Topic Modeling Badge

LASER Institute TM Learning Lab 3

The final activity for each learning lab provides space to work with data and to reflect on how the concepts and techniques introduced in each lab might apply to your own research.

To earn a badge for each lab, you are required to respond to a set of prompts for two parts: 

• In Part I, you will reflect on your understanding of key concepts and begin to think about potential next steps for your own study.

• In Part II, you will create a simple data product in R that demonstrates your ability to apply a data analysis technique introduced in this learning lab.

Part I: Reflect and Plan

Use the institutional library (e.g. NCSU Library), Google Scholar or search engine to locate a research article, presentation, or resource that applies text mining to an educational context or topic of interest. More specifically, locate a text mining study that visualize text data.

1. Provide an APA citation for your selected study.

   • Agrawal, R., Wankhede, V. A., Kumar, A., Luthra, S., Majumdar, A., & Kazancoglu, Y. (2021). An exploratory state-of-the-art review of artificial intelligence applications in circular economy using structural topic modeling. Operations Management Research, 1-18.

2. How does topic modeling address research questions?

   • A text mining approach, known as Structural Topic Modeling (STM), was used to generate different thematic topics of AI applications in CE. Each generated topic was then discussed with shortlisted articles.

Draft a research question for a population you may be interested in studying, or that would be of interest to educational researchers, and that would require the collection of text data and answer the following questions:

What are the trends of positive psychology in education?

1. What text data would need to be collected?

   • May be collect Literature to conduct a systematic literature review, so I can use the text-mining to ananlyze the main topics.

2. For what reason would text data need to be collected in order to address this question?

   • Since I hope to know the main trends in this field, I need to gather a big number of literature.

3. Explain the analytical level at which these text data would need to be collected and analyzed.

   • To the topics level.

Part II: Data Product

Use your case study file to try a small number of topics (e.g., 3) or a large number of topics (e.g., 30) and explain how changing number of topics shape the way you interpret results.

#: I find that the more topics I set, I got more specific topics and might need more summary for my findings. The smaller number of topics I set, I got more broad topics, under which I might find sub-topics as needed.

I highly recommend creating a new R script in your lab-3 folder to complete this task. When your code is ready to share, use the code chunk below to share the final code for your model and answer the questions that follow.

# YOUR FINAL CODE HERE
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.2     ✔ readr     2.1.4
## ✔ forcats   1.0.0     ✔ stringr   1.5.0
## ✔ ggplot2   3.4.2     ✔ tibble    3.2.1
## ✔ lubridate 1.9.2     ✔ tidyr     1.3.0
## ✔ purrr     1.0.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(tidytext)
library(SnowballC)
library(topicmodels)
library(stm)

## stm v1.3.6 successfully loaded. See ?stm for help. 
##  Papers, resources, and other materials at structuraltopicmodel.com

library(ldatuning)
library(knitr)
library(LDAvis)

ts_forum_data <- read_csv("data/ts_forum_data.csv", 
                          col_types = cols(course_id = col_character(),
                                           forum_id = col_character(), 
                                           discussion_id = col_character(), 
                                           post_id = col_character()
                          )
                          
            
)
forums_tidy <- ts_forum_data %>%
  unnest_tokens(output = word, input = post_content) %>%
  anti_join(stop_words, by = "word")

forums_tidy

## # A tibble: 192,160 × 14
##    course_id course_name       forum_id forum_name discussion_id discussion_name
##    <chr>     <chr>             <chr>    <chr>      <chr>         <chr>          
##  1 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  2 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  3 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  4 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  5 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  6 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  7 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  8 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  9 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
## 10 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
## # ℹ 192,150 more rows
## # ℹ 8 more variables: discussion_creator <dbl>, discussion_poster <dbl>,
## #   discussion_reference <chr>, parent_id <dbl>, post_date <chr>,
## #   post_id <chr>, post_title <chr>, word <chr>

forums_tidy %>%
  count(word, sort = TRUE)

## # A tibble: 13,620 × 2
##    word           n
##    <chr>      <int>
##  1 students    6841
##  2 data        4365
##  3 statistics  3103
##  4 school      1488
##  5 questions   1470
##  6 class       1426
##  7 font        1311
##  8 span        1267
##  9 time        1253
## 10 style       1150
## # ℹ 13,610 more rows

forum_quotes <- ts_forum_data %>%
  select(post_content) %>% 
  filter(grepl('time', post_content))

sample_n(forum_quotes,10)

