This document discusses statistical methods for comparing two independent sample means and two independent sample proportions. It provides steps and examples for conducting significance tests to compare population means and proportions. For means, it describes using a z-test where the test statistic is the difference between sample means divided by the pooled standard error. For proportions, it describes using a z-test where the test statistic is the difference between sample proportions divided by the pooled standard error. Examples provided show conducting these tests to analyze differences in housework hours and attitudes between years.
Raimundo Soto - Catholic University of Chile
ERF Training on Advanced Panel Data Techniques Applied to Economic Modelling
29 -31 October, 2018
Cairo, Egypt
The document provides information about matrix operations and properties. It defines what a matrix is and different types of matrices. It then discusses operations like addition, subtraction, multiplication of matrices. It also covers properties such as transpose, inverse, adjoint and determinant of a matrix. It provides examples to illustrate matrix operations and properties such as finding the inverse and determinant of given matrices.
Numerical Investigation of Higher Order Nonlinear Problem in the Calculus Of ...IOSR Journals
This document presents a numerical investigation of higher order nonlinear problems in calculus of variations using the Adomian decomposition method (ADM). It introduces ADM for solving such problems by reducing them to systems of nonlinear algebraic equations. An example problem is provided and solved numerically using both the single-term Haar wavelet series method (STHWS) and ADM. Error calculations and graphs demonstrate that ADM provides more accurate solutions than STHWS, with less complexity and error. The document concludes that ADM performs better for this type of problem in calculus of variations.
This document discusses interpolation and curve fitting techniques. It introduces polynomial interpolation and regression, and describes how to fit polynomials to datasets to interpolate values. Specifically, it covers:
- Using polynomials of order n-1 to fit n data points
- Setting up and solving systems of equations to determine polynomial coefficients
- Newton's interpolation method, which determines coefficients iteratively without inverting matrices
- Examples of applying these techniques to example datasets
The document discusses the conceptual definition of standard deviation. Standard deviation represents the root average of the squared deviations of scores from the mean. It explains that to calculate standard deviation, each score's deviation from the mean is squared, those squared deviations are averaged, and then the square root of the average is taken to determine the standard deviation in the original units of measurement.
The document discusses hypothesis testing to determine if districts with smaller class sizes have higher test scores. It summarizes the steps taken: 1) Estimation to calculate the difference in average test scores between districts with low vs high student-teacher ratios (STRs), 2) Hypothesis testing to determine if the difference is statistically significant by calculating a t-statistic and comparing it to a critical value, 3) Construction of a confidence interval for the difference between the means. The analysis found the difference in average test scores between low and high STR districts was statistically significant based on a t-statistic greater than the critical value.
Raimundo Soto - Catholic University of Chile
ERF Training on Advanced Panel Data Techniques Applied to Economic Modelling
29 -31 October, 2018
Cairo, Egypt
The document provides information about matrix operations and properties. It defines what a matrix is and different types of matrices. It then discusses operations like addition, subtraction, multiplication of matrices. It also covers properties such as transpose, inverse, adjoint and determinant of a matrix. It provides examples to illustrate matrix operations and properties such as finding the inverse and determinant of given matrices.
Numerical Investigation of Higher Order Nonlinear Problem in the Calculus Of ...IOSR Journals
This document presents a numerical investigation of higher order nonlinear problems in calculus of variations using the Adomian decomposition method (ADM). It introduces ADM for solving such problems by reducing them to systems of nonlinear algebraic equations. An example problem is provided and solved numerically using both the single-term Haar wavelet series method (STHWS) and ADM. Error calculations and graphs demonstrate that ADM provides more accurate solutions than STHWS, with less complexity and error. The document concludes that ADM performs better for this type of problem in calculus of variations.
