Quantitative Analysis and Statistical Methods

This flashcard set covers the fundamental concepts of quantitative analysis, including levels of measurement, the distinctions between parametric and nonparametric tests, various statistical assumptions, and the interpretation of statistical outputs like p-values and effect sizes.

Quantitative Analysis

A statistics-heavy method of analyzing data that involves inferential statistics, assumptions, and determining statistical significance and effect size.

Inferential Statistics

A category of statistical tests used to make generalizations or decisions about a population based on sample data.

Parametric Statistical Tests

Robust and accurate inferential tests used primarily for interval and ratio level data that are normally distributed.

Nonparametric Statistical Tests

Inferential tests used for nominal or ordinal level data, small sample sizes, or data that are not normally distributed; they are generally considered less sensitive to detecting change.

Nominal Data

A level of measurement used to assign numbers to distinct categories or labels (e.g., 1 for aphasia, 2 for dementia) with no inherent numerical value.

Ordinal Data

A level of measurement where data are assigned to ranks or severity ratings (e.g., mild, moderate, severe), maintaining a specific order but lacking equal intervals between points.

Interval Data

A level of measurement that uses equal distances between numbers (e.g., standard scores, IQ tests) but lacks an absolute zero point.

Ratio Data

The most robust level of measurement, characterized by equal intervals and an absolute zero point, allowing for addition, subtraction, multiplication, and division (e.g., duration, frequency, pressure).

Normally Distributed Data

Data that, when plotted on a graph, form a unimodal bell curve with most scores clustered around the middle.

Kolmogorov-Smirnov Test

A statistical test used to determine whether a set of data is normally distributed.

Distribution Free

A term used to describe data that are not normally distributed, necessitating the use of nonparametric statistics.

Data Transformation

The process of tweaking or converting numbers (e.g., using square roots) to help data meet the assumption of a normal distribution so parametric tests can be used.

Homogeneity of Variance

An assumption that the amount of variability in scores is similar between different groups.

Levene's Test

A commonly used test to determine the presence of homogeneity of variance between groups.

Sample Size Assumption

The standard in the field that typically requires a sample size of $30$ or more participants to use parametric tests.

Continuous Data

A data category consisting of interval and ratio level measurements that can technically extend to infinity.

Categorical Data

A data category consisting of nominal and ordinal level measurements, which are analyzed using nonparametric tests.

Between Subjects Design

A research design that compares different groups of subjects, such as an experimental group versus a control group.

Within Subjects Design

Also called a single group design, this compares the same subjects across different conditions, such as comparing pre-test scores to post-test scores.

Independent t-test ($t$)

A parametric test used to compare the means of two independent groups on continuous data.

Chi-Square ($\text{X}^2$)

A nonparametric test of independence used for categorical data (nominal or ordinal) often involving frequency counts.

ANOVA (Analysis of Variance)

A parametric test used to determine statistical significance when comparing three or more groups or conditions.

Mann-Whitney U

A nonparametric sister test to the independent t-test used for ordinal data or when parametric assumptions like normality are violated.

Wilcoxon Test

A nonparametric test for paired data used in within-subject research designs when data are not normally distributed.

Kruskal-Wallis ($\text{H}$)

A nonparametric version of the ANOVA used to compare three or more independent groups, especially with small or unbalanced sample sizes.

Main Effect

A measurement in complex studies that indicates whether statistical significance exists anywhere among the groups or conditions before identifying exactly where.

Post Hoc Analysis

Secondary tests (e.g., Newman-Keuls, Tukey, Scheffé) conducted after finding a significant main effect to pinpoint exactly which groups differ from one another.

Calculated Value

The specific numerical result produced by a statistical test (e.g., $t = 1.12$) which is then compared against a critical value.

Critical Value

A threshold value found in statistical tables that the calculated value must exceed to establish statistical significance.

Probability Value ($p$)

Also known as the alpha level; the likelihood that the observed results occurred by chance, with $p < 0.05$ typically indicating statistical significance.

Degrees of Freedom ($df$)

A value reported in statistical results representing the latitude of variation, usually derived from the sample size ($N$).

Effect Size

A metric (e.g., Cohen's $d$) that measures practical significance, indicating whether the detected difference is meaningful enough for clinical application.