## # A tibble: 10 × 1
##    post_content                                                                 
##    <chr>                                                                        
##  1 "I too struggle with how to engage students meaningfully and then assess the…
##  2 "i was not confident that very confident i teaching statistics when joined t…
##  3 "I think that this activity is one that can be used multiple times throughou…
##  4 "I was also thinking along these same lines. I think this is a great way tha…
##  5 "I also filled out the survey to get access  but just recently had time to e…
##  6 "I had used the census at school website in my class before  and I am excite…
##  7 "I agree with this comment.  Sometimes time constraints limit our ability to…
##  8 "I think the task that would be most engaging with my students would probabl…
##  9 "Based on a discussion staerted in UNit 2 INvestigate &amp; Discuss about th…
## 10 "I like the idea of comparing TV time and study time and/or grades"

forums_dtm <- forums_tidy %>%
  count(post_id, word) %>%
  cast_dtm(post_id, word, n)

class(forums_dtm)

## [1] "DocumentTermMatrix"    "simple_triplet_matrix"

forums_dtm

## <<DocumentTermMatrix (documents: 5766, terms: 13620)>>
## Non-/sparse entries: 142641/78390279
## Sparsity           : 100%
## Maximal term length: NA
## Weighting          : term frequency (tf)

temp <- textProcessor(ts_forum_data$post_content, 
                      metadata = ts_forum_data,  
                      lowercase=TRUE, 
                      removestopwords=TRUE, 
                      removenumbers=TRUE,  
                      removepunctuation=TRUE, 
                      wordLengths=c(3,Inf),
                      stem=TRUE,
                      onlycharacter= FALSE, 
                      striphtml=TRUE, 
                      customstopwords=NULL)

## Building corpus... 
## Converting to Lower Case... 
## Removing punctuation... 
## Removing stopwords... 
## Removing numbers... 
## Stemming... 
## Creating Output...

meta <- temp$meta
vocab <- temp$vocab
docs <- temp$documents

stemmed_forums <- ts_forum_data %>%
  unnest_tokens(output = word, input = post_content) %>%
  anti_join(stop_words, by = "word") %>%
  mutate(stem = wordStem(word))

stemmed_forums

## # A tibble: 192,160 × 15
##    course_id course_name       forum_id forum_name discussion_id discussion_name
##    <chr>     <chr>             <chr>    <chr>      <chr>         <chr>          
##  1 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  2 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  3 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  4 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  5 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  6 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  7 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  8 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
##  9 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
## 10 9         Teaching Statist… 126      Investiga… 6822          Not much compa…
## # ℹ 192,150 more rows
## # ℹ 9 more variables: discussion_creator <dbl>, discussion_poster <dbl>,
## #   discussion_reference <chr>, parent_id <dbl>, post_date <chr>,
## #   post_id <chr>, post_title <chr>, word <chr>, stem <chr>

stemmed_dtm <- ts_forum_data %>%
  unnest_tokens(output = word, input = post_content) %>%
  anti_join(stop_words, by = "word") %>%
  mutate(stem = wordStem(word))

stem_counts <- ts_forum_data %>%
  unnest_tokens(output = word, input = post_content) %>%
  anti_join(stop_words, by = "word") %>%
  mutate(stem = wordStem(word)) %>%
  count(stem, sort = TRUE)

stem_counts

## # A tibble: 10,001 × 2
##    stem         n
##    <chr>    <int>
##  1 student   7354
##  2 data      4365
##  3 statist   4161
##  4 question  2470
##  5 teach     1858
##  6 class     1738
##  7 school    1606
##  8 time      1457
##  9 learn     1372
## 10 font      1311
## # ℹ 9,991 more rows

n_distinct(ts_forum_data$forum_name)

## [1] 21

forums_lda <- LDA(forums_dtm, 
                  k = 30, 
                  control = list(seed = 588)
)

forums_lda

## A LDA_VEM topic model with 30 topics.

docs <- temp$documents 
meta <- temp$meta 
vocab <- temp$vocab 

forums_stm <- stm(documents=docs, 
                  data=meta,
                  vocab=vocab, 
                  prevalence =~ course_id + forum_id,
                  K=30,
                  max.em.its=25,
                  verbose = FALSE)

forums_stm

## A topic model with 30 topics, 5781 documents and a 7820 word dictionary.

plot.STM(forums_stm, n = 5)
plot(forums_stm, n = 5)

k_metrics <- FindTopicsNumber(
  forums_dtm,
  topics = seq(10, 75, by = 5),
  metrics = "Griffiths2004",
  method = "Gibbs",
  control = list(),
  mc.cores = NA,
  return_models = FALSE,
  verbose = FALSE,
  libpath = NULL
)

