This document provides an overview of resources for learning data handling and statistics. It recommends several books, including The Cartoon Guide to Statistics, which uses cartoons and examples to explain statistical concepts in an accessible way. It also lists topics that are important to understand, such as samples vs populations, measures of central tendency and variability, probability, and how to interpret data plots and model fits. The document emphasizes that practicing basic data analysis techniques like plotting, fitting, and interpreting results is essential on a daily basis.
This document discusses key concepts in inferential statistics such as populations, parameters, samples, parameter estimates, and sampling distributions. It notes that parameters describe characteristics of populations, which are usually unknown and must be estimated using samples. Parameter estimates from samples will differ from population parameters due to sampling error. This error can be modeled using hypothetical sampling distributions, which show how parameter estimates would vary across many samples. Factors like population variability and sample size affect the standard error of estimates. The central limit theorem states that sampling distributions approach a normal shape as sample size increases. Z-scores and normal distributions can be used to evaluate the probability of obtaining particular sample results given hypotheses about population parameters.
Frequentist inference only seems easy By John MountChester Chen
This is part of Alpine ML Talk Series:
The talk is called “Frequentist inference only seems easy” and is about the theory of simple statistical inference (based on material from this article http://www.win-vector.com/blog/2014/07/frequenstist-inference-only-seems-easy/ ). The talk includes some simple dice games (I bring dice!) that really break the rote methods commonly taught as statistics. This is actually a good thing, as it gives you time and permission to work out how common statistical methods are properly derived from basic principles. This takes a little math (which I develop in the talk), but it changes some statistics from "do this" to "here is why you calculate like this.” It should appeal to people interested in the statistical and machine learning parts of data science.
The document provides an overview of quantitative data analysis and various statistical concepts including the normal distribution, z-tests, confidence intervals, and t-tests. It discusses how the normal distribution was developed by de Moivre and Gauss. It then explains the key properties of the normal distribution and how it can be used to describe many natural phenomena. Examples are provided to illustrate how to calculate and interpret confidence intervals and choose the appropriate statistical test.
In the last column we discussed the use of pooling to get a beMalikPinckney86
In the last column we discussed the use of pooling to get a better
estimate of the standard deviation of the measurement method, es-
sentially the standard deviation of the raw data. But as the last column
implied, most of the time individual measurements are averaged and
decisions must take into account another standard deviation, the stan-
dard deviation of the mean, sometimes called the “standard error” of the
mean. It’s helpful to explore this statistic in more detail: fi rst, to under-
stand why statisticians often recommend a “sledgehammer” approach
to data collection methods; and, second, to see that there might be a
better alternative to this crude tactic. We’ll also see how to answer the
question, “How big should my sample size be?”
For the next few columns, we need to discuss in more detail the ways
statisticians do their theoretical work and the ways we use their results.
I often say that theoretical statisticians live on another planet (they don’t,
of course, but let’s say Saturn), while those of us who apply their results
live on Earth. Why do I say that? Because a lot of theoretical statistics
makes the unrealistic assumption that there is an infi nite amount of data
available to us (statisticians call it an infi nite population of data). When we
have to pay for each measurement, that’s a laughable assumption. We’re
often delighted if we have a random sample of that data, perhaps as many
as three replicate measurements from which we can calculate a mean.
That last sentence contains a telling phrase: “a random sample of that
data.” Statisticians imagine that the infi nite population of data contains
all possible values we might get when we make measurements. Statisti-
cians view our results as a random draw from that infi nite population of
possible results that have been sitting there waiting for us. If we were
to make another set of measurements on the same sample, we’d get
a different set of results. That doesn’t surprise the statisticians (and it
shouldn’t surprise us if we adopt their view)—it’s just another random
draw of all the results that are just waiting to appear.
On Saturn they talk about a mean, but they call it a “true” mean. They
don’t intend to imply that they have a pipeline to the National Institute
of Standards and Technology and thus know the absolutely correct value
for what the mean represents. When they call it a “true mean,” they’re
just saying that it’s based on the infi nite amount of data in the popula-
tion, that’s all.
Statisticians generally use Greek letters for true values—μ for a true
mean, σ for a true standard deviation, δ for a true diff erence, etc.
The technical name for these descriptors (μ, σ, δ) is parameters. You’ve
probably been casual about your use of this word, employing it to refer to,
Statistics in the Laboratory:
Standard Deviation of the Mean
say, the pH you’re varying in your experiments, or the yield you get ...
The document discusses a one-sample t-test used to compare sample data to a standard value. It provides an example comparing intelligence scores of university students to the average score of 100. The sample of 6 students had a mean of 120. Running a one-tailed t-test in SPSS, the results showed the mean score was significantly higher than 100 with t(5)=3.15, p=.02. This allows the inference that the population mean intelligence at the university is greater than the standard score of 100.
The document discusses methodology for conducting an experiment to compare search engine preferences between Bing and Google. It proposes surveying 100 students at Seneca College and having them compare randomized search engine interfaces to choose their preference without revealing results. Sample size calculations, double blinding the surveyors, and other methodological considerations are discussed to avoid bias. Potential issues with scientific fraud like fabrication, falsification, and inappropriate data handling are also examined.
This document discusses various statistical concepts and their applications in clinical laboratories. It defines descriptive statistics, statistical analysis, measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation), probability distributions (binomial, Gaussian, Poisson), and statistical tests (t-test, chi-square, F-test). It provides examples of how these statistical methods are used to monitor laboratory test performance, interpret results, and compare different laboratory instruments and methods.
Random Forests without the Randomness Sept_2023.pptxKirkMonteverde1
A practical deconstruction of one of the oldest algorithmic ("BlackBox") techniques in Data Science. This broad class of non-parametric techniques has come to dominate a statistical field that has recently been popularly rechristened as AI.
