The document discusses multivariate analysis (MVA) techniques that allow analysis of more than two variables at once. It provides an overview of commonly used MVA methods like principal components analysis, cluster analysis, and correspondence analysis. It also discusses Simpson's Paradox, where misleading results can occur from bivariate analysis, and provides examples where introducing additional variables provides better understanding. Multivariate techniques help understand relationships among multiple variables and reduce the chance of spurious findings.
This document discusses multivariate analysis (MVA), which involves observing and analyzing multiple outcome variables simultaneously. It describes key components of MVA like variates, measurement scales, and statistical significance. Various MVA techniques are explained, including cross correlations, single-equation models, vector autoregressions, and cointegration. An example using crime rate data from US states is provided. Applications of MVA in fields like marketing, quality control, process optimization, and research are also mentioned.
The document discusses model specification for multiple regression analysis, focusing on measures of fit including R-squared and standard error of regression, and how to properly interpret these statistics. It emphasizes the importance of random sampling to establish causal relationships and warns of potential biases from non-random samples, such as when evaluating mutual fund performance or estimating political support based on telephone and automobile owners.
The document provides information about descriptive statistics, summarizing qualitative and quantitative data, and various methods for presenting data visually. It discusses frequency distributions, relative and percent frequency distributions, bar graphs, pie charts, dot plots, histograms, and cumulative distributions as ways to summarize data in a clear manner. Guidelines are given for selecting class widths and numbers when creating frequency distributions. Examples using data on hotel ratings and auto repair part costs are presented to illustrate the various statistical and graphical techniques.
The document discusses various statistical concepts related to hypothesis testing including:
- Hypothesis, null hypothesis, and alternative hypothesis
- Types of statistical analyses for testing hypotheses (univariate, bivariate, multivariate)
- Common statistical tests like z-test, t-test, chi-square test, and tests of proportions
- Key steps in hypothesis testing like defining the hypotheses, determining significance levels, calculating test statistics, and making conclusions
- Types I and II errors that can occur in hypothesis testing
Examples are provided to demonstrate how to set up and conduct hypothesis tests using z-test, t-test, chi-square test, and test of proportions.
This document discusses key concepts in descriptive statistics including:
- Measures of central tendency like mean, median, and mode.
- Measures of variability such as range, interquartile range, variance, and standard deviation.
- Frequency distributions, percentages, and probability distributions.
- Population and sample distributions as well as the sampling distribution of the mean and the central limit theorem.
The document contains a frequency distribution table that summarizes data from a questionnaire regarding a university computer service system. The table includes frequencies and percentages for respondent demographics like gender (72% male, 28% female), age group (50% between 21-23 years old, 34% 24-26, 16% over 26), GPA range, and academic program of study. A second section of the questionnaire assessed satisfaction levels of system quality on a 5-point scale.
Hierarchichal species distributions model and Maxentrichardchandler
The document discusses hierarchical species distribution models. It defines hierarchical models as statistical models with conditional probability distributions linking random variables. It then discusses hierarchical modeling approaches for defining state variables of interest, developing state and observation models, and making inferences. Key points include hierarchical point process models can account for non-random sampling through observation models, and count-based hierarchical models are easier to fit than point process models when only count data are available.
This document describes a study that used integrated population models to predict the spatial and temporal dynamics of populations at the edges of species' ranges. The study aimed to understand the mechanisms driving range shifts and their consequences for edge populations. It developed a point process model incorporating survival, reproduction, dispersal, density dependence, and other factors. The model was informed by capture-recapture, distance sampling, and other data types from a study of Canada Warblers. Preliminary results suggest climate strongly affects recruitment at the range edge for this species. Future work will combine observational and experimental data to enable causal inference about range dynamics.
This document discusses multivariate analysis (MVA), which involves observing and analyzing multiple outcome variables simultaneously. It describes key components of MVA like variates, measurement scales, and statistical significance. Various MVA techniques are explained, including cross correlations, single-equation models, vector autoregressions, and cointegration. An example using crime rate data from US states is provided. Applications of MVA in fields like marketing, quality control, process optimization, and research are also mentioned.
The document discusses model specification for multiple regression analysis, focusing on measures of fit including R-squared and standard error of regression, and how to properly interpret these statistics. It emphasizes the importance of random sampling to establish causal relationships and warns of potential biases from non-random samples, such as when evaluating mutual fund performance or estimating political support based on telephone and automobile owners.
The document provides information about descriptive statistics, summarizing qualitative and quantitative data, and various methods for presenting data visually. It discusses frequency distributions, relative and percent frequency distributions, bar graphs, pie charts, dot plots, histograms, and cumulative distributions as ways to summarize data in a clear manner. Guidelines are given for selecting class widths and numbers when creating frequency distributions. Examples using data on hotel ratings and auto repair part costs are presented to illustrate the various statistical and graphical techniques.
The document discusses various statistical concepts related to hypothesis testing including:
- Hypothesis, null hypothesis, and alternative hypothesis
- Types of statistical analyses for testing hypotheses (univariate, bivariate, multivariate)
- Common statistical tests like z-test, t-test, chi-square test, and tests of proportions
- Key steps in hypothesis testing like defining the hypotheses, determining significance levels, calculating test statistics, and making conclusions
- Types I and II errors that can occur in hypothesis testing
Examples are provided to demonstrate how to set up and conduct hypothesis tests using z-test, t-test, chi-square test, and test of proportions.
This document discusses key concepts in descriptive statistics including:
- Measures of central tendency like mean, median, and mode.
- Measures of variability such as range, interquartile range, variance, and standard deviation.
- Frequency distributions, percentages, and probability distributions.
- Population and sample distributions as well as the sampling distribution of the mean and the central limit theorem.