FindTopicsNumber_plot(k_metrics)

## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the ldatuning package.
##   Please report the issue at <https://github.com/nikita-moor/ldatuning/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

toLDAvis(mod = forums_stm, docs = docs)

## Loading required namespace: servr

terms(forums_lda, 5)

##      Topic 1    Topic 2      Topic 3   Topic 4      Topic 5    Topic 6   
## [1,] "students" "resources"  "kids"    "statistics" "time"     "students"
## [2,] "level"    "statistics" "english" "math"       "students" "video"   
## [3,] "levels"   "teaching"   "scores"  "teach"      "class"    "thinking"
## [4,] "size"     "unit"       "cost"    "students"   "survey"   "videos"  
## [5,] "dice"     "mooc"       "pick"    "teaching"   "explore"  "enjoyed" 
##      Topic 7    Topic 8         Topic 9      Topic 10 Topic 11    
## [1,] "school"   "students"      "students"   "li"     "test"      
## [2,] "students" "understanding" "questions"  "strong" "hypothesis"
## [3,] "middle"   "agree"         "assessment" "href"   "difference"
## [4,] "sharing"  "time"          "test"       "https"  "sample"    
## [5,] "teachers" "gapminder"     "locus"      "target" "testing"   
##      Topic 12         Topic 13   Topic 14    Topic 15    Topic 16 Topic 17
## [1,] "school"         "students" "agree"     "questions" "font"   "span"  
## [2,] "students"       "sampling" "students"  "question"  "normal" "style" 
## [3,] "social"         "answers"  "classroom" "students"  "text"   "line"  
## [4,] "time"           "sample"   "makes"     "answer"    "0px"    "height"
## [5,] "transportation" "correct"  "sense"     "start"     "style"  "font"  
##      Topic 18     Topic 19 Topic 20      Topic 21   Topic 22   Topic 23   
## [1,] "activity"   "plots"  "students"    "access"   "data"     "uijy0"    
## [2,] "students"   "data"   "task"        "excel"    "students" "ms"       
## [3,] "experiment" "graph"  "data"        "tuva"     "real"     "gj7bbf88h"
## [4,] "engaged"    "box"    "tasks"       "coasters" "sets"     "gthy0"    
## [5,] "coke"       "class"  "statistical" "roller"   "collect"  "wb9h"     
##      Topic 24      Topic 25 Topic 26      Topic 27     Topic 28     Topic 29
## [1,] "statistics"  "td"     "technology"  "online"     "activities" "div"   
## [2,] "probability" "top"    "students"    "statistics" "project"    "http"  
## [3,] "statistical" "width"  "software"    "education"  "students"   "href"  
## [4,] "grade"       "nice"   "simulations" "href"       "grade"      "https" 
## [5,] "science"     "align"  "computer"    "https"      "lesson"     "target"
##      Topic 30  
## [1,] "stats"   
## [2,] "ap"      
## [3,] "class"   
## [4,] "students"
## [5,] "school"

tidy_lda <- tidy(forums_lda)

tidy_lda

## # A tibble: 408,600 × 3
##    topic term       beta
##    <int> <chr>     <dbl>
##  1     1 2015  3.94e-107
##  2     2 2015  1.00e-  3
##  3     3 2015  7.14e- 11
##  4     4 2015  4.13e-111
##  5     5 2015  1.27e- 28
##  6     6 2015  1.14e- 79
##  7     7 2015  1.66e- 35
##  8     8 2015  5.79e- 27
##  9     9 2015  1.47e-  4
## 10    10 2015  9.24e-  5
## # ℹ 408,590 more rows

top_terms <- tidy_lda %>%
  group_by(topic) %>%
  slice_max(beta, n = 5, with_ties = FALSE) %>%
  ungroup() %>%
  arrange(topic, -beta)