This document discusses key concepts in inferential statistics such as populations, parameters, samples, parameter estimates, and sampling distributions. It notes that parameters describe characteristics of populations, which are usually unknown and must be estimated using samples. Parameter estimates from samples will differ from population parameters due to sampling error. This error can be modeled using hypothetical sampling distributions, which show how parameter estimates would vary across many samples. Factors like population variability and sample size affect the standard error of estimates. The central limit theorem states that sampling distributions approach a normal shape as sample size increases. Z-scores and normal distributions can be used to evaluate the probability of obtaining particular sample results given hypotheses about population parameters.
Frequentist inference only seems easy By John MountChester Chen
This is part of Alpine ML Talk Series:
The talk is called “Frequentist inference only seems easy” and is about the theory of simple statistical inference (based on material from this article http://www.win-vector.com/blog/2014/07/frequenstist-inference-only-seems-easy/ ). The talk includes some simple dice games (I bring dice!) that really break the rote methods commonly taught as statistics. This is actually a good thing, as it gives you time and permission to work out how common statistical methods are properly derived from basic principles. This takes a little math (which I develop in the talk), but it changes some statistics from "do this" to "here is why you calculate like this.” It should appeal to people interested in the statistical and machine learning parts of data science.
The document provides an overview of quantitative data analysis and various statistical concepts including the normal distribution, z-tests, confidence intervals, and t-tests. It discusses how the normal distribution was developed by de Moivre and Gauss. It then explains the key properties of the normal distribution and how it can be used to describe many natural phenomena. Examples are provided to illustrate how to calculate and interpret confidence intervals and choose the appropriate statistical test.
In the last column we discussed the use of pooling to get a beMalikPinckney86
In the last column we discussed the use of pooling to get a better
estimate of the standard deviation of the measurement method, es-
sentially the standard deviation of the raw data. But as the last column
implied, most of the time individual measurements are averaged and
decisions must take into account another standard deviation, the stan-
dard deviation of the mean, sometimes called the “standard error” of the
mean. It’s helpful to explore this statistic in more detail: fi rst, to under-
stand why statisticians often recommend a “sledgehammer” approach
to data collection methods; and, second, to see that there might be a
better alternative to this crude tactic. We’ll also see how to answer the
question, “How big should my sample size be?”
For the next few columns, we need to discuss in more detail the ways
statisticians do their theoretical work and the ways we use their results.
I often say that theoretical statisticians live on another planet (they don’t,
of course, but let’s say Saturn), while those of us who apply their results
live on Earth. Why do I say that? Because a lot of theoretical statistics
makes the unrealistic assumption that there is an infi nite amount of data
available to us (statisticians call it an infi nite population of data). When we
have to pay for each measurement, that’s a laughable assumption. We’re
often delighted if we have a random sample of that data, perhaps as many
as three replicate measurements from which we can calculate a mean.
That last sentence contains a telling phrase: “a random sample of that
data.” Statisticians imagine that the infi nite population of data contains
all possible values we might get when we make measurements. Statisti-
cians view our results as a random draw from that infi nite population of
possible results that have been sitting there waiting for us. If we were
to make another set of measurements on the same sample, we’d get
a different set of results. That doesn’t surprise the statisticians (and it
shouldn’t surprise us if we adopt their view)—it’s just another random
draw of all the results that are just waiting to appear.
On Saturn they talk about a mean, but they call it a “true” mean. They
don’t intend to imply that they have a pipeline to the National Institute
of Standards and Technology and thus know the absolutely correct value
for what the mean represents. When they call it a “true mean,” they’re
just saying that it’s based on the infi nite amount of data in the popula-
tion, that’s all.
Statisticians generally use Greek letters for true values—μ for a true
mean, σ for a true standard deviation, δ for a true diff erence, etc.
The technical name for these descriptors (μ, σ, δ) is parameters. You’ve
probably been casual about your use of this word, employing it to refer to,
Statistics in the Laboratory:
Standard Deviation of the Mean
say, the pH you’re varying in your experiments, or the yield you get ...
The document discusses a one-sample t-test used to compare sample data to a standard value. It provides an example comparing intelligence scores of university students to the average score of 100. The sample of 6 students had a mean of 120. Running a one-tailed t-test in SPSS, the results showed the mean score was significantly higher than 100 with t(5)=3.15, p=.02. This allows the inference that the population mean intelligence at the university is greater than the standard score of 100.
The document discusses methodology for conducting an experiment to compare search engine preferences between Bing and Google. It proposes surveying 100 students at Seneca College and having them compare randomized search engine interfaces to choose their preference without revealing results. Sample size calculations, double blinding the surveyors, and other methodological considerations are discussed to avoid bias. Potential issues with scientific fraud like fabrication, falsification, and inappropriate data handling are also examined.
This document discusses various statistical concepts and their applications in clinical laboratories. It defines descriptive statistics, statistical analysis, measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation), probability distributions (binomial, Gaussian, Poisson), and statistical tests (t-test, chi-square, F-test). It provides examples of how these statistical methods are used to monitor laboratory test performance, interpret results, and compare different laboratory instruments and methods.
Random Forests without the Randomness Sept_2023.pptxKirkMonteverde1
A practical deconstruction of one of the oldest algorithmic ("BlackBox") techniques in Data Science. This broad class of non-parametric techniques has come to dominate a statistical field that has recently been popularly rechristened as AI.
The Seven Habits of Highly Effective StatisticiansStephen Senn
This document provides advice on habits that make statisticians effective. It discusses the importance of understanding causation, control, comparison and counterfactuals when thinking about effectiveness. It warns against proposing habits as causes without proper evaluation. Seven key habits are identified: read, listen, understand, think, do, calculate, and communicate. The document illustrates these habits through examples of invalid inversion, regression to the mean, and statistical mistakes. It emphasizes understanding concepts fundamentally rather than just mathematically and finding simple ways to communicate ideas.