The document contains a frequency distribution table that summarizes data from a questionnaire regarding a university computer service system. The table includes frequencies and percentages for respondent demographics like gender (72% male, 28% female), age group (50% between 21-23 years old, 34% 24-26, 16% over 26), GPA range, and academic program of study. A second section of the questionnaire assessed satisfaction levels of system quality on a 5-point scale.
Hierarchichal species distributions model and Maxentrichardchandler
The document discusses hierarchical species distribution models. It defines hierarchical models as statistical models with conditional probability distributions linking random variables. It then discusses hierarchical modeling approaches for defining state variables of interest, developing state and observation models, and making inferences. Key points include hierarchical point process models can account for non-random sampling through observation models, and count-based hierarchical models are easier to fit than point process models when only count data are available.
This document describes a study that used integrated population models to predict the spatial and temporal dynamics of populations at the edges of species' ranges. The study aimed to understand the mechanisms driving range shifts and their consequences for edge populations. It developed a point process model incorporating survival, reproduction, dispersal, density dependence, and other factors. The model was informed by capture-recapture, distance sampling, and other data types from a study of Canada Warblers. Preliminary results suggest climate strongly affects recruitment at the range edge for this species. Future work will combine observational and experimental data to enable causal inference about range dynamics.
Logistic regression is used when the dependent variable is dichotomous (has two possible outcomes) and can be applied to predict group membership. It forms a best-fitting equation to maximize the probability of correctly classifying cases into categories based on the independent variables. The logistic regression equation transforms the dependent variable into a probability rather than a numerical value to address limitations of linear regression for dichotomous outcomes.
This document summarizes key concepts in data analysis including:
1) Types of variables including nominal, ordinal, interval, and ratio levels of measurement.
2) Types of data including discrete and continuous variables.
3) Descriptions of datasets, data frames, frequency tables, and joint distributions.
4) Components of frequency tables including frequency, relative frequency, cumulative frequency, and relative cumulative frequency.
This document discusses evaluating the normality of data distributions. It covers probability, normal distributions, z-scores, empirical rules, and tests for skewness and kurtosis. Normal distributions are symmetric and bell-shaped. The normality of data can be determined using z-scores and empirical rules. Skewness measures asymmetry in a distribution, while kurtosis measures tail weight. Normality tests like Shapiro-Wilk can determine if a dataset comes from a normal distribution.
Chapter 5 part1- The Sampling Distribution of a Sample Meannszakir
Mathematics, Statistics, Population Distribution vs. Sampling Distribution, The Mean and Standard Deviation of the Sample Mean, Sampling Distribution of a Sample Mean, Central Limit Theorem
This document provides an overview and objectives for Chapter 3 of the textbook "Statistical Techniques in Business and Economics" by Lind. The chapter covers describing data through numerical measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation). It includes examples of computing various measures like the weighted mean, median, mode, and interpreting their relationships. The document also lists learning activities for students such as reading the chapter, watching video lectures, completing practice problems in the book, and participating in an online discussion forum.
This document provides an overview of logistic regression, including when and why it is used, the theory behind it, and how to assess logistic regression models. Logistic regression predicts the probability of categorical outcomes given categorical or continuous predictor variables. It relaxes the normality and linearity assumptions of linear regression. The relationship between predictors and outcomes is modeled using an S-shaped logistic function. Model fit, predictors, and interpretations of coefficients are discussed.
The document provides information about descriptive statistics including how they are used to summarize and organize data from samples and populations. Descriptive statistics include measures of central tendency like the mean, median, and mode as well as measures of variability like range, interquartile range, variance and standard deviation. Examples are given showing how to calculate and present these statistics including frequency distributions, histograms, bar graphs and measures of central tendency and variability.
How to analyse bulk transcriptomic data using Deseq2AdamCribbs1
DESeq2 is used to analyze differential expression from RNA-seq count data using a generalized linear model. It models counts using a gamma-Poisson distribution and estimates dispersion using empirical Bayes shrinkage. Key steps include normalizing counts, estimating dispersion, fitting the linear model, and using Wald and likelihood ratio tests to identify differentially expressed genes while controlling the false discovery rate. Results can be explored using plots of p-values, mean-variance trends, ordination plots, and heatmaps to visualize sample relationships and differentially expressed genes.
This document provides an overview of probability and how it relates to statistics. It defines probability as a method for quantifying the likelihood of outcomes. Probability is measured as a ratio of the number of desired outcomes to the total number of possible outcomes. For outcomes to have a known probability, they must be selected through a random process. The normal distribution is discussed as it relates to probability, with common probabilities and areas under the normal curve defined. The document shows how to calculate probabilities for raw scores on a normal distribution using z-scores. It also demonstrates finding probabilities for ranges of scores and finding z-scores from known proportions.
1. Multinomial logistic regression allows modeling of nominal outcome variables with more than two categories by calculating multiple logistic regression equations to compare each category's probability to a reference category.
2. The document provides an example of using multinomial logistic regression to model student program choice (academic, general, vocational) based on writing score and socioeconomic status.
3. The model results show that writing score significantly impacts the choice between academic and general/vocational programs, while socioeconomic status also influences general versus academic program choice.
Abstract: This PDSG workshop introduces basic concepts of statistics. Concepts covered are mean (average), median, mode, standard deviation discrete vs. continuous, normal distribution, sampling distribution, Z-scores and boxplots.
Level: Fundamental
Requirements: No prior programming or statistics knowledge required.
This document discusses various methods for summarizing and exploring qualitative and quantitative data through tabular and graphical techniques, including frequency distributions, relative frequency distributions, bar graphs, pie charts, histograms, scatter plots, and cross-tabulations. It provides examples and explanations of how to construct and interpret these summaries and graphs using sample customer satisfaction and automobile repair data. The goal is to gain insights about relationships within the data that are not evident from just looking at the original values.
