# Module 4 Key Terms and Definitions

** α=.05: ** convention in social work, social, and behavioral sciences for decision to reject/fail to reject the null hypothesis when analyzing quantitative data.

** alternate hypothesis:** a research hypothesis phrased in terms of the statistical analysis to be performed on observed differences with quantitative data; often designated as Haor H1 (see null hypothesis for more information).

** a priori coding: ** qualitative data analysis utilizing a pre-determined set of coding categories (in contrast to open coding).

** bivariate analysis:** quantitative data analysis approaches evaluating the association or relationship between two variables.

** central tendency: ** quantitative univariate statistical approaches (e.g., mean, median, mode) that serve as indicators of how data cluster around a “common” value.

** chi-square (χ2) test:** bivariate quantitative statistical analysis for evaluating an association between two categorical variables based on the observed and expected proportions in a variable x variable contingency table; evaluated using criterion values based on the

*χ2*-distribution and degrees of freedom.

** coding: ** means of creating categories out of themes present in qualitative data for analysis.

** confidence interval (CI):** range of statistical test values that would arise by chance at the determined probability level (usually 95% confidence interval in social work, social, and behavioral science).

** context:** descriptive information in qualitative research that aides the interpretation of coded data.

** correlation:** bivariate quantitative statistical analysis for evaluating an association between two interval (continuous) variables based on the “best” fitting line for the observed data points.

** correlation coefficient (r):** the statistical value computed in correlation analysis which helps determine statistical significance, strength, and direction of the relationship between two variables.

** degrees of freedom: ** a component of many inferential statistics approaches based on a computation related to the number of cases in a data set and, depending on the statistical test, the number of groups being compared.

** descriptive statistics:** a set of univariate analysis approaches used to describe how a sample is distributed along various dimensions, particularly frequency, central tendency, and variability.

** F-statistic:** sample statistic computed using group means, standard of deviation, and both within and between group degrees of freedom; compared to criterion values based on the

*F*-distribution.

** field notes:** supplemental information in qualitative data and analysis that provide insight into the context of data collected from participants and the thinking process of the investigator analyzing the data.

** frequency:** univariate quantitative statistical information concerning how a sample distributes on a (categorical) variable or some combination of categories for multiple categorical variables (subgroups) based on the count of numbers in each group.

** histogram: ** a univariate graphing approach showing the frequency with which values appear in a sample.

** homoscedascity:** principle in quantitative data analysis involving data in relation to a “best” fitting line, reflecting how the data points cluster around that line; refers to the degree that these distances between data points and the line are similar.

** independent samples t-test:** bivariate quantitative statistical analysis for comparing mean scores (interval variable) for exactly two groups (categorical variable); evaluated using criterion values based on the

*t*-distribution and degrees of freedom.

** inferential statistics: ** set of quantitative data analysis approaches based on drawing inferences about a population based on data from a sample; these approaches have specific assumptions and limitations that need to be evaluated and addressed for accurate interpretation of the results.

** Kruskal-Wallis H test: ** a non-parametric quantitative statistical analysis used when assumptions related to normal distribution and sample size are violated; analog to the parametric one-way analysis of variance (Anova) compares rank order of data points in groups rather than actual data values and group means.

** kurtosis: ** one dimension for evaluating a sample’s distribution on an interval (continuous) variable, specifically how it meets criteria for normal distributions regarding concentration of data in the center versus tails of the distribution curve.

** mean:** univariate quantitative statistic indicating one facet of central tendency (often called “average”); particularly susceptible to distortion from outliers and small sample sizes.

** median:** univariate quantitative statistic indicating one facet of central tendency (often called “50thpercentile”); half of cases fall below and half fall above this value.

** mode:** univariate quantitative statistic indicating one facet of central tendency, represents the most common value in the data (note there may be more than one mode present).

** non-parametric tests:** inferential quantitative statistical analyses that are not dependent on assumptions of normal distribution or large sample size (in contrast to parametric tests).

** normal distribution:** distribution of values on an interval (continuous) variable that falls on a curve that is (a) symmetrical around the mean, and (b) specific proportions of cases fall within 1 standard deviation, 2 standard deviations, 3 standard deviations and more from the mean (symmetrically above and below the mean); often depicted as a “bell-shaped” graph.

