (think your left foot) |
| normal | A specific shape that can be precisely defined by an equation. |
| outlier | An extreme score, in a boxplot it is indicated as outside the whiskers |
| percentile | Transformations of raw scores indicating placement in the distribution |
| percentile rank | Rank gives cumulative percentage |
| polygon | A graph consisting of a line that connects a series of dots. A dot is placed above each score or interval so that the height of the dot corresponds to the frequency. |
| positively skewed distribution | A distribution where the scores pile up on the left side and taper off to the right. (think your right foot) |
| range | The distance from the upper real limit of the highest score to the lower real limit of the lowest score; the total distance from the absolute highest point to the lowest point in the distribution. |
| relative frequency | The proportion of the total distribution rather than the absolute frequency. Used for population distributions for which the absolute number of individuals is not known for each category. |
| stem and leaf graph (stem plot) | Way to share specific data points and spread based on base unit (stem) and final significant digit (leaf) |
| symmetrical distribution | A distribution where the left-hand side is a mirror image of the right-hand side. |
| tail(s) of a distribution | A section on either side of a distribution where the frequency tapers down toward zero as the X values become more extreme. |
| whiskers | Vertical lines in a box plot the designate the spread of the data points. |
Descriptive Statistics Terminology
| bimodal | A distribution with two modes. |
| central tendency | A statistical measures that identifies a single score (usually a central value) to serve as a representative for the entire group. |
| line graph | A display in which points connected by straight lines show several different means obtained from different groups or treatment conditions. Also used to show different medians, proportions, or other sample statistics. |
| major mode | The taller peak of two modes with unequal frequencies. |
| median | The score that divides a distribution exactly in half. |
| minor mode | The shorter peak of two modes with unequal frequencies. |
| mode | The score with the greatest frequency overall (major), or the greatest frequency within the set of neighboring scores (minor). |
| multimodal | A distribution with more than two modes. |
| (normal) symmetrical distribution | A distribution where the left-hand side is a mirror image of the right-hand side. |
| weighted mean | The average of two means, calculated so that each mean is weighted by the number of scores it represents. |
Dispersion Measures Vocabulary
| biased statistic | A statistic that, on average, consistently tends to overestimate (or underestimate) the corresponding population parameter. |
| degrees of freedom (df) | Degrees of freedom = df = n – 1, measures the number of scores that are free to vary when computing SS for sample data. The value of df also describes how well a t statistic estimates a z-score. |
| deviation score | The distance (and direction) from the mean to a specific score. Deviation = X – μ. |
| error variance | Unexplained, unsystematic differences that are not caused by any known factor. |
| mean squared deviation | The mean squared deviation equals the population variance. Variance is the average squared distance from the mean. |
| population standard deviation (σ) | The square root of the population variance; a measure of the standard distance from the mean. |
| population variance (σ2) | The average squared distance from the mean; the mean of the squared deviations. |
| range | The distance from the upper real limit of the highest score to the lower real limit of the lowest score; the total distance from the absolute highest point to the lowest point in the distribution. |
| sample standard deviation (s) | The square root of the sample variance. |
| sample variance (s2) | The sum of the squared deviations divided by df = n – 1. An unbiased estimate of the population variance. |
| sum of squares (SS) | The sum of the squared deviation scores. |
| unbiased statistic | A statistic that, on average, provides an accurate estimate of the corresponding population parameter. The sample mean and sample variance are unbiased statistics. |
Z-score & more Terminology
| z-score | standardized version for raw score. calculated knowing the x-value, mean and standard deviation. |
| Empirical Rule | 68-98-99
68% of all scores within 1 standard deviation of the mean; 95% of all scores within 2 standard deviations of the mean; 99% of all scores within 3 standard deviations of the mean; |
| (normal) symmetrical distribution | A distribution where the left-hand side is a mirror image of the right-hand side. “Gaussian curve” |
| probability | expected relative frequency value of a particular outcome |
| relative frequency | number of times an event/outcome takes place relative to the number of times it could have taken place |
| probability in normal distributions | connected to area under the normal curve, can also interpret as percentage of total who fall into that event/outcome |
| probability distribution | describes probability of all possible outcomes for an activity |
| percentile | transformation of proportion where proportion is decimals and percentage is multiplying by 100 to get a % |