top_terms %>%
  mutate(term = reorder_within(term, beta, topic)) %>%
  group_by(topic, term) %>%    
  arrange(desc(beta)) %>%  
  ungroup() %>%
  ggplot(aes(beta, term, fill = as.factor(topic))) +
  geom_col(show.legend = FALSE) +
  scale_y_reordered() +
  labs(title = "Top 5 terms in each LDA topic",
       x = expression(beta), y = NULL) +
  facet_wrap(~ topic, ncol = 4, scales = "free")

td_beta <- tidy(forums_lda)

td_gamma <- tidy(forums_lda, matrix = "gamma")

td_beta

## # A tibble: 408,600 × 3
##    topic term       beta
##    <int> <chr>     <dbl>
##  1     1 2015  3.94e-107
##  2     2 2015  1.00e-  3
##  3     3 2015  7.14e- 11
##  4     4 2015  4.13e-111
##  5     5 2015  1.27e- 28
##  6     6 2015  1.14e- 79
##  7     7 2015  1.66e- 35
##  8     8 2015  5.79e- 27
##  9     9 2015  1.47e-  4
## 10    10 2015  9.24e-  5
## # ℹ 408,590 more rows

td_gamma

## # A tibble: 172,980 × 3
##    document topic    gamma
##    <chr>    <int>    <dbl>
##  1 11295        1 0.00201 
##  2 12711        1 0.000259
##  3 12725        1 0.0211  
##  4 12733        1 0.00233 
##  5 12743        1 0.00746 
##  6 12744        1 0.00392 
##  7 12756        1 0.0211  
##  8 12757        1 0.00292 
##  9 12775        1 0.00292 
## 10 12816        1 0.00292 
## # ℹ 172,970 more rows

top_terms <- td_beta %>%
  arrange(beta) %>%
  group_by(topic) %>%
  top_n(7, beta) %>%
  arrange(-beta) %>%
  select(topic, term) %>%
  summarise(terms = list(term)) %>%
  mutate(terms = map(terms, paste, collapse = ", ")) %>% 
  unnest()

## Warning: `cols` is now required when using `unnest()`.
## ℹ Please use `cols = c(terms)`.

gamma_terms <- td_gamma %>%
  group_by(topic) %>%
  summarise(gamma = mean(gamma)) %>%
  arrange(desc(gamma)) %>%
  left_join(top_terms, by = "topic") %>%
  mutate(topic = paste0("Topic ", topic),
         topic = reorder(topic, gamma))

gamma_terms %>%
  select(topic, gamma, terms) %>%
  kable(digits = 3, 
        col.names = c("Topic", "Expected topic proportion", "Top 7 terms"))

Topic	Expected topic proportion	Top 7 terms
Topic 4	0.067	statistics, math, teach, students, teaching, school, level
Topic 22	0.059	data, students, real, sets, collect, analysis, collection
Topic 2	0.058	resources, statistics, teaching, unit, mooc, learning, teachers
Topic 20	0.049	students, task, data, tasks, statistical, cycle, question
Topic 15	0.047	questions, question, students, answer, start, thinking, posing
Topic 8	0.046	students, understanding, agree, time, gapminder, standard, calculations
Topic 9	0.045	students, questions, assessment, test, locus, understand, understanding
Topic 30	0.044	stats, ap, class, students, school, math, stat
Topic 6	0.041	students, video, thinking, videos, enjoyed, skills, critical
Topic 7	0.041	school, students, middle, sharing, teachers, statistical, tools
Topic 28	0.040	activities, project, students, grade, lesson, class, plan
Topic 14	0.038	agree, students, classroom, makes, sense, hands, real
Topic 26	0.037	technology, students, software, simulations, computer, calculator, tools
Topic 18	0.036	activity, students, experiment, engaged, coke, pepsi, class
Topic 5	0.036	time, students, class, survey, explore, topic, student
Topic 1	0.036	students, level, levels, size, dice, sample, trials
Topic 24	0.032	statistics, probability, statistical, grade, science, teaching, teach
Topic 13	0.030	students, sampling, answers, sample, correct, population, results
Topic 11	0.028	test, hypothesis, difference, sample, testing, chance, results
Topic 12	0.024	school, students, social, time, transportation, media, studies
Topic 10	0.023	li, strong, href, https, target, _blank, statistics
Topic 19	0.022	plots, data, graph, box, class, graphs, median
Topic 21	0.021	access, excel, tuva, coasters, roller, steel, statcrunch
Topic 16	0.018	font, normal, text, 0px, style, color, rgb
Topic 29	0.018	div, http, href, https, target, amp, _blank
Topic 27	0.015	online, statistics, education, href, https, mathematics, http
Topic 3	0.014	kids, english, scores, cost, pick, agreed, stick
Topic 17	0.014	span, style, line, height, font, quot, size
Topic 25	0.013	td, top, width, nice, align, easy, tr
Topic 23	0.007	uijy0, ms, gj7bbf88h, gthy0, wb9h, 9, uijndkm77bbf8apif99h