Logistic regression is used to predict categorical outcomes. The presented document discusses logistic regression, including its objectives, assumptions, key terms, and an example application to predicting basketball match outcomes. Logistic regression uses maximum likelihood estimation to model the relationship between a binary dependent variable and independent variables. The document provides an illustrated example of conducting logistic regression in SPSS to predict match results based on variables like passes, rebounds, free throws, and blocks.
This document discusses logistic regression, including:
- Logistic regression can be used when the dependent variable is binary and predicts the probability of an event occurring.
- The logistic regression equation calculates the log odds of an event occurring based on independent variables.
- Logistic regression is commonly used in medical research when variables are a mix of categorical and continuous.
This document discusses how to conduct spot speed studies to collect traffic speed data. It outlines the objectives of spot speed studies which include determining characteristics like the mean, median, mode and 85th percentile speed. It describes different speed study considerations and parameters of interest. It also covers how to analyze spot speed study data, check if the speed distribution is normal, and how to determine the required sample size.
1. The document discusses univariate analysis, which describes the distribution of individual variables. It involves examining the frequency of categorical variables and testing for symmetry in continuous variables.
2. The steps of data analysis are outlined as: 1) Univariate analysis of each variable, 2) Bivariate analysis of associations between pairs of variables, and 3) Multivariate analysis using regression models to examine relationships between multiple variables.
3. Univariate analysis in SPSS includes generating frequency distributions for categorical variables and exploring continuous variables using normal Q-Q plots and tests of normality, as well as examining summaries including the mean, median, and standard deviation.
The document discusses key concepts in statistics and risk management including probability, sampling, measures of central tendency, dispersion, and graphical presentation of data. It covers probability distributions like Poisson and exponential that can be applied to business continuity and risk analysis. Forecasting techniques like moving average and exponential smoothing are also summarized.
This document summarizes key topics in developing and validating predictive classifiers based on gene expression profiling. It discusses the importance of clear study objectives, feature selection methods, model types, and proper evaluation of classifiers using cross-validation to estimate prediction accuracy, rather than overfitting to the training data. Complex feature selection and model fitting are unlikely to help for high-dimensional genomic data. Simple classification methods like linear discriminant analysis often perform best.
Presentation at Advanced Intelligent Systems for Sustainable Development (AISSD 2021) 20-22 August 2021 organized by the scientific research group in Egypt with Collaboration with Faculty of Computers and AI, Cairo University and the Chinese University in Egypt
Logistic regression is used when the dependent variable is dichotomous (has two possible outcomes) and can be applied to predict group membership. It forms a best-fitting equation to maximize the probability of correctly classifying cases into categories based on the independent variables. The logistic regression equation transforms the dependent variable into a probability rather than a numerical value to address limitations of linear regression for dichotomous outcomes.
This document summarizes key concepts in data analysis including:
1) Types of variables including nominal, ordinal, interval, and ratio levels of measurement.
2) Types of data including discrete and continuous variables.
3) Descriptions of datasets, data frames, frequency tables, and joint distributions.
4) Components of frequency tables including frequency, relative frequency, cumulative frequency, and relative cumulative frequency.
This document discusses evaluating the normality of data distributions. It covers probability, normal distributions, z-scores, empirical rules, and tests for skewness and kurtosis. Normal distributions are symmetric and bell-shaped. The normality of data can be determined using z-scores and empirical rules. Skewness measures asymmetry in a distribution, while kurtosis measures tail weight. Normality tests like Shapiro-Wilk can determine if a dataset comes from a normal distribution.
Chapter 5 part1- The Sampling Distribution of a Sample Meannszakir
Mathematics, Statistics, Population Distribution vs. Sampling Distribution, The Mean and Standard Deviation of the Sample Mean, Sampling Distribution of a Sample Mean, Central Limit Theorem
This document provides an overview and objectives for Chapter 3 of the textbook "Statistical Techniques in Business and Economics" by Lind. The chapter covers describing data through numerical measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation). It includes examples of computing various measures like the weighted mean, median, mode, and interpreting their relationships. The document also lists learning activities for students such as reading the chapter, watching video lectures, completing practice problems in the book, and participating in an online discussion forum.
This document provides an overview of logistic regression, including when and why it is used, the theory behind it, and how to assess logistic regression models. Logistic regression predicts the probability of categorical outcomes given categorical or continuous predictor variables. It relaxes the normality and linearity assumptions of linear regression. The relationship between predictors and outcomes is modeled using an S-shaped logistic function. Model fit, predictors, and interpretations of coefficients are discussed.
The document provides information about descriptive statistics including how they are used to summarize and organize data from samples and populations. Descriptive statistics include measures of central tendency like the mean, median, and mode as well as measures of variability like range, interquartile range, variance and standard deviation. Examples are given showing how to calculate and present these statistics including frequency distributions, histograms, bar graphs and measures of central tendency and variability.
How to analyse bulk transcriptomic data using Deseq2AdamCribbs1
DESeq2 is used to analyze differential expression from RNA-seq count data using a generalized linear model. It models counts using a gamma-Poisson distribution and estimates dispersion using empirical Bayes shrinkage. Key steps include normalizing counts, estimating dispersion, fitting the linear model, and using Wald and likelihood ratio tests to identify differentially expressed genes while controlling the false discovery rate. Results can be explored using plots of p-values, mean-variance trends, ordination plots, and heatmaps to visualize sample relationships and differentially expressed genes.
This document provides an overview of probability and how it relates to statistics. It defines probability as a method for quantifying the likelihood of outcomes. Probability is measured as a ratio of the number of desired outcomes to the total number of possible outcomes. For outcomes to have a known probability, they must be selected through a random process. The normal distribution is discussed as it relates to probability, with common probabilities and areas under the normal curve defined. The document shows how to calculate probabilities for raw scores on a normal distribution using z-scores. It also demonstrates finding probabilities for ranges of scores and finding z-scores from known proportions.