The document discusses objectives and concepts related to statistical analysis in biology, including:
- Types of data, graphs, and statistical analyses such as mean, standard deviation, and chi square analysis.
- Calculating and interpreting the mean and standard deviation of a data set to describe variability.
- Using standard deviation to compare the spread of data between samples and determine significance.
- Performing hypothesis testing using calculated t values, t tables, and p values to determine if differences between data sets are statistically significant.
The Role of Agent-Based Modelling in Extending the Concept of Bounded Rationa...Edmund Chattoe-Brown
A seminar given to the Judgement and Decision Making Research Group in the Department of Neuroscience, Psychology and Behaviour, University of Leicester kindly asked me to give a seminar on 25 January 2023 on "The Role of Agent-Based Modelling in Extending the Concept of Bounded Rationality". It discusses the challenges to different research methods of dealing with subjective accounts and models a situation where people can be rational but communicate and have incomplete information about both the number of choices and their payoff. The model is based on this paper: https://doi.org/10.1007/s11299-009-0060-7 One interesting result is that, without coercion or mass media, minority groups may be disadvantaged in their decision making by hegemonic discourse.
This document is the preface to "The History of Mathematics: A Brief Course Answers to Questions and Problems" by Roger Cooke. It explains that the solutions manual is intended for instructors and not students directly, and contains the author's personal views in response to questions from the textbook. The preface notes that references and citations from the textbook are included for context but the literature list is not. It aims to promote discussion and critical thinking rather than provide definitive answers.
Statistical hypothesis testing is an important tool for scientists to critically evaluate hypotheses using empirical data. It helps keep scientists honest by requiring them to statistically test their ideas rather than accepting them uncritically. One should be skeptical of any paper that claims an alternative hypothesis is supported without providing a statistical test. A key statistical test is the chi-square test, which compares observed data to expected frequencies under the null hypothesis. It calculates a test statistic and compares it to critical values in tables to determine if the null hypothesis can be rejected in favor of the alternative hypothesis. Proper use of statistical testing is part of the scientific method and moral imperative for scientists.
1. The document provides an overview of key statistical concepts including populations and samples, the mean, standard deviation, and statistical models. It explains that the mean and standard deviation are used to measure how well a model fits the data and describes the variability.
2. It discusses the differences between samples and populations and how statistics like the mean and standard deviation from a sample can be used to make estimates about the overall population. Confidence intervals are presented as a way to indicate the reliability of sample estimates.
3. The document covers important statistical topics like effect sizes, which provide a standardized measure of the magnitude of an observed effect, and the differences between statistical and practical significance.
Module-2_Notes-with-Example for data sciencepujashri1975
The document discusses several key concepts in probability and statistics:
- Conditional probability is the probability of one event occurring given that another event has already occurred.
- The binomial distribution models the probability of success in a fixed number of binary experiments. It applies when there are a fixed number of trials, two possible outcomes, and the same probability of success on each trial.
- The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. Many real-world variables approximate a normal distribution.
- Other concepts discussed include range, interquartile range, variance, and standard deviation. The interquartile range describes the spread of a dataset's middle 50%
This document provides an overview of standard deviation and z-scores. It begins by listing the key learning objectives which are to describe the importance of variation in distributions, understand how to calculate standard deviation, describe what a z-score is and how to calculate them, and learn the Greek letters for mean and standard deviation. It then provides explanations and examples of how to calculate and interpret standard deviation as a measure of variation, how to convert values to z-scores based on the mean and standard deviation, and the importance of ensuring distributions are normal before using these statistical techniques. It emphasizes understanding the concepts rather than just memorizing formulas.
This document discusses different types of data and statistical concepts. It begins by describing the major types of data: numerical, categorical, and ordinal. Numerical data represents quantitative measurements, categorical data has no inherent mathematical meaning, and ordinal data has categorical categories with a mathematical order. It then discusses statistical measures like the mean, median, mode, standard deviation, variance, percentiles, moments, covariance, correlation, conditional probability, and Bayes' theorem. Examples are provided to help explain each concept.
This document summarizes an R boot camp focusing on statistics. It includes an agenda that covers introducing the lab component, R basics, descriptive statistics in R, revisiting installation instructions, and measures of variability in R. Descriptive statistics are presented as ways to characterize data through measures of central tendency, shape, and variability. Examples are provided in R for calculating the mean, median, mode, range, percentiles, variance, standard deviation, and coefficient of variation. The central limit theorem and standardizing scores are also discussed. Real-world applications of R for clean and messy data are mentioned.
Online Course: Real Statistics: A Radical ApproachAsad Zaman
Modern statistics has been built on fatally flawed foundations of the failed logical positivist philosophy. This philosophy rejects unobservables as a basis for human knowledge. Since probability and causality are inherently unobservable, conventional statistics in inherently incapable of providing a satisfactory approach to these concepts. These slides announce a new approach to the discipline, which rejects the past century of developments based on a positivist approach. This online course (register via HTTP://bit.ly/ocRSRA ) will rebuild the entire discipline on a realist philosophy, creating a radically different methodology from the one currently in use all over the world.
The document provides guidance for creating a scientific poster presentation. It includes templates for the typical sections of an introduction, materials and methods, results, and conclusions. Key points emphasized are keeping word counts low, using visual elements like figures and illustrations over dense text, and ensuring figures are large and legible from a distance. The overall goal is to concisely communicate the essential information and findings of a scientific study or experiment.
This document provides an overview of various techniques for visualizing and summarizing numerical data, including scatterplots, dot plots, histograms, the mean, median, variance, standard deviation, percentiles, box plots, and transformations. It discusses how these metrics and visualizations can be used to describe the center, spread, shape, and outliers of distributions.
