Skip to content

Commit

Permalink
fully render website to remove old doc files
Browse files Browse the repository at this point in the history
  • Loading branch information
atheobold committed Mar 20, 2024
1 parent f49336b commit 0f8be3a
Show file tree
Hide file tree
Showing 231 changed files with 10,546 additions and 24,309 deletions.
8 changes: 5 additions & 3 deletions _freeze/weeks/week-9/execute-results/html.json
Original file line number Diff line number Diff line change
@@ -1,9 +1,11 @@
{
"hash": "66b8828aa8f6cb3171e3aa91a40443f5",
"hash": "8339fd2aac3f8ccc23420f0545dabd80",
"result": {
"engine": "knitr",
"markdown": "---\ntitle: \"Week 9: Inference for Many Means (ANOVA)\"\nformat: \n html: \n number-sections: true\n number-depth: 2\n section-divs: true\neditor: visual\nexecute: \n echo: true\n warning: false\n message: false\n---\n\n\n\n\nWelcome!\n\nIn this week's coursework we are transitioning into our last topic of the quarter---comparing multiple means. These comparisons have a specific name, ANalysis of VAriance (ANOVA).\n\nWe are going to use all of the simulation-based methods we learned previously for this new context. An ANOVA relies on a new statistic, the $F$-statistic, to summarize how different 3 or more means are from each other.\n\nThe primary focus of an ANOVA is to detect if the means of 3 or more groups are different. Because of this we focus on hypothesis tests for a difference in the group means and **do not** use confidence intervals. We will generate permutation distributions of $F$-statistics that we could have observed **if the null hypothesis was true** (there is no difference in the group means).\n\n## Learning Outcomes\n\nBy the end of this coursework you should be able to:\n\n- describe what an ANOVA tests for\n\n- use a visualization to outline how the following are calculated:\n\n - total sum of squares\n - group sum of squares\n - residual sum of squares\n\n- describe why the mean squares of groups is called the \"between group variability\"\n\n- describe why the mean square error is called the \"within group variability\"\n\n- outline how an F-statistic is calculated\n\n- explain what a \"large\" or a \"small\" F-statistic indicates\n\n- describe the conditions for performing an ANOVA procedure\n\n- outline when it is appropriate to use an $F$-distribution in an ANOVA\n\n- explain the similarities and differences between parametric ($F$-based) methods and non-parametric (simulation-based) methods\n\n- use R to:\n\n - generate a permutation distribution for F-statistics\n - visualize the permutation distribution\n - calculate the observed F-statistic statistic\n - calculate a p-value for a hypothesis test\n\n# Prepare\n\n## Textbook Reading\n\n::: column-margin\n\n::: {.cell}\n::: {.cell-output-display}\n![](../images/ims.jpeg){width=50%}\n:::\n:::\n\n:::\n\n[**Required Reading:** Inference for Comparing Many Means](https://openintro-ims.netlify.app/inference-many-means.html)\n\n### Reading Guide -- Due Monday by the start of class\n\n[Download the Word Document](reading-guide/week9-reading.docx)\n\n## Concept Quiz -- Due Monday by the start of class\n\n1. Which of the following are true about the mean squares between groups? (Select all that apply)\n\n- it is a standardized measure of the variability in responses between groups\n- it compares the mean of each group to the overall mean across all groups\n- it compares the observations within each group to the mean of that group\n- it is used as the numerator in an F-statistic\n- it is used as the denominator in an F-statistic\n- it is found by dividing the sum of squares between groups by the number of groups minus 1 ($k$ - 1)\n- it is found by dividing the sum of squares between groups by the sample size minus the number of groups ($n - k$)\n\n2. Which of the following are true about the mean square errors? (Select all that apply)\n\n- it is a standardized measure of the variability in responses within each group\n- it compares the mean of each group to the overall mean across all groups\n- it compares the observations within each group to the mean of that group\n- it is used as the numerator in an F-statistic\n- it is used as the denominator in an F-statistic\n- it is found by dividing the sum of square errors by the number of groups minus 1 ($k$ - 1)\n- it is found by dividing the sum of square errors by the sample size minus the number of groups ($n - k$)\n\n3. An F-statistic uses which formula?\n\n- $\\frac{MSG}{MSE}$\n\n- $\\frac{SSG}{SSE}$\n\n- $\\frac{MSE}{MSG}$\n\n- $\\frac{SSE}{SSG}$\n\n4. Ideally, in an ANOVA we'd like to see... (select all that apply)\n\n- large variability in the means of the groups\n- small variability in the means of the groups\n- large variability in the observations within each group\n- small variability in the observations within each group\n\n5. If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a 5% significance level, then... (select all that apply)\n\n- we can then conclude that all the means are different from one another.\n\n- the variability between groups is higher than the variability within groups.\n\n- the pairwise analysis will identify at least one pair of means that are significantly different.\n\n- an appropriate $\\alpha$ to be used in pairwise comparisons is $\\frac{0.05}{4} = 0.0125$ since there are four groups.\n\n6. True or false, as the total sample size increases, the degrees of freedom for the residuals increases.\n\n7. True or false, the constant variance condition can be somewhat relaxed when the sample sizes are large.\n\n8. True or false, the independence assumption can be relaxed when the total sample size is large.\n\n9. True or false, the normality condition is very important when the sample sizes of each group are small.\n\n## R Tutorial -- Due Wednesday by the start of class\n\n[**Required Tutorial:** Comparing many means with ANOVA](https://openintro.shinyapps.io/ims-05-infer-08/)\n",