| z – distribution | Standardized Unit Normal table aka unit normal table, indicates area for associated z-score |
| body of distribution | typically area that includes the mean area shaded |
| tail of distribution | typically the smaller region shaded |
| gamblers fallacy | |
| random sampling | every person in population/group has equal chance of being selected |
| statistical independence | two outcomes/variables are unrelated and unique |
| odds ratio | how likely will an event/outcome occur |
| law of large numbers | as a sample size grows, its mean gets closer to the average of the whole population |
| Central Limit Theorem | The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. |
| Distribution of Sample Means | The distribution of sample means is defined as the set of means from all the possible random samples of a specific size (n) selected from a specific population. |
| sampling error | A sampling error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data. As a result, the results found in the sample do not represent the results that would be obtained from the entire population. |
| standard error of the mean | considered the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population. |
t-test terminology
| between-subjects research design | An alternative term for an independent-measures design. |
| dependent t-test | In a within-in subjects design, a hypothesis test that evaluates the statistical significance of the mean difference between two scores from the same set of participants. AKA paired t-test |
| difference scores | The difference between two measurements obtained for a single subject. D = X2 – X1 |
| homogeneity of variance | An assumption that the two populations from which the samples were obtained have equal variances. |
| independent-measures t statistic | In a between-subjects design, a hypothesis test that evaluates the statistical significance of the mean difference between two separate groups of participants. |
| independent-measures research design | A research design that uses a separate sample for each treatment condition or each population being compared. |
| individual differences | The naturally occurring differences from one individual to another that may cause the individuals to have different scores. |
| matched-subjects design | A research study where the individuals in one sample are matched one-to-one with the individuals in a second sample. The matching is based on a variable considered relevant to the study. |
| order effects | The effects of participating in one treatment that may influence the scores in the following treatment. |
| pooled variance | A single measure of sample variance that is obtained by averaging two sample variances. It is a weighted mean of the two variances. |
| related-samples designs | Two research designs that are statistically equivalent. The scores in one set are directly related, one-to-one, with the scores in the second set. |
| repeated-measures research design | A research design in which the different groups of scores are all obtained from the same group of participants. Also known as within-subjects design. |
| within-subjects research design | A research design in which the different groups of scores are all obtained from the same group of participants. Also known as repeated-measures design. |
ANOVA vocabulary
| F-ratio | The test statistic for analysis of variance is called an F-ratio and compares the differences (variance) between treatments with the differences (variance) that are expected by chance. |
| analysis of variance (ANOVA) | A hypothesis-testing procedure that is used to evaluate mean differences between two or more treatments (or populations). |
| ANOVA summary table | A table that shows the source of variability (between treatments, within treatments, and total variability), SS, df, MS, and F. |
| between-treatments variance | Values used to measure and describe the differences between treatments (mean differences). |
| distribution of F-ratios | All of the possible F values when Ho is true. |
| error term (within-subjects variance) | For ANOVA, the denominator of the F-ratio is called the error term. The error term provides a measure of the variance caused by random, unsystematic differences. When the treatment effect is zero (H0 is true), the error term measures the same sources of variance as the numerator of the F-ratio, so the value of the F-ratio is expected to be nearly equal to 1.00. |
| eta squared | A measure of effect size based on the percentage of variance accounted for by the sample mean differences. |
| experimentwise alpha level | The risk of a Type I error that accumulates as you do more and more separate tests. |
| factor | In analysis of variance, an independent variable (or quasi-independent variable) is called a factor. |
| G | Grand Mean (mean of all scores) |
| interaction | unique relationship between 2 factors with two-way ANOVA |
| interactive plot | graph of interaction for 2-way ANOVA |
| k | number of groups/levels/conditions/treatments |
| levels | In an experiment, the different values of the independent variable selected to create and define the treatment conditions. In other research studies, the different values of a factor. AKA groups/conditions/treatments |
| mean square (MS) | In analysis of variance, a sample variance is called a mean square or MS, indicating that variance measures the mean of the squared deviations. |