The document provides an overview of populations, samples, and key concepts in descriptive statistics. It discusses how samples are used to make inferences about populations. Key points include:
- Samples are subsets of populations used for study due to constraints on time and resources.
- Descriptive statistics like means, medians, and histograms are calculated from samples to learn about characteristics of interest in populations.
- Categorical data can be summarized using frequency distributions and sample proportions.
- Different measures of center like the mean, median, and trimmed mean are used to summarize data, with the choice dependent on factors like outliers and distribution shape.
The document provides reminders and instructions for a Zoom meeting on the topic of introduction to statistics. Key points include:
- Attendance is required and participants should find a quiet place, arrive on time, dress appropriately, keep microphones muted when not speaking, and keep cameras on.
- Participants should avoid distractions and ask questions using the raise hand feature.
- The meeting will cover topics like measures of central tendency, types of data and distributions.
This document provides an overview of descriptive statistics. It discusses key topics including measures of central tendency (mean, median, mode), measures of variability (range, IQR, variance, standard deviation, skewness, kurtosis), probability and probability distributions (binomial distribution), and how descriptive statistics is used to understand and describe data. Descriptive statistics involves numerically summarizing and presenting data through methods such as graphs, tables, and calculations without inferring conclusions about a population.
This document summarizes the frequently asked questions (FAQs) for The Data Science course on Udemy. It addresses questions about receiving course bonuses, certificates of completion, technical issues with videos or quizzes not loading, downloading course materials, book recommendations for after finishing the course, and downloading video lectures. Specific lecture questions are also addressed, such as assumptions about data coming from a population vs sample, the relationship between random and representative samples, examples of true zeros, defining the null hypothesis, creating histograms in Excel, and knowing when to use one-tailed vs two-tailed statistical tests.
Module Five Normal Distributions & Hypothesis TestingTop of F.docxroushhsiu
Module Five: Normal Distributions & Hypothesis Testing
Top of Form
Bottom of Form
·
Introduction & Goals
This week's investigations introduce and explore one of the most common distributions (one you may be familiar with): the Normal Distribution. In our explorations of the distribution and its associated curve, we will revisit the question of "What is typical?" and look at the likelihood (probability) that certain observations would occur in a given population with a variable that is normally distributed. We will apply our work with Normal Distributions to briefly explore some big concepts of inferential statistics, including the Central Limit Theorem and Hypothesis Testing. There are a lot of new ideas in this week’s work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical model, its applications and limitations
· Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed difference in two means
· Use technology to perform a hypothesis test comparing means (z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means (t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT (Scholastic Aptitude Test) and the ACT (American College Test). The scores for these tests are scaled so that they follow a normal distribution.
· The SAT reported that its scores were normally distributed with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the SAT, he achieves a score of 1080. On the ACT, he achieves a score of 30. He cannot decide which score is the better one to send with his college applications.
. Question: Which test score is the stronger score to send to his colleges?
· A hypothetical group called SAT Prep claims that students who take their SAT Preparatory course score higher on the SAT than the general population. To support their claim, they site a study in which a random sample of 50 SAT Prep students had a mean SAT score of 1000. They claim that since this mean is higher than the known mean of 896 for all SAT scores, their program must improve SAT scores.
. Question: Is this difference in the mean scores statistically significant? Does SAT Prep truly improve SAT Scores?
.
Investigation 1: What is Normal?
One reason for gathering data is to see which observations are most likely. For instance, when we looked at the raisin data in DoW #3, we were looking to see what the most likely number of raisins was for each brand of raisins. We cannot ever be certain of the exact number of raisins in a box (because it varies) ...
EV Charging at MFH Properties by Whitaker JamiesonForth
Whitaker Jamieson, Senior Specialist at Forth, gave this presentation at the Forth Addressing The Challenges of Charging at Multi-Family Housing webinar on June 11, 2024.
The Seven Habits of Highly Effective StatisticiansStephen Senn
This document provides advice on habits that make statisticians effective. It discusses the importance of understanding causation, control, comparison and counterfactuals when thinking about effectiveness. It warns against proposing habits as causes without proper evaluation. Seven key habits are identified: read, listen, understand, think, do, calculate, and communicate. The document illustrates these habits through examples of invalid inversion, regression to the mean, and statistical mistakes. It emphasizes understanding concepts fundamentally rather than just mathematically and finding simple ways to communicate ideas.
The document discusses objectives and concepts related to statistical analysis in biology, including:
- Types of data, graphs, and statistical analyses such as mean, standard deviation, and chi square analysis.
- Calculating and interpreting the mean and standard deviation of a data set to describe variability.
- Using standard deviation to compare the spread of data between samples and determine significance.
- Performing hypothesis testing using calculated t values, t tables, and p values to determine if differences between data sets are statistically significant.
The Role of Agent-Based Modelling in Extending the Concept of Bounded Rationa...Edmund Chattoe-Brown
A seminar given to the Judgement and Decision Making Research Group in the Department of Neuroscience, Psychology and Behaviour, University of Leicester kindly asked me to give a seminar on 25 January 2023 on "The Role of Agent-Based Modelling in Extending the Concept of Bounded Rationality". It discusses the challenges to different research methods of dealing with subjective accounts and models a situation where people can be rational but communicate and have incomplete information about both the number of choices and their payoff. The model is based on this paper: https://doi.org/10.1007/s11299-009-0060-7 One interesting result is that, without coercion or mass media, minority groups may be disadvantaged in their decision making by hegemonic discourse.
This document is the preface to "The History of Mathematics: A Brief Course Answers to Questions and Problems" by Roger Cooke. It explains that the solutions manual is intended for instructors and not students directly, and contains the author's personal views in response to questions from the textbook. The preface notes that references and citations from the textbook are included for context but the literature list is not. It aims to promote discussion and critical thinking rather than provide definitive answers.