1. Multinomial logistic regression allows modeling of nominal outcome variables with more than two categories by calculating multiple logistic regression equations to compare each category's probability to a reference category.
2. The document provides an example of using multinomial logistic regression to model student program choice (academic, general, vocational) based on writing score and socioeconomic status.
3. The model results show that writing score significantly impacts the choice between academic and general/vocational programs, while socioeconomic status also influences general versus academic program choice.
Abstract: This PDSG workshop introduces basic concepts of statistics. Concepts covered are mean (average), median, mode, standard deviation discrete vs. continuous, normal distribution, sampling distribution, Z-scores and boxplots.
Level: Fundamental
Requirements: No prior programming or statistics knowledge required.
This document discusses various methods for summarizing and exploring qualitative and quantitative data through tabular and graphical techniques, including frequency distributions, relative frequency distributions, bar graphs, pie charts, histograms, scatter plots, and cross-tabulations. It provides examples and explanations of how to construct and interpret these summaries and graphs using sample customer satisfaction and automobile repair data. The goal is to gain insights about relationships within the data that are not evident from just looking at the original values.
Logistic regression is used to predict categorical outcomes. The presented document discusses logistic regression, including its objectives, assumptions, key terms, and an example application to predicting basketball match outcomes. Logistic regression uses maximum likelihood estimation to model the relationship between a binary dependent variable and independent variables. The document provides an illustrated example of conducting logistic regression in SPSS to predict match results based on variables like passes, rebounds, free throws, and blocks.
This document discusses logistic regression, including:
- Logistic regression can be used when the dependent variable is binary and predicts the probability of an event occurring.
- The logistic regression equation calculates the log odds of an event occurring based on independent variables.
- Logistic regression is commonly used in medical research when variables are a mix of categorical and continuous.
This document discusses how to conduct spot speed studies to collect traffic speed data. It outlines the objectives of spot speed studies which include determining characteristics like the mean, median, mode and 85th percentile speed. It describes different speed study considerations and parameters of interest. It also covers how to analyze spot speed study data, check if the speed distribution is normal, and how to determine the required sample size.
1. The document discusses univariate analysis, which describes the distribution of individual variables. It involves examining the frequency of categorical variables and testing for symmetry in continuous variables.
2. The steps of data analysis are outlined as: 1) Univariate analysis of each variable, 2) Bivariate analysis of associations between pairs of variables, and 3) Multivariate analysis using regression models to examine relationships between multiple variables.
3. Univariate analysis in SPSS includes generating frequency distributions for categorical variables and exploring continuous variables using normal Q-Q plots and tests of normality, as well as examining summaries including the mean, median, and standard deviation.
The document discusses key concepts in statistics and risk management including probability, sampling, measures of central tendency, dispersion, and graphical presentation of data. It covers probability distributions like Poisson and exponential that can be applied to business continuity and risk analysis. Forecasting techniques like moving average and exponential smoothing are also summarized.
This document summarizes key topics in developing and validating predictive classifiers based on gene expression profiling. It discusses the importance of clear study objectives, feature selection methods, model types, and proper evaluation of classifiers using cross-validation to estimate prediction accuracy, rather than overfitting to the training data. Complex feature selection and model fitting are unlikely to help for high-dimensional genomic data. Simple classification methods like linear discriminant analysis often perform best.
Presentation at Advanced Intelligent Systems for Sustainable Development (AISSD 2021) 20-22 August 2021 organized by the scientific research group in Egypt with Collaboration with Faculty of Computers and AI, Cairo University and the Chinese University in Egypt
4 26 2013 1 IME 674 Quality Assurance Reliability EXAM TERM PROJECT INFO...Robin Beregovska
The document provides information about an exam and term project for an IME quality assurance course. It discusses control charts and introduces X-bar and R charts. The key points are:
- Exam 1 will cover lectures 1-4 and chapters 1-6 and is approximately one week away.
- The term project can be a quality analysis of real process data or a report on current state of art of an SPC topic, and is 10 pages or less.
- Control charts like X-bar and R charts can be used to monitor processes and identify assignable causes, with X-bar charts monitoring the mean and R charts monitoring variation. Control limits are calculated using historical sample data.
Simple math for anomaly detection toufic boubez - metafor software - monito...tboubez
This is my presentation at Monitorama PDX in Portland on May 5, 2014
Simple math to get some signal out of your noisy sea of data
You’ve instrumented your system and application to the hilt. You can now “measure all the things”. Your team has set up thousands of metrics collecting millions of data points a day. Now what?
Most IT ops teams only keep an eye on a small fraction of the metrics they collect because analyzing this mountain of data and extracting signal from the noise is not easy. The choice of what analytic method to use ranges from simple statistical analysis to sophisticated machine learning techniques. And one algorithm doesn’t fit all data.
This document discusses sampling techniques and concepts in statistics. It begins by outlining learning objectives related to sampling, errors, and statistical analysis. It then discusses reasons for sampling such as saving money and time compared to a census. The document contrasts random and non-random sampling methods. It provides examples of random sampling techniques including simple random sampling, systematic random sampling, stratified random sampling, and cluster sampling. It also discusses non-random convenience sampling and sources of non-sampling errors. Finally, it introduces the concepts of sampling distributions and the central limit theorem, and provides examples of using normal approximations.
This document provides an overview of cluster analysis techniques. It defines cluster analysis as classifying cases into homogeneous groups based on a set of variables. The document then discusses how cluster analysis can be used in marketing research for market segmentation, understanding consumer behaviors, and identifying new product opportunities. It outlines the typical steps to conduct a cluster analysis, including selecting a distance measure and clustering algorithm, determining the number of clusters, and validating the analysis. Specific clustering methods like hierarchical, k-means, and deciding the number of clusters using the elbow rule are explained. The document concludes with an example of conducting a cluster analysis in SPSS.
