Topics and Links

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This is a list of the "topics" that we will cover in this class. The level of detail presented here will expand as the course continues to be developed. Note that as further web pages are developed, links to those pages will be added here.

Please note that I have taken full advantage of the concept that these are web pages. That is, should you print out these pages there is every reason to believe that the printed version will be excessively long and that page breaks will occur in some inconvenient places. Viewing the pages in a browser does not have that problem, although I do recommend that you set the default font to be size 14.
  1. Module 0 -- math that is a prerequisite for this course.
    1. The skills that the Math Department has determined to be essential before even starting this course.
    2. Students must pass the test on this material with a score of 90 or higher before they will be allowed to take a real test that counts.
    3. Student scores on the Module 0 test do not count for the real course.
    4. Here is a link to a presentation of each of the 6 Module 0 topics.
    5. Here is the link to a practice test for Module 0.
  2. Rules of the Road -- How the class is run, instructor responsibilities, student responsibilities.
    1. Grading for Math 160(r)
    2. Software Installation
    3. Test Selection
  3. Overview of the course
    1. Descriptive Statistics
    2. Inferential Statistics
      • Population
      • Sample
    3. Probability
    4. A Video to start looking at an overview of the course, and a background page to download and print.
    5. A Video to continue looking at an overview of descriptive statistics and a background page to download and print.
  4. Materials
    1. Books
    2. Tables
    3. Calculators
    4. Computers
      • Kinds
      • Software
      • Internet
  5. Software (short list -- see: Wikipedia for more)
    1. Minitab
    2. SPSS
    3. SAS
    4. Excel
    5. MIDAS
    6. S
    7. R
  6. Beginning to use R
    1. A Video of a start to using RStudio, Topic 5
    2. A Video that continues looking at a start to using RStudio
    3. First Steps in R
    4. Options for using our files
    5. Using gnrnd4 on a pc -- new file
    6. New demonstration, using the USB drive, on a PC
    7. New demonstration, using the USB drive, on a Mac
    8. Web page to generate values using GNRND4
  7. Data
    1. Population
    2. Sample
    3. Variables – 1, 2, many
    4. Kinds of Data also see web sequence
  8. Descriptive Measures
    1. Discussion: Measures of Central Tendency
    2. Computing in R: Measures of Central Tendency
      A Video that shows finding measures of central tendency and the background page used in that video.
      A Video that again shows finding measures of central tendency with comments on the stability of the mean and median along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
      [Worksheet: PC version]
      [Worksheet: Mac Version]
      [Special insert on real data: Real World Data 01]
      [Exercise: Finding mean, median, and mode]
    3. Discussion: Measures of Dispersion
    4. Computing in R: measures of Dispersion
      A Video that shows finding measures of dispersion and the background page used in that video.
      [Exercise: Finding range, quartiles, standard deviation]
    5. Discussion: Graphs -- 1 variable
    6. Computing in R: Graphs -- 1 variable
    7. Classifications of Distributions
      A Video that presents examples of five different distributions and a link to the R script used in the video so that you can download and run the script.
    8. Discussion: Graphs -- 2 variables
      A Video that shows scatter plots along with the background page used in that video
    9. Computing in R: Scatter (Line) plots
      A Video that shows making a scatter plot in R along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    10. Discussion: Frequency Tables -- Discrete Values
      A Video that presents the topic of frequency tables along with the background page used in that video.
    11. Computing in R: Frequency Tables -- Discrete Values
      A Video that shows making a frequency table using R and then codifying that with a function along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    12. Discussion: Frequency Tables -- Grouped Values
      A Video that presents the topic of frequency tables for grouped data along with the background page used in that video.
    13. Computing in R: Frequency Tables -- Grouped Values
      A Video that shows making a frequency table for continuous values using R and then codifying that with a function, along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    14. Getting Measures from Grouped Data
      A Video that presents the topic of getting some desciptive measures from a frequency table for grouped data along with the background page used in that video.