Statistical hypothesis testing is an important tool for scientists to critically evaluate hypotheses using empirical data. It helps keep scientists honest by requiring them to statistically test their ideas rather than accepting them uncritically. One should be skeptical of any paper that claims an alternative hypothesis is supported without providing a statistical test. A key statistical test is the chi-square test, which compares observed data to expected frequencies under the null hypothesis. It calculates a test statistic and compares it to critical values in tables to determine if the null hypothesis can be rejected in favor of the alternative hypothesis. Proper use of statistical testing is part of the scientific method and moral imperative for scientists.
1. The document provides an overview of key statistical concepts including populations and samples, the mean, standard deviation, and statistical models. It explains that the mean and standard deviation are used to measure how well a model fits the data and describes the variability.
2. It discusses the differences between samples and populations and how statistics like the mean and standard deviation from a sample can be used to make estimates about the overall population. Confidence intervals are presented as a way to indicate the reliability of sample estimates.
3. The document covers important statistical topics like effect sizes, which provide a standardized measure of the magnitude of an observed effect, and the differences between statistical and practical significance.
Module-2_Notes-with-Example for data sciencepujashri1975
The document discusses several key concepts in probability and statistics:
- Conditional probability is the probability of one event occurring given that another event has already occurred.
- The binomial distribution models the probability of success in a fixed number of binary experiments. It applies when there are a fixed number of trials, two possible outcomes, and the same probability of success on each trial.
- The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is characterized by its mean and standard deviation. Many real-world variables approximate a normal distribution.
- Other concepts discussed include range, interquartile range, variance, and standard deviation. The interquartile range describes the spread of a dataset's middle 50%
This document provides an overview of standard deviation and z-scores. It begins by listing the key learning objectives which are to describe the importance of variation in distributions, understand how to calculate standard deviation, describe what a z-score is and how to calculate them, and learn the Greek letters for mean and standard deviation. It then provides explanations and examples of how to calculate and interpret standard deviation as a measure of variation, how to convert values to z-scores based on the mean and standard deviation, and the importance of ensuring distributions are normal before using these statistical techniques. It emphasizes understanding the concepts rather than just memorizing formulas.
This document discusses different types of data and statistical concepts. It begins by describing the major types of data: numerical, categorical, and ordinal. Numerical data represents quantitative measurements, categorical data has no inherent mathematical meaning, and ordinal data has categorical categories with a mathematical order. It then discusses statistical measures like the mean, median, mode, standard deviation, variance, percentiles, moments, covariance, correlation, conditional probability, and Bayes' theorem. Examples are provided to help explain each concept.
This document summarizes an R boot camp focusing on statistics. It includes an agenda that covers introducing the lab component, R basics, descriptive statistics in R, revisiting installation instructions, and measures of variability in R. Descriptive statistics are presented as ways to characterize data through measures of central tendency, shape, and variability. Examples are provided in R for calculating the mean, median, mode, range, percentiles, variance, standard deviation, and coefficient of variation. The central limit theorem and standardizing scores are also discussed. Real-world applications of R for clean and messy data are mentioned.
Online Course: Real Statistics: A Radical ApproachAsad Zaman
Modern statistics has been built on fatally flawed foundations of the failed logical positivist philosophy. This philosophy rejects unobservables as a basis for human knowledge. Since probability and causality are inherently unobservable, conventional statistics in inherently incapable of providing a satisfactory approach to these concepts. These slides announce a new approach to the discipline, which rejects the past century of developments based on a positivist approach. This online course (register via HTTP://bit.ly/ocRSRA ) will rebuild the entire discipline on a realist philosophy, creating a radically different methodology from the one currently in use all over the world.
The document provides guidance for creating a scientific poster presentation. It includes templates for the typical sections of an introduction, materials and methods, results, and conclusions. Key points emphasized are keeping word counts low, using visual elements like figures and illustrations over dense text, and ensuring figures are large and legible from a distance. The overall goal is to concisely communicate the essential information and findings of a scientific study or experiment.
This document provides an overview of various techniques for visualizing and summarizing numerical data, including scatterplots, dot plots, histograms, the mean, median, variance, standard deviation, percentiles, box plots, and transformations. It discusses how these metrics and visualizations can be used to describe the center, spread, shape, and outliers of distributions.
The document provides an overview of populations, samples, and key concepts in descriptive statistics. It discusses how samples are used to make inferences about populations. Key points include:
- Samples are subsets of populations used for study due to constraints on time and resources.
- Descriptive statistics like means, medians, and histograms are calculated from samples to learn about characteristics of interest in populations.
- Categorical data can be summarized using frequency distributions and sample proportions.
- Different measures of center like the mean, median, and trimmed mean are used to summarize data, with the choice dependent on factors like outliers and distribution shape.
The document provides reminders and instructions for a Zoom meeting on the topic of introduction to statistics. Key points include:
- Attendance is required and participants should find a quiet place, arrive on time, dress appropriately, keep microphones muted when not speaking, and keep cameras on.
- Participants should avoid distractions and ask questions using the raise hand feature.
- The meeting will cover topics like measures of central tendency, types of data and distributions.
This document provides an overview of descriptive statistics. It discusses key topics including measures of central tendency (mean, median, mode), measures of variability (range, IQR, variance, standard deviation, skewness, kurtosis), probability and probability distributions (binomial distribution), and how descriptive statistics is used to understand and describe data. Descriptive statistics involves numerically summarizing and presenting data through methods such as graphs, tables, and calculations without inferring conclusions about a population.
This document summarizes the frequently asked questions (FAQs) for The Data Science course on Udemy. It addresses questions about receiving course bonuses, certificates of completion, technical issues with videos or quizzes not loading, downloading course materials, book recommendations for after finishing the course, and downloading video lectures. Specific lecture questions are also addressed, such as assumptions about data coming from a population vs sample, the relationship between random and representative samples, examples of true zeros, defining the null hypothesis, creating histograms in Excel, and knowing when to use one-tailed vs two-tailed statistical tests.