This document discusses interpolation and curve fitting techniques. It introduces polynomial interpolation and regression, and describes how to fit polynomials to datasets to interpolate values. Specifically, it covers:
- Using polynomials of order n-1 to fit n data points
- Setting up and solving systems of equations to determine polynomial coefficients
- Newton's interpolation method, which determines coefficients iteratively without inverting matrices
- Examples of applying these techniques to example datasets
The document discusses the conceptual definition of standard deviation. Standard deviation represents the root average of the squared deviations of scores from the mean. It explains that to calculate standard deviation, each score's deviation from the mean is squared, those squared deviations are averaged, and then the square root of the average is taken to determine the standard deviation in the original units of measurement.
The document discusses hypothesis testing to determine if districts with smaller class sizes have higher test scores. It summarizes the steps taken: 1) Estimation to calculate the difference in average test scores between districts with low vs high student-teacher ratios (STRs), 2) Hypothesis testing to determine if the difference is statistically significant by calculating a t-statistic and comparing it to a critical value, 3) Construction of a confidence interval for the difference between the means. The analysis found the difference in average test scores between low and high STR districts was statistically significant based on a t-statistic greater than the critical value.
Hybrid Block Method for the Solution of First Order Initial Value Problems of...iosrjce
Method of collocation of the differential system and interpolation of the approximate solution which
is a combination of power series and exponential function at some selected grid and off-grid points to generate
a linear multistep method which is implemented in block method is considered in this paper. The basic
properties of the block method which include; consistency, convergence and stability interval is verified. The
method is tested on some numerical experiments and found to have better stability condition and better
approximation than the existing methods
This document provides an overview of the key topics in Chapter 6 on the normal distribution, including:
1) It introduces continuous probability distributions and defines the normal distribution as the most important continuous probability distribution.
2) It explains how the normal distribution can be standardized to have a mean of 0 and standard deviation of 1, known as the standardized normal distribution.
3) It outlines the types of problems that will be solved using the normal distribution, including finding probabilities and percentiles for both the normal and standardized normal distribution.
The document discusses how to calculate standard deviation and variance for both ungrouped and grouped data. It provides step-by-step instructions for finding the mean, deviations from the mean, summing the squared deviations, and using these values to calculate standard deviation and variance through standard formulas. Standard deviation measures how spread out numbers are from the mean, while variance is the square of the standard deviation.
1. The document announces that students should bring any exam 1 grade questions without delay, and that the homework for exam 2 has been uploaded and may be updated. It also notes that the last day to drop the class is February 4th and there is no class on that date.
2. The document covers topics from the last class including computing 3x3 determinants, determinants of triangular matrices, and techniques for larger matrices.
3. The document then provides examples of computing determinants and discusses important properties including that row operations do not change the determinant value while row interchanges flip the sign, and multiplying a row scales the determinant.
The document provides data on teen abortion rates from 1980 to 2002. It then explains how to calculate the standard deviation of this data, which measures how spread out the values are. It performs the calculation and finds that the standard deviation of teen abortion rates from 1980 to 2002 is 7.87.
The document discusses using standard deviation to analyze how spread out data is from the mean. It provides an example of two classes that had the same average quiz score but different standard deviations, indicating the scores were more varied in one class than the other. Standard deviation is calculated by taking the square root of the average of the squared distances from the mean, providing a measure of how concentrated or dispersed the data is.
1) The document discusses standard deviation and variance as measures of how dispersed data points are from the mean. It provides formulas to calculate population variance, sample variance, population standard deviation, and sample standard deviation.
2) Examples are given to demonstrate calculating variance and standard deviation from raw data sets and frequency distributions. This helps determine which data set or person is more consistent.
3) The empirical rule is described, stating that approximately 68%, 95%, and 99.7% of values in a bell-shaped distribution fall within 1, 2, and 3 standard deviations of the mean, respectively.
This document provides examples for a statistics lab involving random variables, probability distributions, and confidence intervals.
[1] It asks whether rolling a die is a discrete or continuous random variable and to calculate the mean and standard deviation of rolling a 4-sided die.
[2] The mean of rolling the 4-sided die is calculated as 2.5 and the standard deviation is calculated as 1.118.