    15. Automating Values from Grouped Data
      A Video that shows the R statements to get some descriptive measures from a frequency table of intervals and then codifying that with a function, along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    16. Percentiles
      A Video that presents the concept of percentiles and shows related R statements along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    17. Quick demo of all of this
    18. Worksheet 02: Descriptive measures
      Worksheet 03: Descriptive measures
      Worksheet 03.1: Descriptive measures
      Worksheet 03.2: Descriptive measures
      Worksheet 03.3: Descriptive measures for Grouped Data
      Worksheet 03.4: Descriptive measures Again
  9. Linear relations
    1. Linear Regression and Correlation
      A Video that presents the concept of linear regression along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
      A Video that presents the concept of correlation along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
      A Video that presents doing linear regressions and finding the correlation coefficient, along with residual values, in R along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    2. Mathematical Computation of same
    3. Interpolation and Extrapolation
    4. Residuals
    5. Five scripts to download and run:
      1. Topic 8a help
      2. Topic 8
      3. Topic 8 four examples
      4. Topic 8 various
      5. Topic 8 review
    6. Script for start of linear regression
    7. Script for more on linear regression
    8. Script for yet another demo of linear regression
    9. Script and file for a real world data demo of linear regression
    10. Worksheet 04: Linear Regression, Residuals, Correlation
      Worksheet 05: More Linear Regression
      Worksheet 06: More Linear Regression
      Worksheet 06a: Strange Residuals
  10. Sampling
    Here is a link to a script used to demonstrate each of the 6 types of sampling.
    1. Simple random sample
    2. Sample of convenience
    3. Stratified sample
    4. Cluster sample
    5. Systematic sample
    6. Voluntary Response sample
  11. Descriptive statistics in a sample vs. in a population
  12. Probability, a long introduction (A list of terms) and a script to illustrate this (to be used after reading the web page).
    A Video that presents the concepts of probability along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    A Video that presents more of the concepts of probability along with the background page used in that video.
    1. Discrete Cases and a script to investigate this.
      A Video that presents discrete probability distributions along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    2. The Binomial Distribution , a script to investigate this, and a script of more examples
      A Video that presents binomial distributions along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    3. Continuous Cases and script to investigate this.
      A Video that presents made up continous probability distributions along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    4. The Normal Distribution and script to investigate this.
      A Video that presents part one of the Normal probability distribution along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
      A Video that presents part two of the Normal probability distribution along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    5. Student's t Distribution and script to investigate this.
      A Video that presents the Student's-t probability distribution along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    6. Assessing Normality and script to investigate this.
    7. Proportions (within certain restrictions) and script to investigate this.
    8. Normal approximation of the Binomial (within certain restrictions) and script to investigate this.
    9. χ² Distribution
    10. Summary Table of Commands
    11. Addendum: directions to download a script from this web site to your USB drive.
    12. Worksheet on Distributions (still under development)
  13. Looking the means of samples
    1. The Sample Mean and Its Mean and Standard Deviation along with two scripts to further examine this topic. We have a basic script that does this and we have a special script that mimics the work on the web page.
    2. Using the distribution of sample means
  14. Confidence Intervals
    1. Confidence Interval for Population Mean, μ, based on the sample mean when σ is known
      A Video that presents Part 1 on finding a confidence interval for the mean of a population when σ, the standard deviation of the population, is known along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
      A Video that presents Part 2 on finding a confidence interval for the mean of a population when σ, the standard deviation of the population, is known. This video continues the use of the background page and the script given above in Part 1.
      1. a script to be used to explore some of this topic.
      2. a randomized worksheet on confidence intervals for the mean when σ is known
      3. a static, pdf version of such a worksheet
      4. the console output for solving the static version
      5. a script uses multiple samples to explore this topic.
      6. Yet another script to examine this item (this is probably the best script for this topic).
    2. Find Sample Size for specified Margin of Error.
      1. a randomized worksheet on finding a required sample size for a given margin of error when σ is known
      2. a static, pdf version of such a worksheet
      3. the console output for solving the static version
      4. Another script to examine this item (this is probably the best script for this topic).
    3. Confidence Interval for the population mean, μ, based on the sample mean when σ is unknown
      1. a script to be used to explore some of this topic.
      2. a randomized worksheet on confidence intervals for the mean when σ is unknown
      3. a static, pdf version of such a worksheet
      4. the console output for solving the static version
      5. Another script to examine this item (this is probably the best script for this topic).
    4. Confidence Interval for a Population Proportion
      1. a script to be used to explore some of this topic.
      2. a randomized worksheet on confidence intervals for population proportions
      3. a static, pdf version of such a worksheet
      4. the console output for solving the static version
      5. Generate a population of 10,000 dots, up to 7 different colors, with goal proportions of each specified color
      6. Another script to examine this item (this is probably the best script for this topic).
    5. Confidence Interval for the Population Standard Deviation
      1. a randomized worksheet on confidence intervals for the population standard deviation
      2. a static, pdf version of such a worksheet
      3. the console output for solving the static version
      4. Another script to examine this item (this is probably the best script for this topic).
  15. Hypotheses
  16. Hypothesis test for Population Mean, based on the sample mean, σ known and script to investigate this.
    A Video that presents a null hypothesis for the mean of a population when σ, the standard deviation of the population, is known along with the background page used in that video, and a link to the R script used in the video so that you can download and run the script.