Module Five Normal Distributions & Hypothesis TestingTop of F.docxroushhsiu
Module Five: Normal Distributions & Hypothesis Testing
Top of Form
Bottom of Form
·
Introduction & Goals
This week's investigations introduce and explore one of the most common distributions (one you may be familiar with): the Normal Distribution. In our explorations of the distribution and its associated curve, we will revisit the question of "What is typical?" and look at the likelihood (probability) that certain observations would occur in a given population with a variable that is normally distributed. We will apply our work with Normal Distributions to briefly explore some big concepts of inferential statistics, including the Central Limit Theorem and Hypothesis Testing. There are a lot of new ideas in this week’s work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical model, its applications and limitations
· Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed difference in two means
· Use technology to perform a hypothesis test comparing means (z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means (t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT (Scholastic Aptitude Test) and the ACT (American College Test). The scores for these tests are scaled so that they follow a normal distribution.
· The SAT reported that its scores were normally distributed with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the SAT, he achieves a score of 1080. On the ACT, he achieves a score of 30. He cannot decide which score is the better one to send with his college applications.
. Question: Which test score is the stronger score to send to his colleges?
· A hypothetical group called SAT Prep claims that students who take their SAT Preparatory course score higher on the SAT than the general population. To support their claim, they site a study in which a random sample of 50 SAT Prep students had a mean SAT score of 1000. They claim that since this mean is higher than the known mean of 896 for all SAT scores, their program must improve SAT scores.
. Question: Is this difference in the mean scores statistically significant? Does SAT Prep truly improve SAT Scores?
.
Investigation 1: What is Normal?
One reason for gathering data is to see which observations are most likely. For instance, when we looked at the raisin data in DoW #3, we were looking to see what the most likely number of raisins was for each brand of raisins. We cannot ever be certain of the exact number of raisins in a box (because it varies) ...
EV Charging at MFH Properties by Whitaker JamiesonForth
Whitaker Jamieson, Senior Specialist at Forth, gave this presentation at the Forth Addressing The Challenges of Charging at Multi-Family Housing webinar on June 11, 2024.
Understanding Catalytic Converter Theft:
What is a Catalytic Converter?: Learn about the function of catalytic converters in vehicles and why they are targeted by thieves.
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Parking Strategies: Tips on where and how to park your vehicle to reduce the risk of theft, such as parking in well-lit areas or secure garages.
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Etching and Marking: The benefits of etching your vehicle’s VIN on the catalytic converter or using a catalytic converter marking kit to make it traceable and less appealing to thieves.
Surveillance and Monitoring: Recommendations for using security cameras and motion-sensor lights to deter thieves.
Statistics and Insights:
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Recent Trends: Current trends and patterns in catalytic converter thefts to help you stay aware of emerging hotspots and tactics used by thieves.
Benefits of This Presentation:
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Practical Tips: Gain actionable insights and tips to effectively prevent catalytic converter theft.
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This presentation aims to equip you with the knowledge and tools needed to protect your vehicle from catalytic converter theft, ensuring you are prepared and proactive in safeguarding your property.
What Could Be Behind Your Mercedes Sprinter's Power Loss on Uphill RoadsSprinter Gurus
Unlock the secrets behind your Mercedes Sprinter's uphill power loss with our comprehensive presentation. From fuel filter blockages to turbocharger troubles, we uncover the culprits and empower you to reclaim your vehicle's peak performance. Conquer every ascent with confidence and ensure a thrilling journey every time.
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Expanding Access to Affordable At-Home EV Charging by Vanessa WarheitForth
Vanessa Warheit, Co-Founder of EV Charging for All, gave this presentation at the Forth Addressing The Challenges of Charging at Multi-Family Housing webinar on June 11, 2024.
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1. Data Handling/Statistics
There is no substitute for books—
— you need professional help!
My personal favorites, from which this lecture is drawn:
•The Cartoon Guide to Statistics, L. Gonick & W. Smith
•Data Reduction in the Physical Sciences, P. R. Bevington
•Workshop Statistics, A. J. Rossman & B. L. Chance
•Numerical Recipes, W.H. Press, B.P. Flannery, S.A. Teukolsky
and W.T.Vetterling
•Origin 6.1 Users Manual, MicroCal Corporation
2. Outline
•Our motto
•What those books look like
•Stuff you need to be able to look up
•Samples & Populations
•Mean, Standard Deviation, Standard Error
•Probability
•Random Variables
•Propagation of Errors
•Stuff you must be able to do on a daily basis
•Plot
•Fit
•Interpret
3. Our Motto
That which can be taught can be learned.
The “progress” of civilization relies being able to
do more and more things while thinking less and
less about them.
An opposing, non-CMC IGERT
viewpoint
5. The Cartoon
Guide to
Statistics
In this example, the author
provides step-by-step analysis
of the statistics of a poll.
Similar logic and style tell
you how to tell two populations
apart, whether your measley
five replicate runs truly
represent the situation, etc.
The Cartoon Guide gives an
enjoyable account of statistics in
scientific and everyday life.
6. Bevington
Bevington is really good at introducing
basic concepts, along with simple code
that really, really works. Our lab uses a
lot of Bevington code, often translated from
Fortran to Visual Basic.
7. “Workshop Statistics”
This book has a website full of data that it
tells you how to analyze. The test cases are
often pretty interesting, too.
Many little shadow boxes provide info.
8. “Numerical Recipes”
A more modern and thicker version of Bevington.
Code comes in Fortran, C, Basic (others?). Includes
advanced topics like digital filtering, but harder to read
on the simpler things. With this plus Bevington and a
lot of time, you can fit, smooth, filter practically
anything.