"supporting": [],
"markdown": "---\ntitle: \"Week 9: Inference for Many Means (ANOVA)\"\nformat: \n html: \n number-sections: true\n number-depth: 2\n section-divs: true\neditor: visual\nexecute: \n echo: true\n warning: false\n message: false\n---\n\n\n\n\nWelcome!\n\nIn this week's coursework we are transitioning into our last topic of the quarter---comparing multiple means. These comparisons have a specific name, ANalysis of VAriance (ANOVA).\n\nWe are going to use all of the simulation-based methods we learned previously for this new context. An ANOVA relies on a new statistic, the $F$-statistic, to summarize how different 3 or more means are from each other.\n\nThe primary focus of an ANOVA is to detect if the means of 3 or more groups are different. Because of this we focus on hypothesis tests for a difference in the group means and **do not** use confidence intervals. We will generate permutation distributions of $F$-statistics that we could have observed **if the null hypothesis was true** (there is no difference in the group means).\n\n## Learning Outcomes\n\nBy the end of this coursework you should be able to:\n\n- describe what an ANOVA tests for\n\n- use a visualization to outline how the following are calculated:\n\n - total sum of squares\n - group sum of squares\n - residual sum of squares\n\n- describe why the mean squares of groups is called the \"between group variability\"\n\n- describe why the mean square error is called the \"within group variability\"\n\n- outline how an F-statistic is calculated\n\n- explain what a \"large\" or a \"small\" F-statistic indicates\n\n- describe the conditions for performing an ANOVA procedure\n\n- outline when it is appropriate to use an $F$-distribution in an ANOVA\n\n- explain the similarities and differences between parametric ($F$-based) methods and non-parametric (simulation-based) methods\n\n- use R to:\n\n - generate a permutation distribution for F-statistics\n - visualize the permutation distribution\n - calculate the observed F-statistic statistic\n - calculate a p-value for a hypothesis test\n\n# Prepare\n\n## Textbook Reading\n\n::: column-margin\n\n::: {.cell}\n::: {.cell-output-display}\n![](../images/ims.jpeg){width=50%}\n:::\n:::\n\n:::\n\n[**Required Reading:** Inference for Comparing Many Means](https://openintro-ims.netlify.app/inference-many-means.html)\n\n### Reading Guide -- Due Monday by the start of class\n\n[Download the Word Document](reading-guide/week9-reading.docx)\n\n## Concept Quiz -- Due Monday by the start of class\n\n1. Which of the following are true about the mean squares between groups? (Select all that apply)\n\n- it is a standardized measure of the variability in responses between groups\n- it compares the mean of each group to the overall mean across all groups\n- it compares the observations within each group to the mean of that group\n- it is used as the numerator in an F-statistic\n- it is used as the denominator in an F-statistic\n- it is found by dividing the sum of squares between groups by the number of groups minus 1 ($k$ - 1)\n- it is found by dividing the sum of squares between groups by the sample size minus the number of groups ($n - k$)\n\n2. Which of the following are true about the mean square errors? (Select all that apply)\n\n- it is a standardized measure of the variability in responses within each group\n- it compares the mean of each group to the overall mean across all groups\n- it compares the observations within each group to the mean of that group\n- it is used as the numerator in an F-statistic\n- it is used as the denominator in an F-statistic\n- it is found by dividing the sum of square errors by the number of groups minus 1 ($k$ - 1)\n- it is found by dividing the sum of square errors by the sample size minus the number of groups ($n - k$)\n\n3. An F-statistic uses which formula?\n\n- $\\frac{MSG}{MSE}$\n\n- $\\frac{SSG}{SSE}$\n\n- $\\frac{MSE}{MSG}$\n\n- $\\frac{SSE}{SSG}$\n\n4. Ideally, in an ANOVA we'd like to see... (select all that apply)\n\n- large differences in the means of the groups\n- small differences in the means of the groups\n- large variability in the observations within each group\n- small variability in the observations within each group\n\n5. If the null hypothesis that the means of four groups are all the same is rejected using ANOVA at a 5% significance level, then... (select all that apply)\n\n- we can then conclude that all the means are different from one another.\n\n- the variability between groups is higher than the variability within groups.\n\n- we can then conclude that at least one mean is different from the others.\n\n- the pairwise analysis will identify at least one pair of means that are significantly different.\n\n- an appropriate $\\alpha$ to be used in pairwise comparisons is $\\frac{0.05}{4} = 0.0125$ since there are four groups.\n\n6. True or false, as the total sample size increases, the degrees of freedom for the residuals increases.\n\n7. True or false, the constant variance condition can be somewhat relaxed when the sample sizes are large.\n\n8. True or false, the independence assumption can be relaxed when the total sample size is large.\n\n9. True or false, the normality condition is very important when the sample sizes of each group are small.\n\n## R Tutorial -- Due Wednesday by the start of class\n\n[**Required Tutorial:** Comparing many means with ANOVA](https://openintro.shinyapps.io/ims-05-infer-08/)\n",
"supporting": [
"week-9_files"
],
"filters": [
"rmarkdown/pagebreak.lua"
],
Expand Down
6 changes: 3 additions & 3 deletions docs/LICENSE.html
Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">