    1. an early script to be used to explore some of this topic.
    2. a randomized worksheet on testing a hypothesis about the mean when σ is known
    3. a static, pdf version of such a worksheet
    4. the console output for solving the static version
  17. Hypothesis test for Population Mean, based on the sample mean, σ unknown and script to investigate this.
    1. a script to be used to explore some of this topic.
    2. a randomized worksheet on testing a hypothesis about the mean when σ is unknown
    3. a static, pdf version of such a worksheet
    4. the console output for solving the static version
    5. Video Example 1: shows solving a typical problem. The file topic 16 1 background.pdf holds the background for the video. The file topic 16 1.R holds the script used to calculate the results shown in the video.
    6. Video Example 2: shows solving a typical problem. The file topic 16 2 background.pdf holds the background for the video. The file topic 16 2.R holds the script used to calculate the results shown in the video.
  18. Hypothesis Test for Population Proportion and script to investigate this.
    1. a script to be used to explore some of this topic.
    2. a randomized worksheet on testing a hypothesis about the population proportion
    3. a static, pdf version of such a worksheet
    4. the console output for solving the static version
    5. Video Example: shows solving a typical problem. The file topic 17 1 background.pdf holds the background for the video. The file topic 17 1.R holds the script used to calculate the results shown in the video.
  19. Hypothesis Test for Population Standard Deviation for normal population and script to investigate this.
    1. a randomized worksheet on testing a hypothesis about the population proportion
    2. a static, pdf version of such a worksheet
    3. the console output for solving the static version
  20. The Power of a Test
  21. Two Populations -- an introduction
    video explanation
  22. Two Populations; Two Independent Samples, σ's known
    and script to investigate this.
    A Video to compare to earlier work and the background page to download and print.
    1. Confidence Interval for the difference between means
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
    2. Hypothesis Test for the difference between means
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
    3. Randomized Worksheet for CI and Hypothesis test, sigma known
      1. a static, pdf version of such a worksheet
      2. the console output for solving the static version
  23. Two Populations; two independent samples, σ's unknown
    and script to investigate this.
    A Video to compare to earlier work and the background page to download and print.
    1. Confidence Interval for the difference between means
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
    2. Hypothesis Test for the difference between means
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
      3. Real world example: a script and a required data file.
    3. Randomized Worksheet for CI and Hypothesis test, sigma unknown
      1. a static, pdf version of such a worksheet
      2. the console output for solving the static version
  24. One Population; Paired Samples
    and script to investigate this.
    A Video to look at an example of paired values, and a background page to download and print, along with the R script used in the video.
    1. Confidence Interval for the difference between means
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
    2. Hypothesis Test for the difference between means
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
  25. Two Populations; Proportions
    and script to investigate this.
    A Video to look at an example of comparing proportions in two populations, and a background page to download and print, along with the R script used in the video.
    1. Confidence Interval for the difference between proportions
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
    2. Hypothesis Test for the difference between proportions
      1. a script to be used to explore some of this topic.
      2. a script uses multiple samples to explore this topic.
  26. Two Populations; Independent Samples -- Variance
    A Video to start looking at comparing variances in two populations, and a background page to download and print.
    A Video to look at the F distribution used in comparing variances in two populations, and a background page to download and print.
    A Video to look at an example of comparing variances in two populations, and a background page to download and print, along with the R script used in this video.
    1. The F-distribution
    2. Confidence Interval for the ratio of two variancies
    3. Hypothesis Test for the "difference between" two variances
    4. A script to demonstrate how to use some textbook tables for the F-distribution.
    5. Randomized Worksheet for CI and Hypothesis test for two variances
      1. a static, pdf version of such a worksheet
      2. the console output for solving the static version
  27. χ² tests for distributions
    1. Goodness of Fit: the χ² test and a video presentations of the goodness of fit along with background page to download and print and the R-script topic 26c.R used in that video.
      1. A script to demonstrate the χ² distribution of our computed values.
      2. Yet another script to look at a specific case comparing multiple proportion tests to one goodness of fit test. This script makes reference to a population of dots and that population is shown in goodness dots.pdf. Within that population the script looks at a sample from two blocks and they shown in the file blocks of dots.pdf.
    2. Independence and χ² test for independence
      A Video to start looking at Independence of characteristics in a population, and a background page to download and print.
      A Video to look at Computing Independence measures in R and a background page to download and print, along with the R script used in this video.
      1. Generate examples of population with two independent discrete variables and then take samples of it.
      2. Example(s) of analyzing contingency tables
  28. Multiple testing issues; Sample Size Issues
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©Roger M. Palay     Saline, MI 48176     December, 2022