9. Stuff you need to be able to look up
Samples vs. Populations
The world as we
understand it, based
on science.
The world as God
understands it, based
on omniscience.
Statistics is not art but artifice–a bridge to help us
understand phenomena, based on limited observations.
10. Our problem
Sitting behind the target, can
we say with some specific level of
confidence whether a circle
drawn around this single arrow
(a measurement) hits the
bullseye (the population mean)?
Measuring a molecular weight by
one Zimm plot, can we say with
any certainty that we have obtained
the same answer God would have
gotten?
12. Sample View: direct, experimental, tangible
The single most important thing about this is the reduction
In standard deviation or standard error of the mean according
To inverse root n.
)
large
(for
1
~
2
n
n
s
s
Three times better takes 9 times longer (or costs
9 times more, or takes 9 times more disk space).
If you remembered nothing else from this lecture, it
would be a success!
13. Population View: conceptual,
layered with arcana!
The purple equation in the table is an expression of the central
limit theorem. If we measure many averages, we do not
always get the same average:
).
"
Cartoon...
"
(from
"
deviation
standard
and
mean
with
on
distributi
normal
a
approaches
itself
)
large
(for
then
,
deviation
standard
and
mean
with
population
a
from
size
of
samples
random
takes
one
if
“
variable!
random
a
itself
is
n
x
n
n
x
14. Huh? It means…if you want to estimate , which only
God really knows, you should measure many averages, each
involving n data points, figure their standard deviation,
and multiply by n1/2. This is hard work!
A lot of times, is approximated by s.
If you wanted to estimate the population average ,
the best you can do is to measure many averages and
averaging those.
A lot of times is approximated by x.
IT’S HARD TO KNOW WHAT GOD DOES.
I think the in the purple equation should be an s, but the equation only works in the limit
of large n anyhow, so there is no difference.
15. You got to compromise, fool!
The t-distribution was invented by
a statistician named Gosset, who was forced
by his employer (the Guinness brewery!)
to publish under a pseudonym.
He chose “Student” and his t-distribution is
known as student’s t.
The student’s t distribution helps us assign confidence in
our imperfect experiments on small samples.
Input: desired confidence level, estimate of population
mean (or estimated probability),
estimated error of the mean (or probability).
Output: ± something
16. Probability
…is another arcane concept in the “population” category: something
we would like to know but cannot. As a concept, it’s
wonderful. The true mean of a distribution of mass is given as the
probability of that mass times the mass. The standard deviation
follows a similarly simple rule. In what follows, F means a
normalized frequency (think mole fraction!) and P is a probability
density. P(x)dx represents the number of things (think molecules)
with property x (think mass) between x+dx/2 and x-dx/2.
x
all
x
all
x
F
x
x
xF
2
2
)
(
)
(
)
(
Discrete system
dx
x
P
x
dx
x
xP
)
(
)
(
)
(
2
2
Continuous system
17. Here’s a normal probability density distribution from
“Workshop…” where you use actual data to discover.
68% of results
2 95% of results
18. What it means
Although you don’t usually know the distribution,
(either or ) about 68% of your measurements will
fall within 1 of ….if the distribution is a “normal”,
bell-shaped curve. t-tests allow you to kinda play this
backwards: given a finite sample size, with some
average, x, and standard deviation, s—inferior to
and , respectively—how far away do we think the true
is?
19. Details
No way I could do it better than “Cartoon…”
or “Workshop…”
Remember…this is the part of the lecture
entitled “things you must be able to look up.”
20. Propagation of errors
Suppose you give 30 people a ruler and ask them to measure
the length and width of a room. Owing to general
incompetence, otherwise known as human nature,
you will get not one answer but many. Your averages
will be L and W, and standard deviations sW and sL.
Now, you want to buy carpet, so need area A = L·W.
What is the uncertainty in A due to the measurement errors
in L and W?
Answer! There is no telling….but you have several options
to estimate it.
21. A = L·W example
Here are your measured data:
ft
W
ft
L
2
19
1
30
2
2
2
average
2
2
min
2
2
max
65)
(560
:
area
reported
65
2
490
-
620
:
y
uncertaint
estimated
557
2
490
620
490
17
29
620
20
31
ft
ft
ft
A
ft
ft
W
L
A
ft
ft
W
L
A
You can consider “most” and “least” cases:
22. Another way
We can use a formula for how propagates.
Suppose some function y (think area) depends on
two measured quantities t and s (think length &
width). Then the variance in y follows this rule:
2
2
2
2
2
s
t
y
s
y
t
y
Aren’t you glad you took partial differential equations?
What??!! You didn’t? Well, sign up. PDE is the bare
minimum math for scientists.
23. Translation in our case, where A = L·W:
2
2
2
2
2
2
2
2
2
W
L
W
L
A
L
W
W
A
L
A
Problem: we don’t know W, L, L or W! These are
population numbers we could only get if we had the
entire planet measure this particular room. We therefore
assume that our measurement set is large enough (n=30)
That we can use our measured averages for W and L and
our standard deviations for L and W.
25. Error propagation caveats
The equation, 2
2
2
2
2
s
t
y
s
y
t
y
, assumes
normal behavior. Large systematic errors—for example,
3 euroguys who report their values in metric units—are not
taken into consideration properly. In many cases, there
will be good knowledge a priori about the uncertainty in
one or more parameters: in photon counting, if N is
the number of photons detected, then N = (N)1/2 . Systematic
error that is not included in this estimate, so photon folk are
well advised to just repeat experiments to determine
real standard deviations that do take systematic errors into
account.