Introduction. Data presentation
Frequency distribution. Distribution center indicators. RMS. Covariance. Effects of
diversification. Choice of the weighing method.
More: https://ek.biem.sumdu.edu.ua/
This presentation deals with the formal presentation of anomaly detection and outlier analysis and types of anomalies and outliers. Different approaches to tackel anomaly detection problems.
Application of Machine Learning in AgricultureAman Vasisht
With the growing trend of machine learning, it is needless to say how machine learning can help reap benefits in agriculture. It will be boon for the farmer welfare.
SPSS Step-by-Step Tutorial and Statistical Guides by StatsworkStats Statswork
This document provides an overview of cluster analysis techniques used in marketing research. It defines cluster analysis as classifying cases into homogeneous groups based on a set of variables. Cluster analysis can be used for market segmentation, understanding buyer behaviors, and identifying new product opportunities in marketing research. The document outlines the steps to conduct cluster analysis, including selecting a distance measure and clustering algorithm, determining the number of clusters, and validating the analysis. It provides examples of hierarchical and non-hierarchical clustering methods like k-means and discusses choosing between these approaches. SPSS is used to demonstrate a cluster analysis example analyzing supermarket customer data.
An Introduction to Factor analysis pptMukesh Bisht
This document discusses exploratory factor analysis (EFA). EFA is used to identify underlying factors that explain the pattern of correlations within a set of observed variables. The document outlines the steps of EFA, including testing assumptions, constructing a correlation matrix, determining the number of factors, rotating factors, and interpreting the factor loadings. It provides an example of running EFA on a dataset with 11 physical performance and anthropometric variables from 21 participants. The analysis extracts 3 factors that explain over 80% of the total variance.
The Normal Distribution is a symmetrical probability distribution where most results are located in the middle and few are spread on both sides. It has the shape of a bell and can entirely be described by its mean and standard deviation.
This document discusses exploratory factor analysis (EFA). EFA is used to identify underlying factors that explain the pattern of correlations within a set of observed variables. The document outlines the steps of EFA including testing assumptions, constructing a correlation matrix, determining the number of factors, rotating factors, and interpreting the factor loadings. It provides an example of running EFA on a dataset with 11 physical performance and anthropometric variables from 21 participants. The analysis extracts 3 factors that explain over 80% of the total variance.
This document discusses different sampling techniques that can be used to analyze large datasets. It defines key sampling concepts like the target population, sampling frame, and sampling unit. Probability sampling techniques described include simple random sampling, systematic sampling, stratified sampling, cluster sampling, and probability proportional to size sampling. Non-probability sampling techniques include convenience sampling and purposive sampling. The document also covers how to calculate sample sizes needed to estimate proportions and means within a desired level of accuracy. Stratified sampling can help reduce variability and improve efficiency by dividing the population into relevant subgroups.
One of the most important, yet often overlooked, aspects of predictive modeling is the transformation of data to create model inputs, better known as feature engineering (FE). This talk will go into the theoretical background behind FE, showing how it leverages existing data to produce better modeling results. It will then detail some important FE techniques that should be in every data scientist’s tool kit.
The document discusses various measures used to summarize sample data, including measures of central tendency (location) and spread (dispersion). It describes how to calculate the arithmetic mean, mode, and median of raw data and frequency tables. The mean is the average value, the mode is the most frequent observation, and the median is the middle value when data is ordered from lowest to highest. For skewed data, the mode or median may better indicate central tendency than the mean. The document also introduces the interquartile range as a measure of spread and shows how to calculate percentiles from raw and grouped frequency data.
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Discussion on Vector Databases, Unstructured Data and AI
https://www.meetup.com/unstructured-data-meetup-new-york/
This meetup is for people working in unstructured data. Speakers will come present about related topics such as vector databases, LLMs, and managing data at scale. The intended audience of this group includes roles like machine learning engineers, data scientists, data engineers, software engineers, and PMs.This meetup was formerly Milvus Meetup, and is sponsored by Zilliz maintainers of Milvus.
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataKiwi Creative
Harness the power of AI-backed reports, benchmarking and data analysis to predict trends and detect anomalies in your marketing efforts.
Peter Caputa, CEO at Databox, reveals how you can discover the strategies and tools to increase your growth rate (and margins!).
From metrics to track to data habits to pick up, enhance your reporting for powerful insights to improve your B2B tech company's marketing.
- - -
This is the webinar recording from the June 2024 HubSpot User Group (HUG) for B2B Technology USA.
Watch the video recording at https://youtu.be/5vjwGfPN9lw
Sign up for future HUG events at https://events.hubspot.com/b2b-technology-usa/
Analysis insight about a Flyball dog competition team's performanceroli9797
Insight of my analysis about a Flyball dog competition team's last year performance. Find more: https://github.com/rolandnagy-ds/flyball_race_analysis/tree/main
End-to-end pipeline agility - Berlin Buzzwords 2024Lars Albertsson
We describe how we achieve high change agility in data engineering by eliminating the fear of breaking downstream data pipelines through end-to-end pipeline testing, and by using schema metaprogramming to safely eliminate boilerplate involved in changes that affect whole pipelines.
A quick poll on agility in changing pipelines from end to end indicated a huge span in capabilities. For the question "How long time does it take for all downstream pipelines to be adapted to an upstream change," the median response was 6 months, but some respondents could do it in less than a day. When quantitative data engineering differences between the best and worst are measured, the span is often 100x-1000x, sometimes even more.