plot(forums_stm, n = 7)

ts_forum_data_reduced <-ts_forum_data$post_content[-temp$docs.removed]

findThoughts(forums_stm,
             texts = ts_forum_data_reduced,
             topics = 2, 
             n = 10,
             thresh = 0.5)

## 
##  Topic 2: 
##       Elaina   I have found that when I bookmark a lot of useful resources  I never go back to look at them. I intend to when I bookmark them  but then I get busy with other things. You have to put in the time now to go through the information and figure out how you are going to use these resources. I don't teach Algebra 2  so I can't give you any suggestions for that. I teach AP Statistics  but my plan is to finish the MOOC and then go back and make some specific plans on how to implement this into my teaching next year. If I don't use it right now  I will forget and never come back.
##      I mentioned this in the earlier discussion forum  but I think it is important. <span style=\color: rgb(51  51  51); font-family: UniversRoman  Arial  sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 22.4px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline !important; float: none; background-color: rgb(255  255  255);\">I have found that when I bookmark a lot of useful resources  I never go back to look at them. I intend to when I bookmark them  but then I get busy with other things. You have to put in the time now to go through the information and figure out how you are going to use these resources.</span>  <span style=\"color: rgb(51  51  51); font-family: UniversRoman  Arial  sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 22.4px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 1; word-spacing: 0px; -webkit-text-stroke-width: 0px; display: inline !important; float: none; background-color: rgb(255  255  255);\">I recently finished an Online Masters in Education and I regret that I didn't go back during that course and figure out exactly how I was going to use the resources. I finished with a lot of bookmarks and research papers that I probably won't go back and look at.</span> "
##      Dear Keith thank you so much for your suggestion and i will break down learning objectives.
##      I was wondering the same thing because I could find the information and examples very helpful in future teaching situations and I had thought about putting everything on a jump drive but putting the pdfs into google docs sounds like a swell idea! Thanks!
##      Hello Dina  your excitement perked my interest. I must say I did not really bother about these tools as I was reading them but promised myself to look closer and learn more after I read your comments. Your excitement tells me that there must be something in there that I should take a closer look on. Thanks for the vibes.
##      The American Statistical Association released a document recently that is worth looking at. It is freely available at:  http://www.amstat.org/education/SET/SET.pdf.  Definitely worth a read. Lots of great information  and good examples  the demonstrate what this unit is emphasizing.

findThoughts(forums_stm,
             texts = ts_forum_data_reduced,
             topics = 16, 
             n = 10,
             thresh = 0.5)