26. Stuff you must know how
to do on daily basis
0 2 4 6 8 10
0
5000
10000
15000
20000
25000
Larger Particle
30.9 g/ml
Parameter Value Error
------------------------------------------------------------
A -0.00267 44.94619
B 2.25237E-7 8.46749E-10
------------------------------------------------------------
R SD N P
------------------------------------------------------------
0.99987 118.8859 21 <0.0001
------------------------------------------------------------
/Hz
q2/1010cm-2
Plot!!!
r=0.99987
r2=0.9997
99.97% of the trend can be explained
by the fitted relation.
Intercept = 0.003 ± 45
(i.e., zero!)
27. The same data
0 2 4 6 8 10 12
0.0
0.5
1.0
1.5
2.0
2.5
3.0 Larger Particle
30.9 g/ml
twilight users rcueto e739
Parameter Value Error
------------------------------------------------------------
A 2.2725E-7 7.62107E-10
B -3.09723E-20 1.43575E-20
------------------------------------------------------------
R SD N P
------------------------------------------------------------
-0.44355 2.01583E-9 21 0.044
------------------------------------------------------------
D
app
/
cm
2
s
-1
q2/1010cm-2
How to find
this file!
r=0.444
r2=0.20
Only 20% of the data can be
explained by the line! While
depended on q2, Dapp does not!
28. 0 10 20 30
0
5
10
15
20
25
[6/7/01 13:44 "/Rhapp" (2452067)]
Linear Regression for BigSilk_Ravgnm:
Y = A + B * X
Parameter Value Error
------------------------------------------------------------
A 20.88925 0.19213
B 0.01762 0.01105
------------------------------------------------------------
R SD N P
------------------------------------------------------------
0.62332 0.28434 6 0.18611
------------------------------------------------------------
Range of Rg
values obsreved in MALLS
(3/5)
1/2
Rh
R
h
/nm
c/g-ml
-1
Plot showing 95% confidence limits.
Excel doesn’t excel at this!
29. Interpreting data: Life on the bleeding edge of
cutting technology. Or is that bleating edge?
1E7
10
2E7
3E6
n = 0.324 +/- 0.04
df
= 3.12 +/- 0.44
R
g
/nm
M
The noise level in individual runs is much less than
The run-to-run variation. That’s why many runs are
a good idea. More would be good here, but we are
still overcoming the shock that we can do this at all!
30. Correlation Caveat!
Correlation Cause. No, Correlation=Association.
Chart Title y = 35.441x + 57.996
R2
= 0.5782
0
10
20
30
40
50
60
70
80
90
0.0000 0.2000 0.4000 0.6000 0.8000 1.0000
TV's per person
Life
Expectancy
Country Life Expectancy People per TV TV's per person
Angola 44 200 0.0050
Australia 76.5 2 0.5000
Cambodia 49.5 177 0.0056
Canada 76.5 1.7 0.5882
China 70 8 0.1250
Egypt 60.5 15 0.0667
France 78 2.6 0.3846
Haiti 53.5 234 0.0043
Iraq 67 18 0.0556
Japan 79 1.8 0.5556
Madagascar 52.5 92 0.0109
Mexico 72 6.6 0.1515
Morocco 64.5 21 0.0476
Pakistan 56.5 73 0.0137
Russia 69 3.2 0.3125
South Africa 64 11 0.0909
SriLanka 71.5 28 0.0357
Uganda 51 191 0.0052
United Kingdom 76 3 0.3333
United States 75.5 1.3 0.7692
Vietnam 65 29 0.0345
Yemen 50 38 0.0263
58% of life expectancy is associated with TV’s.
Would we save lives by sending TV’s to Uganda?
Excel does not automatically
provide estimates!
31. Linearize it!
Observant scientists are adept at seeing curvature. Train
your eye by looking for defects in wallpaper, door trim,
lumber bought at Home Depot, etc. And try to straighten
out your data, rather than let the computer fit a nonlinear form,
which it is quite happy to do!
Chart Title y = -0.1156x + 70.717
R2
= 0.6461
0
10
20
30
40
50
60
70
80
90
0 50 100 150 200 250
People per TV
Life
Expectancy
Linearity is
improved by
plotting Life vs.
people per TV
rather than TV’s
per people.
32. These 4 plots all have the
Same slopes, intercepts and
r values!
Plots are pictures of
science, worth
thousands of words
in boring tables.
33. From whence do those lines come?
Least squares fitting.
“Linear Fits”
the fitted coefficients
appear in linear part
expression. e.g..
y =a+bx+cx2+dx3
An analytical “best fit” exists!
“Nonlinear fits”
At least some of the fitted coefficients
appear in transcendental
arguments. e.g.,
y =a+be-cx+dcos(ex)
Best fit found by trial & error.
Beware false solutions! Try
several initial guesses!
34. All data points are not created equal.
Since that one point has
so much error (or noise) should
we really worry about minimizing
its square? No.
n
i i
fit
i y
y
1
2
2
2 )
(
We should minimize “chisquared.”
n is the # of degrees of freedom
n n-# of parameters fitted
Goodness of fit parameter that should
be unity for a “fit within error”
n
i i
fit
i
reduced
y
y
1
2
2
2 )
(
1
n
35. 2 caveats
•Chi-square lower than unity is meaningless…if you
trust your 2 estimates in the first place.
•Fitting too many parameters will lower 2 but this may
be just doing a better and better job of fitting the noise!
•A fit should go smoothly THROUGH the noise, not
follow it!
•There is such a thing as enforcing a “parsimonious” fit
by minimizing a quantity a bit more complicated than 2.
This is done when you have a-priori information that the
fitted line must be “smooth”.
36. Achtung! Warning!
This lecture is an example of a very dangerous
phenomenon: “what you need to know.” Before you were
born, I took a statistics course somewhere in undergraduate
school. Most of this stuff I learned from experience….um…
experiments. A proper math course, or a course from LSU’s
Department of Experimental Statistics would firm up your
knowledge greatly.
AND BUY THOSE BOOKS! YOU WILL NEED THEM!