A long time ago, we suffered at Spotify from fear of changing pipelines due to not knowing what the impact might be downstream. We made plans for a technical solution to test pipelines end-to-end to mitigate that fear, but the effort failed for cultural reasons. We eventually solved this challenge, but in a different context. In this presentation we will describe how we test full pipelines effectively by manipulating workflow orchestration, which enables us to make changes in pipelines without fear of breaking downstream.
Making schema changes that affect many jobs also involves a lot of toil and boilerplate. Using schema-on-read mitigates some of it, but has drawbacks since it makes it more difficult to detect errors early. We will describe how we have rejected this tradeoff by applying schema metaprogramming, eliminating boilerplate but keeping the protection of static typing, thereby further improving agility to quickly modify data pipelines without fear.
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeWalaa Eldin Moustafa
Dynamic policy enforcement is becoming an increasingly important topic in today’s world where data privacy and compliance is a top priority for companies, individuals, and regulators alike. In these slides, we discuss how LinkedIn implements a powerful dynamic policy enforcement engine, called ViewShift, and integrates it within its data lake. We show the query engine architecture and how catalog implementations can automatically route table resolutions to compliance-enforcing SQL views. Such views have a set of very interesting properties: (1) They are auto-generated from declarative data annotations. (2) They respect user-level consent and preferences (3) They are context-aware, encoding a different set of transformations for different use cases (4) They are portable; while the SQL logic is only implemented in one SQL dialect, it is accessible in all engines.
#SQL #Views #Privacy #Compliance #DataLake
1. Multivariate Analysis
• Many statistical techniques focus on just
one or two variables
• Multivariate analysis (MVA) techniques
allow more than two variables to be
analysed at once
– Multiple regression is not typically included
under this heading, but can be thought of as a
multivariate analysis
2. Outline of Lectures
• We will cover
– Why MVA is useful and important
• Simpson’s Paradox
– Some commonly used techniques
• Principal components
• Cluster analysis
• Correspondence analysis
• Others if time permits
– Market segmentation methods
– An overview of MVA methods and their niches
3. Simpson’s Paradox
• Example: 44% of male
applicants are admitted by
a university, but only 33%
of female applicants
• Does this mean there is
unfair discrimination?
• University investigates
and breaks down figures
for Engineering and
English programmes
Male Female
Accept 35 20
Refuse
entry
45 40
Total 80 60
4. Simpson’s Paradox
• No relationship between sex
and acceptance for either
programme
– So no evidence of
discrimination
• Why?
– More females apply for the
English programme, but it it
hard to get into
– More males applied to
Engineering, which has a
higher acceptance rate than
English
• Must look deeper than single
cross-tab to find this out
Engineer-
ing
Male Female
Accept 30 10
Refuse
entry
30 10
Total 60 20
English Male Female
Accept 5 10
Refuse
entry
15 30
Total 20 40
5. Another Example
• A study of graduates’ salaries showed negative
association between economists’ starting salary
and the level of the degree
– i.e. PhDs earned less than Masters degree holders, who
in turn earned less than those with just a Bachelor’s
degree
– Why?
• The data was split into three employment sectors
– Teaching, government and private industry
– Each sector showed a positive relationship
– Employer type was confounded with degree level
6.
7. Simpson’s Paradox
• In each of these examples, the bivariate
analysis (cross-tabulation or correlation)
gave misleading results
• Introducing another variable gave a better
understanding of the data
– It even reversed the initial conclusions
8. Many Variables
• Commonly have many relevant variables in
market research surveys
– E.g. one not atypical survey had ~2000 variables
– Typically researchers pore over many crosstabs
– However it can be difficult to make sense of these, and
the crosstabs may be misleading
• MVA can help summarise the data
– E.g. factor analysis and segmentation based on
agreement ratings on 20 attitude statements
• MVA can also reduce the chance of obtaining
spurious results
9. Multivariate Analysis Methods
• Two general types of MVA technique
– Analysis of dependence
• Where one (or more) variables are dependent
variables, to be explained or predicted by others
– E.g. Multiple regression, PLS, MDA
– Analysis of interdependence
• No variables thought of as “dependent”
• Look at the relationships among variables, objects or
cases
– E.g. cluster analysis, factor analysis
10. Principal Components
• Identify underlying dimensions or principal
components of a distribution
• Helps understand the joint or common
variation among a set of variables
• Probably the most commonly used method
of deriving “factors” in factor analysis
(before rotation)
11. Principal Components
• The first principal component is identified as the
vector (or equivalently the linear combination of
variables) on which the most data variation can be
projected
• The 2nd principal component is a vector
perpendicular to the first, chosen so that it
contains as much of the remaining variation as
possible
• And so on for the 3rd principal component, the 4th,
the 5th etc.
12. Principal Components - Examples
• Ellipse, ellipsoid, sphere
• Rugby ball
• Pen
• Frying pan
• Banana
• CD
• Book
13. Multivariate Normal Distribution
• Generalisation of the univariate normal
• Determined by the mean (vector) and
covariance matrix
• E.g. Standard bivariate normal
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14. Example – Crime Rates by State
The PRINCOMP Procedure
Observations 50
Variables 7
Simple Statistics
Murder Rape Robbery Assault Burglary Larceny Auto_Theft
Mean 7.444000000 25.73400000 124.0920000 211.3000000 1291.904000 2671.288000 377.5260000
StD 3.866768941 10.75962995 88.3485672 100.2530492 432.455711 725.908707 193.3944175
Crime Rates per 100,000 Population by State
Obs State Murder Rape Robbery Assault Burglary Larceny Auto_Theft
1 Alabama 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7
2 Alaska 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3
3 Arizona 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5
4 Arkansas 8.8 27.6 83.2 203.4 972.6 1862.1 183.4
5 California 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5
… … ... ... ... ... ... ... ...