## 
##  Topic 16: 
##       <!--[if !supportLists]-->·         <!--[endif]--><span dir=\LTR\"></span>Do wooden coasters tend to have the same maximum height as coasters made from steel? Does anything surprise you?      The height of steel coaster tends to be higher than the height of wooden coaster back in the populations.      What surprising me:      Although the box-plot of height of both types of coasters have outliers  the mean and median in both are almost same. In addition  sample observations looks like follow approximately normal distribution although outliers are exist.      In terms of spread  the observations of wooden type  which is the old version  is more homogeneous than the steel type which is the newest version. In addition  the standard deviation of steel group is almost double compared to the wooden group      <!--[if !supportLists]-->·         <!--[endif]--><span dir=\"LTR\"></span>Do steel roller coasters tend to have longer drops than wooden roller coasters?      The drop of steel coaster tends to be longer than the drop of wooden coaster back in the populations because the median for the drops of steel coaster lies outside the box of wooden coaster (more than half of the steel coaster are above than three quarters of the wooden group).      I confused about using Age-14 or Age-15 guidelines in the guidelines for analysis file. The sample sizes of 54 and 100 are outside the range 20 and 40 as found in Age-14. So which one we have to use here is it Age-14 or Age-15 guidelines?      <!--[if !supportLists]-->·         <!--[endif]--><span dir=\"LTR\"></span>Based on what you found  predict what might be reasonable to expect for the height of the new wooden or steel roller coasters opening soon.      I expect the height would be ft100 and ft150 for the wooden and steel coaster respectively   "
##      <!--[if !supportLists]-->·         <!--[endif]--><span dir=\LTR\"></span>Are there any differences between the top speeds of older  newer or more recent roller coasters? Explain.      Yes there is differences  the newest coaster tends to be faster than the recent coaster and the recent tends to be faster than the oldest (by substitution the newest tends to be faster than the oldest) back in the populations. I used this rule because the median for one of the samples lies outside the box for the other samples. E.g.  more than half of the newest coasters are above three-quarters of the recent coasters.      <!--[if !supportLists]-->·         <!--[endif]--><span dir=\"LTR\"></span>Does the type of material make a difference in speed?      The speed of steel coaster tends to be faster than that of a wooden coaster. The distance between medians of MAD<sub>steel</sub>60 minus MAD<sub>wooden</sub>55 = 5mph is greater than about 1/5 of overall visible spread (70-50=20) equals four or .2(20)=4mph.      <!--[if !supportLists]-->·         <!--[endif]--><span dir=\"LTR\"></span>If you were going to ride a coaster that was built before 1980  what would you expect for the top speed? what about if you were riding a newer roller coaster?      I expect the top speed of a coaster that was built before 1980 equals 65.5mph and for the newer coaster equals 56mph built between 1980 and 1999 and if newest built in 2000 or later equals 50mph.   "
##      <!--[if !supportLists]-->·         <!--[endif]--><span dir=\LTR\"></span>Is there a difference in track length between roller coasters that are inverted or not?      The track length of inverted coaster tends to be shorter than that of without inversion. The distance between medians of MAD<sub>steel</sub>2759.5 minus MAD<sub>wooden</sub>3180 = - 420.5ft is greater than about 1/5 of overall visible spread (1659.25 - 4591.5= -2932.25) which equals -586.45 or .2(-2932.25)= -586.45ft. The minus sign here can be translated to the word of shorter.      <!--[if !supportLists]-->·         <!--[endif]--><span dir=\"LTR\"></span>Has track length of coasters changed much over the years?      Based on the least squares line the track length of coasters was not change much over the years (regression parameter = 13.1ft)  where this change was positive over the years and the coefficient of determination was found very small with 0.03.   "
##      In accordance to the physics laws  the speed can increase with the body weight (and body´s weight use to be related to its height). Thus  I began by comparing the maximum height with top-speed  of all roller coasters  and they linear relation was found (Figure 1). Then I thought if this would happen with roler coasters with distinct type of materials (steel/wood). And I also found a linear relation between these variable for different materials (Figure 2). However the maximum lenght of steel roller coasters tend to be bigger than the wooden roller coaster  as we can also observed in the box-plot (Figure 3).
##      Ana  after reading your post  as well as the first post by Pat Engle  it got me thinking about your investigation.  You concluded that ultimately  steel coasters have a higher max height than wood tracks.  An unsurprising result is that steel coasters also have a longer track length than wood tracks.  Pat  however  was interested in whether or not the duration of these rides were different.  In spite of the higher max heights and longer tracks  he was unable to conclude that one type of track had a longer duration.  I wonder how much of this result is confounded by the notion that longer tracks with higher max heights also require a longer climb to get up to the peak.  In my roller coaster riding experience  this seems to be the longest portion of the entire ride.
##      I was surprised to see that there was much more spread in speeds of steel coasters. My first guess was that the slower steel coasters were mainly older coasters  but highlighting the \older\" (pre-1980) coasters showed that that wasn't really the case (they are highlighted in blue). "
##      I was interested in exploring StatKey to visualize the comparison of means among wooden and steel rollercoasters. I am not sure if I pulled it off from the browser that I used  but this is my attempt. :-)       Question 1: Do steel and wooden rollercoasters differ in speed?    <img width=\625\" height=\"350\" src=\"data:image/png;base64 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
##      I remember when Paul the octopus was making these picks on TV.  It made me think of the bookmaker's strategy of releasing a \free\" pick to his clients.  Half of the clients would receive one pick  and the other half would receive the opposite pick...the bookmaker is now guaranteed to be correct for half of his clients.  He can then continue this process among those who received a correct pick for the next several weeks.  After 8 weeks  he then charges a premium for access to his next pick.  In this case  the bookmaker is randomly picking a winner to half of his remaining clients each week  but from the lens of the gambler  it appears as though the bookmaker has some mystical insight  as he just went 8/8 on his previous picks.  The gambler may now be inclined to pay a pretty penny for access to the bookmaker's next pick.  "
##      I used Tuva to model this and liked the simplicity of being able to compare a variety of variables at once.  I was also surprised that the wood coasters tended to be faster.
##      Follow as stated by Faisal...     H<sub>a</sub>: any parameter ≠ such value      the p-value is the probability of getting a statistic <u>as extreme as</u> the observed statistic  if the null hypothesis is true.      H<sub>a</sub>: any parameter &gt; such value      the p-value is the probability of getting a statistic <u>as extreme or more extreme than</u> the observed statistic  if the null hypothesis is true.      H<sub>a</sub>: any parameter &lt; such value      the p-value is the probability of getting a statistic <u>as extreme or less extreme than</u> the observed statistic  if the null hypothesis is true.