** null hypothesis:** a research hypothesis phrased in terms of no statistically significant difference based on statistical analysis to be performed with quantitative data; often designated as H0 (see alternative hypothesis for more information).

** one-sample t-test:** univariate quantitative statistical analysis for comparing a group’s mean score (interval variable) to a specific standard value; evaluated using criterion values based on the

*t*-distribution and degrees of freedom.

** one-tailed test:** comparison statistic is based on probability related to one tail of the normal distribution, rather than both tails, because the hypothesis being tested is directional (more than or less than hypothesis) instead of a bidirectional “difference” hypothesis (in contrast to a two-tailed test).

** one-way analysis of variance (Anova) test:** bivariate quantitative statistical analysis for comparing mean scores (interval variable) for two or more groups (categorical variable); evaluated using the

*F*-distribution and degrees of freedom.

** open coding: ** qualitative data analysis utilizing coding categories that emerge out of the data being analyzed (in contrast to

*a priori*coding)

** outliers:** data points that are exceptionally different from the majority of cases in a sample; having potential to greatly distort central tendency measures like the mean.

** p-value:** a probability value computed in inferential quantitative statistical analyses, used to interpret statistical test values in terms of rejecting or failing to reject the null hypothesis.

** parametric tests:** inferential quantitative statistical analyses that are dependent on assumptions of normal distribution and sufficiently large sample size (in contrast to non-parametric tests).

** percentage:** univariate quantitative statistical information concerning how a sample distributes on a (categorical) variable or some combination of categories for multiple categorical variables (subgroups) calculated as the proportion of the total in each group (out of 100%).

** population parameters:** values for central tendency and variability (dispersion) for an entire population; when data are not available for the entire population, sample statistics are utilized to estimate population parameters while recognizing the probability of error in these estimates.

** probability:** a mathematical/statistical concept concerned with computing the likelihood of an event occurring; the inverse (the likelihood of an event not occurring) may also be computed; probability forms the logic basis underlying inferential statistics.

** projective test:** an observational measurement technique used to reveal internal thought processes or personality traits as individuals respond to ambiguous stimuli (words, images, objects, scenarios/situations, music, or other forms of presentation).

** proportion:** the segment or portion something represents of the whole (usually presented in fraction or percent format).

** range:** the mathematical difference between the lowest and highest values in a sample data set, or the lowest to highest possible values for a measurement tool.

** rank sum test/Wilcoxon-Mann-Whitney U test:** a non-parametric quantitative statistical analysis used when assumptions related to normal distribution and sample size are violated; analog to the parametric independent samples

*t*-test, compares rank order of data points in groups rather than actual data values and group means.

** sample statistics:** values for central tendency and variability (dispersion) for a sample of cases drawn from a whole population; when data are not available for the entire population, sample statistics are utilized to estimate population parameters while recognizing the probability of error in these estimates

** scatterplot:** a bivariate graphing approach showing data points for the paired values of each case in a sample (x-axis and y-axis reflect the values for the two variables).

** skew:** one dimension for evaluating a sample’s distribution on an interval (continuous) variable, specifically how it meets criteria for normal distributions regarding symmetry of data around the mean.

** standard deviation:** a sample statistic used to estimate population variance, computed as the square root of the sample variance.

** t-statistic:** sample statistic computed using group means and standard of deviation; compared to criterion values based on the

*t*-distribution.

** two-tailed test:** comparison statistic is based on probability related to both tails of the normal distribution because the hypothesis being tested is bidirectional (unequal) instead of a unidirectional “greater” or “less” than hypothesis (in contrast to one-tailed test).

** transcription: ** a common step in preparing qualitative data for analysis, constructing a verbatim written record of the information provided by each study participant.

** univariate analyses:** quantitative data analysis approaches evaluating data for one variable at a time (e.g., frequency, proportion, central tendency, variability/dispersion).

** variance: ** quantitative univariate computed statistical value that serves as an indicator of how values are dispersed (vary) for either a population or a sample (see standard deviation).

** verbatim: ** word-for-word reporting, in exactly the same words, to preserve the original meaning of what was originally said.

** Wilcoxon-Mann-Whitney test (U test)/rank sum test:** a non-parametric quantitative statistical analysis used when assumptions related to normal distribution and sample size are violated; analog to the parametric independent samples

*t*-test, compares rank order of data points in groups rather than actual data values and group means.