11: T-tests
- Page ID
- 57577
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)By the end of this chapter, you will be able to:
- Know when to use a t-test
- Understand the design setup for a t-test
- Interpret a t-test result
- Read a journal article that uses t-tests
Key Terms
- Assumptions of a t-test
- T-test as a ratio
And here is your first inferential statistics test: the independent t-test. The purpose of the independent t-test is to test if the means of two groups are the same or different. You are trying to detect if one group is higher or lower than the other, or if the two groups are similar.
- 11.1: When to Use the Independent T-test
- This page discusses the t-test as a statistical method for comparing means between two groups, highlighting the importance of data visualization. It explains that figures can indicate similarities or differences between groups, but emphasizes that numerical results from the t-test are required to demonstrate statistical significance.
- 11.2: Design Set Up
- This page explains the three essential components of setting up a design: independent variables (categorical groups like males vs. females), dependent variables (continuous measures such as income levels), and hypotheses (including null and alternative hypotheses regarding group means).
- 11.3: Commentary
- This page addresses misconceptions about t-tests in statistics, noting their importance in comparing two groups and the complexities of group categorization. It emphasizes the need for clear conceptualization and caution against oversimplification, stressing the significance of maintaining demographic equivalence and careful group assignments.
- 11.4: T-test Assumptions
- This page discusses the importance of assumptions in statistical tests, particularly the homogeneity of variance for valid results. Levene’s test is introduced as a method to check this assumption, with significant results indicating unreliability. The t-test is noted for its robustness despite some violations, although caution is advised. An ideal sample size is approximately 30 per group to maintain reliability, and imbalances can compromise findings.
- 11.5: Reading T-tests
- This page explains t-tests in statistical analyses, focusing on interpreting significance through t-test and p-values. A t-test is significant if the t-test value surpasses 1.96 and the p-value is below .05. It underscores the importance of the true variance to error variance ratio and suggests prioritizing p-values over t-values.
- 11.6: T-Tests You Need to Know for the Examination for Professional Practice in Psychology (EPPP) Licensing Exam
- This page explains three types of Student t-tests: single sample, independent samples, and correlated samples (paired t-test). It also discusses two correlation types: point biserial (true dichotomy) and biserial (artificial dichotomy). Despite differences in group definition, both correlations can produce similar outcomes.
- 11.7: Reading Articles That Involve a T-test
- This page offers guidance on effectively reading statistical articles that employ t-tests. It stresses understanding the research question, outlining hypotheses, and correctly interpreting results while focusing on the data. Key advice includes avoiding criticism of methods and complex interpretations, and emphasizing conceptual thinking about variable relationships.
- 11.8: Reading T-tests from Journal Articles
- This page discusses a study by Conrad et al. (2017) examining gender differences in psychiatric behaviors among non-incarcerated youth, particularly noting an increase in female juvenile participation. Findings show significant differences in mental health symptoms and sexual behaviors between genders, with girls exhibiting more internalizing issues. The study emphasizes the need for tailored interventions and acknowledges concerns about sample size and statistical power in correlating results.
- 11.9: Summary
- This page discusses T-tests, which are used to evaluate mean differences between two groups. While they may seem simple for individual analyses, they are essential for more extensive statistical evaluations.
- 11.10: Discussion Questions
- This page discusses the t-test, a statistical method used to compare the means of two groups. It covers variations in differences, effect sizes, and confidence intervals while highlighting the assumptions of normality, independence, and homogeneity of variance. Additionally, it emphasizes the importance of evaluating research questions, methodologies, results, assumptions, and implications when reading journal articles that utilize t-tests.