<title>STAT 313 / 513 - Winter 2024</title>
<title>STAT 313 / 513</title>
<style>
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
Expand Down Expand Up @@ -97,7 +97,7 @@
</a>
<div class="sidebar-tools-main tools-wide">
<a href="https://github.com/atheobold/stat-313-website" title="GitHub organization" class="quarto-navigation-tool px-1" aria-label="GitHub organization"><i class="bi bi-github"></i></a>
<a href="https://posit.cloud/spaces/352796/join?access_code=1UXvC0avaZPdFlXCzQUZqFAUdLgGFehApPhyVxjo" title="" class="quarto-navigation-tool px-1" aria-label="RStudio Cloud"><i class="bi bi-cloud-fill"></i></a>
<a href="https://posit.cloud/" title="" class="quarto-navigation-tool px-1" aria-label="RStudio Cloud"><i class="bi bi-cloud-fill"></i></a>
<a href="https://canvas.calpoly.edu" title="Cal Poly Canvas" class="quarto-navigation-tool px-1" aria-label="Cal Poly Canvas"><i class="bi bi-person-fill"></i></a>
</div>
</div>
Expand Down Expand Up @@ -271,7 +271,7 @@
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./weeks/week-9.Rmd" class="sidebar-item-text sidebar-link">
<a href="./weeks/week-9.html" class="sidebar-item-text sidebar-link">
<span class="menu-text">Week 9</span></a>
</div>
</li>
Expand Down
Loading

0 comments on commit 0f8be3a

Please sign in to comment.