2: Mean Differences
- Page ID
- 22193
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 2.1: Inferential Statistics and Hypothesis Testing
- So far we've been using statistics to mostly describe a sample. But we can do so much more with what we've learned about probability and the Standard Normal Curve. I'll show you!
- 2.1.1: Growth Mindset
- 2.1.2: Samples and Populations Refresher
- 2.1.2.1: Can Samples Predict Populations?
- 2.1.2.2: Descriptive versus Inferential Statistics
- 2.1.3: The Research Hypothesis and the Null Hypothesis
- 2.1.4: Null Hypothesis Significance Testing
- 2.1.5: Critical Values, p-values, and Significance
- 2.1.5.1: Critical Values
- 2.1.5.2: Summary of p-values and NHST
- 2.1.6: Steps of the Hypothesis Testing Process
- 2.1.7: The Two Errors in Null Hypothesis Significance Testing
- 2.1.7.1: Power and Sample Size
- 2.1.7.2: The p-value of a Test
- 2.2: One Sample t-test
- Using what we just learned about Null Hypothesis Significance Testing, we can now test to see if our sample seems to be from the population.
- 2.2.1: Predicting a Population Mean
- 2.2.2: Introduction to One-Sample t-tests
- 2.2.3: One-Sample t-test Calculations
- 2.2.3.1: Table of Critical t-scores
- 2.2.4: Reporting Results
- 2.2.4.1: Descriptive and Inferential Calculations and Conclusion Example
- 2.2.5: Confidence Intervals
- 2.2.5.1: Practice with Confidence Interval Calculations
- 2.3: Independent Samples t-test
- But what if you want to compare two groups, not a sample to a population?
- 2.3.1: Introduction to Independent Samples t-test
- 2.3.1.1: Another way to introduce independent sample t-tests...
- 2.3.2: Independent Samples t-test Equation
- 2.3.3: Hypotheses with Two Samples
- 2.3.4: Practice! Movies and Mood
- 2.3.4.1: More Practice! Growth Mindset
- 2.3.5: When to NOT use the Independent Samples t-test
- 2.3.5.1: Non-Parametric Independent Sample t-Test
- 2.4: Dependent Samples t-test
- What do you do when your two groups are related?
- 2.5: BG ANOVA
- What do you do to compare three unrelated groups?
- 2.5.1: Why ANOVA?
- 2.5.1.1: Observing and Interpreting Variability
- 2.5.1.2: Ratio of Variability
- 2.5.2: Introduction to ANOVA's Sum of Squares
- 2.5.2.1: Summary of ANOVA Summary Table
- 2.5.3: Hypotheses in ANOVA
- 2.5.4: Practice with Job Applicants
- 2.5.4.1: Table of Critical F-Scores
- 2.5.5: Introduction to Pairwise Comparisons
- 2.5.5.1: Pairwise Comparison Post Hoc Tests for Critical Values of Mean Differences
- 2.5.6: Practice on Mindset Data
- 2.5.7: On the Relationship Between ANOVA and the Student t Test
- 2.5.8: Non-Parametric Analysis Between Multiple Groups
- 2.6: RM ANOVA
- But what if your three groups are related?
- 2.7: Factorial ANOVA (Two-Way)
- But what if you have two independent variables, each with at least two levels? What do you do then?!
- 2.7.1: Introduction to Factorial Designs
- 2.7.1.1: Factorial Notations and Square Tables
- 2.7.2: Introduction to Main Effects and Interactions
- 2.7.2.1: Example with Main Effects and Interactions
- 2.7.2.2: Graphing Main Effects and Interactions
- 2.7.2.3: Interpreting Main Effects and Interactions in Graphs
- 2.7.2.4: Interpreting Interactions- Do Main Effects Matter?
- 2.7.2.5: Interpreting Beyond 2x2 in Graphs
- 2.7.3: Two-Way ANOVA Summary Table
- 2.7.3.1: Calculating Sum of Squares for the Factorial ANOVA Summary Table
- 2.7.4: When Should You Conduct Post-Hoc Pairwise Comparisons?
- 2.7.5: Practice with a 2x2 Factorial Design- Attention
- 2.7.5.1: Practice 2x3 Factorial ANOVA on Mindset
- 2.7.6: Choosing the Correct Analysis- Mean Comparison Edition