16. Eigenvectors
Prin1 Prin2 Prin3 Prin4 Prin5 Prin6 Prin7
Murder 0.300279 -.629174 0.178245 -.232114 0.538123 0.259117 0.267593
Rape 0.431759 -.169435 -.244198 0.062216 0.188471 -.773271 -.296485
Robbery 0.396875 0.042247 0.495861 -.557989 -.519977 -.114385 -.003903
Assault 0.396652 -.343528 -.069510 0.629804 -.506651 0.172363 0.191745
Burglary 0.440157 0.203341 -.209895 -.057555 0.101033 0.535987 -.648117
Larceny 0.357360 0.402319 -.539231 -.234890 0.030099 0.039406 0.601690
Auto_Theft 0.295177 0.502421 0.568384 0.419238 0.369753 -.057298 0.147046
• 2-3 components explain 76%-87% of the variance
• First principal component has uniform variable weights, so
is a general crime level indicator
• Second principal component appears to contrast violent
versus property crimes
• Third component is harder to interpret
17. Cluster Analysis
• Techniques for identifying separate groups
of similar cases
– Similarity of cases is either specified directly in
a distance matrix, or defined in terms of some
distance function
• Also used to summarise data by defining
segments of similar cases in the data
– This use of cluster analysis is known as
“dissection”
18. Clustering Techniques
• Two main types of cluster analysis methods
– Hierarchical cluster analysis
• Each cluster (starting with the whole dataset) is divided into
two, then divided again, and so on
– Iterative methods
• k-means clustering (PROC FASTCLUS)
• Analogous non-parametric density estimation method
– Also other methods
• Overlapping clusters
• Fuzzy clusters
19. Applications
• Market segmentation is usually conducted
using some form of cluster analysis to
divide people into segments
– Other methods such as latent class models or
archetypal analysis are sometimes used instead
• It is also possible to cluster other items such
as products/SKUs, image attributes, brands
20. Tandem Segmentation
• One general method is to conduct a factor
analysis, followed by a cluster analysis
• This approach has been criticised for losing
information and not yielding as much
discrimination as cluster analysis alone
• However it can make it easier to design the
distance function, and to interpret the results
21. Tandem k-means Example
proc factor data=datafile n=6 rotate=varimax round reorder flag=.54 scree out=scores;
var reasons1-reasons15 usage1-usage10;
run;
proc fastclus data=scores maxc=4 seed=109162319 maxiter=50;
var factor1-factor6;
run;
• Have used the default unweighted Euclidean distance
function, which is not sensible in every context
• Also note that k-means results depend on the initial cluster
centroids (determined here by the seed)
• Typically k-means is very prone to local maxima
– Run at least 20 times to ensure reasonable maximum
22. Selected Outputs
19th run of 5 segments
Cluster Summary
Maximum Distance
RMS Std from Seed Nearest Distance Between
Cluster Frequency Deviation to Observation Cluster Cluster Centroids
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
1 433 0.9010 4.5524 4 2.0325
2 471 0.8487 4.5902 4 1.8959
3 505 0.9080 5.3159 4 2.0486
4 870 0.6982 4.2724 2 1.8959
5 433 0.9300 4.9425 4 2.0308
23. Selected Outputs
19th run of 5 segments
FASTCLUS Procedure: Replace=RANDOM Radius=0 Maxclusters=5 Maxiter=100 Converge=0.02
Statistics for Variables
Variable Total STD Within STD R-Squared RSQ/(1-RSQ)
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
FACTOR1 1.000000 0.788183 0.379684 0.612082
FACTOR2 1.000000 0.893187 0.203395 0.255327
FACTOR3 1.000000 0.809710 0.345337 0.527503
FACTOR4 1.000000 0.733956 0.462104 0.859095
FACTOR5 1.000000 0.948424 0.101820 0.113363
FACTOR6 1.000000 0.838418 0.298092 0.424689
OVER-ALL 1.000000 0.838231 0.298405 0.425324
Pseudo F Statistic = 287.84
Approximate Expected Over-All R-Squared = 0.37027
Cubic Clustering Criterion = -26.135
WARNING: The two above values are invalid for correlated variables.