ts_forum_data_reduced <-ts_forum_data$post_content[-temp$docs.removed]

findThoughts(forums_stm,
             texts = ts_forum_data_reduced,
             topics = 23, 
             n = 10,
             thresh = 0.5)

## 
##  Topic 23: 
##       It is hard sometimes.  We have ti84s but we do not have motion detectors or anything like that.  I find that going over how to access the applications or have them right down the pathway to use the technology before hand helps to save time when we are actually going to use technology in my room.
##      I agree - the likelihood of error calculating SD by hand just makes taking the risk not worth it.  I think it is important  however  to reinforce the use of z and t tables just so they have the exposure to that visual aspect of it - the symmetry / functionality of the curve  etc.  It's a more tangible way of understanding where those probabilities come from.  I think this makes explaining two-sided vs single sided hypotheses easier too.
##      We also use the TI-84s every day. I have also used the motion detectors withe the TI-84.   Geogabra is a really cool application too. We did a lot with Geograbra last year in one of the workshops I attended. It takes some getting used to  but once you get the hang of it  it is very useful.  This summer we were studying the refraction angles of light in water. I was able to take a picture of the light rays  and then draw the angles over the picture and Geograbra calculated the angles. It was awesome!
##      I agree that hand calculations are very important.  Without them students can not see where the numbers are coming from.  I make my students hand calculate everything the first time they learn it.  After the chapter is over they can use technology to its fullest extent.
##      I agree.  Most students learn by doing  especially with a generation of students who have been brought up with touch screens and technology that is verging on  if not fully converging with  full virtual reality.  The ability to directly manipulate data sets and alter the parameters of simulations is key to obtaining an intuitive understanding.
##      I also think the visual representation and numerical computation achieved by digital simulation provide such an efficiency that puts the focus where it needs to be.
##      Ashley    I like to use EDIP (explain  demonstrate  imitate  practice) for new technology.  It Does help if you have a computer for each student or pair of students.  I had to teach statistics in rooms without computers for years. The best I could do was EDT  Explain  Demonstrate  Tell (I made that up). I'd have them tell me what to do step by step as I did it on my computer and showed it on a smart board. It is much much better for them to have their hands on the computers!  :) Bonnie
##      I also think it is worthwhile to do the calculations by hand at least once. However  many students complain about how long it takes  and they immediately forget the purpose of the calculations once they can use their calculator instead.
##      At my school we have technology day where every teacher on just grade level will reserved the computer cart to use technology in their room. Sometimes if my co-teachers are not using the whole cart  I might grab 5 computers to have station to squeeze in more technology usages in my classroom. The only downfall of using technology is that it is a computer and they do have a mind of their own. Sometimes  the internet services might be moving slow or the computers need to updated which tend to make technology day more like a headache than an enjoying experience for the students and teacher. However  I do feel that technology is needed in order to run a full functioning classroom.
##      I struggle with incorporating technology other than the TI84 because students cannot use anything other than the calculator on the AP Statistics exam. I find it hard to justify using class time for a computer program that will not be allowed on test day. However  my students that go on to take Stats in college do not use the calculator but instead use statistical programs. I have definitely heard of students using StatCrunch more so than the other programs you listed. If you had to choose  I would probably go with that one.

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