| mixed design | Factorial ANOVA – 1 factor is between group and 1 factor is within group/repeated measure |
| n | samples size for level/conditon/treatment/group |
| N | total sample |
| pairwise comparisons | To go back through the data and compare the individual treatments two at a time. |
| post hoc tests | A test that is conducted after an ANOVA with more than two treatment conditions where the null hypothesis was rejected. The purpose of post hoc tests is to determine exactly which treatment conditions are significantly different. |
| Scheffe test | A test that uses an F-ratio to evaluate the significance of the difference between any two treatment conditions. One of the safest of all possible post hoc tests. |
| T | sum of scores for each level/condition/treatment/group |
| testwise alpha level | Systematic differences that are caused by changing treatment conditions. |
| Tukey’s HSD test | A test that allows you to compute a single value that determines the minimum difference between treatment means that is necessary for significance. A commonly used post hoc test. |
| within-treatments variance | The differences that exist inside each treatment condition. |
Correlation and Regression Terminology
| Y-intercept | The value of Y when X = 0. In the linear equation, the value of a. |
| analysis of regression | Evaluating the significance of a regression equation by computing an F-ratio comparing the predicted variance (MS) in the numerator and the unpredicted variance (MS) in the denominator. |
| coefficient of determination | The degree to the variability in one variable can be predicted by its relationship with another variable: determination measured by r2. |
| correlation | A statistical value that measures and describes the direction and degree of relationship between two variables. The sign (+/–) indicates the direction of the relationship. The numerical value (0.0 to 1.0) indicates the strength or consistency of the relationship. The type (Pearson or Spearman) indicates the form of the relationship. Also known as correlation coefficient. |
| correlation matrix | A table that shows the results from multiple correlations and uses footnotes to indicate which correlations are significant. |
| dichotomous variable | A variable with only two values. Also called a binomial variable. |
| linear equation | An equation of the form Y = bX + a expressing the relationship between two variables X and Y. |
| linear relationship | A relationship between two variables where a specific increase in one variable is always accompanied by a specific increase (or decrease) in the other variable. |
| negative correlation | A relationship between two variables where increases in one variable tend to be accompanied by decreases in the other variable. |
| partial correlation | A partial correlation measures the relationship between two variables while controlling the influence of a third variable by holding it constant. |
| Pearson correlation | A measure of the direction and degree of linear relationship between two variables. |
| perfect correlation | A relationship where the actual data points perfectly fit the specific form being measured. For a Pearson correlation, the data points fit perfectly on a straight line. |
| phi-coefficient | A correlation between two variables both of which are dichotomous |
| point-biserial correlation | A correlation between two variables where one of the variables is dichotomous. |
| positive correlation | A relationship between two variables where increases in one variable tend to be accompanied by increases in the other variable. |
| residual | Error between the predicted and actual Y values, used in least-squares to build regression line |
Chi-Square Terminology
| chi-square distribution | The theoretical distribution of chi-square values that would be obtained if the null hypothesis was true. |
| chi-square statistic | A test statistic that evaluates the discrepancy between a set of observed frequencies and a set of expected frequencies. |
| chi-square test for goodness-of-fit | A test that uses the proportions found in sample data to test a hypothesis about the corresponding proportions in the general population. |
| chi-square test for independence | A test that uses the frequencies found in sample data to test a hypothesis about the relationship between two variables in the population. |
| Cramér’s V | A modification of the phi-coefficient to be used when one or both variables consist of more than two categories |
| contingency table | Also called crosstabs. Identifies frequencies for each level of the variable(s) |
| distribution-free test | Also called a nonparametric test. A test that does not test hypotheses about parameters or make assumptions about parameters. The data usually consist of frequencies. |
| expected frequencies | Hypothetical, ideal frequencies that are predicted from the null hypothesis. |
| nonparametric test | A test that does not test hypotheses about parameters or make assumptions about parameters. The data usually consist of frequencies. |
| observed frequencies | The actual frequencies that are found in the sample data. |
| parametric test | A test evaluating hypotheses about population parameters and making assumptions about parameters. Also, a test requiring numerical scores. |
| phi-coefficient | A correlational measure of relationship when both variables consist of exactly two categories. A measure of effect size for the test for independence. |