25. Cluster Analysis Options
• There are several choices of how to form clusters in
hierarchical cluster analysis
– Single linkage
– Average linkage
– Density linkage
– Ward’s method
– Many others
• Ward’s method (like k-means) tends to form equal sized,
roundish clusters
• Average linkage generally forms roundish clusters with
equal variance
• Density linkage can identify clusters of different shapes
28. Cluster Analysis Issues
• Distance definition
– Weighted Euclidean distance often works well, if weights are chosen
intelligently
• Cluster shape
– Shape of clusters found is determined by method, so choose method
appropriately
• Hierarchical methods usually take more computation time than k-
means
• However multiple runs are more important for k-means, since it can be
badly affected by local minima
• Adjusting for response styles can also be worthwhile
– Some people give more positive responses overall than others
– Clusters may simply reflect these response styles unless this is adjusted
for, e.g. by standardising responses across attributes for each respondent
29. MVA - FASTCLUS
• PROC FASTCLUS in SAS tries to minimise the
root mean square difference between the data
points and their corresponding cluster means
– Iterates until convergence is reached on this criterion
– However it often reaches a local minimum
– Can be useful to run many times with different seeds
and choose the best set of clusters based on this RMS
criterion
• See http://www.clustan.com/k-
means_critique.html for more k-means issues
32. Howard-Harris Approach
• Provides automatic approach to choosing seeds for k-
means clustering
• Chooses initial seeds by fixed procedure
– Takes variable with highest variance, splits the data at the mean,
and calculates centroids of the resulting two groups
– Applies k-means with these centroids as initial seeds
– This yields a 2 cluster solution
– Choose the cluster with the higher within-cluster variance
– Choose the variable with the highest variance within that cluster,
split the cluster as above, and repeat to give a 3 cluster solution
– Repeat until have reached a set number of clusters
• I believe this approach is used by the ESPRI software
package (after variables are standardised by their range)
33. Another “Clustering” Method
• One alternative approach to identifying clusters is to fit a
finite mixture model
– Assume the overall distribution is a mixture of several normal
distributions
– Typically this model is fit using some variant of the EM algorithm
• E.g. weka.clusterers.EM method in WEKA data mining package
• See WEKA tutorial for an example using Fisher’s iris data
• Advantages of this method include:
– Probability model allows for statistical tests
– Handles missing data within model fitting process
– Can extend this approach to define clusters based on model
parameters, e.g. regression coefficients
• Also known as latent class modeling
37. Correspondence Analysis
• Provides a graphical summary of the interactions
in a table
• Also known as a perceptual map
– But so are many other charts
• Can be very useful
– E.g. to provide overview of cluster results
• However the correct interpretation is less than
intuitive, and this leads many researchers astray
39. Interpretation
• Correspondence analysis plots should be
interpreted by looking at points relative to the
origin
– Points that are in similar directions are positively
associated
– Points that are on opposite sides of the origin are
negatively associated
– Points that are far from the origin exhibit the strongest
associations
• Also the results reflect relative associations, not
just which rows are highest or lowest overall
40. Software for
Correspondence Analysis
• Earlier chart was created using a specialised package
called BRANDMAP
• Can also do correspondence analysis in most major
statistical packages
• For example, using PROC CORRESP in SAS:
*---Perform Simple Correspondence Analysis—Example 1 in SAS OnlineDoc;
proc corresp all data=Cars outc=Coor;
tables Marital, Origin;
run;
*---Plot the Simple Correspondence Analysis Results---;
%plotit(data=Coor, datatype=corresp)
42. Canonical Discriminant Analysis
• Predicts a discrete response from continuous
predictor variables
• Aims to determine which of g groups each
respondent belongs to, based on the predictors
• Finds the linear combination of the predictors with
the highest correlation with group membership
– Called the first canonical variate
• Repeat to find further canonical variates that are
uncorrelated with the previous ones
– Produces maximum of g-1 canonical variates
44. Discriminant Analysis
• Discriminant analysis also refers to a wider
family of techniques
– Still for discrete response, continuous
predictors
– Produces discriminant functions that classify
observations into groups
• These can be linear or quadratic functions
• Can also be based on non-parametric techniques
– Often train on one dataset, then test on another
45. CHAID
• Chi-squared Automatic Interaction Detection
• For discrete response and many discrete predictors
– Common situation in market research
• Produces a tree structure
– Nodes get purer, more different from each other
• Uses a chi-squared test statistic to determine best
variable to split on at each node
– Also tries various ways of merging categories, making
a Bonferroni adjustment for multiple tests
– Stops when no more “statistically significant” splits can
be found
47. Titanic Survival Example
• Adults (20%)
• /
• /
• Men
• /
• /
• / Children (45%)
• /
• All passengers
•
• 3rd class or crew (46%)
• /
• /
• Women
•
•
• 1st or 2nd class passenger (93%)
48. CHAID Software
• Available in SAS Enterprise Miner (if you have
enough money)
– Was provided as a free macro until SAS decided to
market it as a data mining technique
– TREEDISC.SAS – still available on the web, although
apparently not on the SAS web site
• Also implemented in at least one standalone
package
• Developed in 1970s
• Other tree-based techniques available
– Will discuss these later
49. TREEDISC Macro
%treedisc(data=survey2, depvar=bs,
nominal=c o p q x ae af ag ai: aj al am ao ap aw bf_1 bf_2 ck cn:,
ordinal=lifestag t u v w y ab ah ak,
ordfloat=ac ad an aq ar as av,
options=list noformat read,maxdepth=3,
trace=medium, draw=gr, leaf=50,
outtree=all);
• Need to specify type of each variable
– Nominal, Ordinal, Ordinal with a floating value
50. Partial Least Squares (PLS)
• Multivariate generalisation of regression
– Have model of form Y=XB+E
– Also extract factors underlying the predictors
– These are chosen to explain both the response variation
and the variation among predictors
• Results are often more powerful than principal
components regression
• PLS also refers to a more general technique for
fitting general path models, not discussed here
51. Structural Equation Modeling (SEM)
• General method for fitting and testing path
analysis models, based on covariances
• Also known as LISREL
• Implemented in SAS in PROC CALIS
• Fits specified causal structures (path
models) that usually involve factors or
latent variables
– Confirmatory analysis
54. Results
• All parameters are statistically significant, with a high correlation
being found between the latent traits of academic and job success
• However the overall chi-squared value for the model is 111.3, with 4
d.f., so the model does not fit the observed covariances perfectly
55. Latent Variable Models
• Have seen that both latent trait and latent
class models can be useful
– Latent traits for factor analysis and SEM
– Latent class for probabilistic segmentation
• Mplus software can now fit combined latent
trait and latent class models
– Appears very powerful
– Subsumes a wide range of multivariate analyses
56. Broader MVA Issues
• Preliminaries
– EDA is usually very worthwhile
• Univariate summaries, e.g. histograms
• Scatterplot matrix
• Multivariate profiles, spider-web plots
– Missing data
• Establish amount (by variable, and overall) and pattern (across
individuals)
• Think about reasons for missing data
• Treat missing data appropriately – e.g. impute, or build into
model fitting
57. MVA Issues
• Preliminaries (continued)
– Check for outliers
• Large values of Mahalonobis’ D2
• Testing results
– Some methods provide statistical tests
– But others do not
• Cross-validation gives a useful check on the results
– Leave-1-out cross-validation
– Split-sample training and test datasets
» Sometimes 3 groups needed
» For model building, training and testing