[3] It then has the student calculate descriptive statistics like the mean and median of various data samples and compares how centered they are around the true parameter.
MAT 540(Str) Education Organization - snaptutorial.comranga5
This document contains 20 sets of final exam questions and 5 sets of midterm exam questions for the course MAT 540. Each exam set includes multiple choice and short answer questions testing concepts like probability, forecasting, simulation, and decision analysis. Sample questions assess understanding of key terms, calculations, and analyses related to quantitative methods and modeling uncertainty.
1. The standard deviation is a measure of how spread out numbers are from the average value.
2. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
3. When only a sample of data is available rather than the entire population, the sample standard deviation is estimated using N-1 in the denominator rather than N to reduce bias, though some bias still remains for small samples.
This document contains practice exam questions and answers for the MAT 540 class. It includes 20 sets of final exam questions and 5 sets of midterm exam questions. Each exam set contains around 30-40 multiple choice or short answer questions covering topics like probability, forecasting, simulation, and decision analysis. The questions assess understanding of key concepts and ability to perform related calculations.
The document provides an introduction to the ISPCMS project. It will have 4 team members working over 6 weeks. The project uses a Pentium IV processor with 256MB RAM and 40GB hard drive running Windows NT. It will be developed using Visual Basic 6.0 and Oracle 9i. The software engineering paradigm will use a prototype model. The objective of ISPCMS is to provide fast processing of consumer applications, automatic billing, easier payment acceptance, and computerized plan setup with data security. It will have various forms like new connection, disconnection, billing, payment, customer details, and payment details. There is potential to further expand the project into a complete ISPCMS system.
Anthony Plumridge, Principal Lecturer, School of Economics, University of the West of England, Bristol, talks to the SWO Future Skills seminar on key sectors in the region and West of England Area.
Hybrid Block Method for the Solution of First Order Initial Value Problems of...iosrjce
Method of collocation of the differential system and interpolation of the approximate solution which
is a combination of power series and exponential function at some selected grid and off-grid points to generate
a linear multistep method which is implemented in block method is considered in this paper. The basic
properties of the block method which include; consistency, convergence and stability interval is verified. The
method is tested on some numerical experiments and found to have better stability condition and better
approximation than the existing methods
This document provides an overview of the key topics in Chapter 6 on the normal distribution, including:
1) It introduces continuous probability distributions and defines the normal distribution as the most important continuous probability distribution.
2) It explains how the normal distribution can be standardized to have a mean of 0 and standard deviation of 1, known as the standardized normal distribution.
3) It outlines the types of problems that will be solved using the normal distribution, including finding probabilities and percentiles for both the normal and standardized normal distribution.
The document discusses how to calculate standard deviation and variance for both ungrouped and grouped data. It provides step-by-step instructions for finding the mean, deviations from the mean, summing the squared deviations, and using these values to calculate standard deviation and variance through standard formulas. Standard deviation measures how spread out numbers are from the mean, while variance is the square of the standard deviation.
1. The document announces that students should bring any exam 1 grade questions without delay, and that the homework for exam 2 has been uploaded and may be updated. It also notes that the last day to drop the class is February 4th and there is no class on that date.
2. The document covers topics from the last class including computing 3x3 determinants, determinants of triangular matrices, and techniques for larger matrices.
3. The document then provides examples of computing determinants and discusses important properties including that row operations do not change the determinant value while row interchanges flip the sign, and multiplying a row scales the determinant.
The document provides data on teen abortion rates from 1980 to 2002. It then explains how to calculate the standard deviation of this data, which measures how spread out the values are. It performs the calculation and finds that the standard deviation of teen abortion rates from 1980 to 2002 is 7.87.
The document discusses using standard deviation to analyze how spread out data is from the mean. It provides an example of two classes that had the same average quiz score but different standard deviations, indicating the scores were more varied in one class than the other. Standard deviation is calculated by taking the square root of the average of the squared distances from the mean, providing a measure of how concentrated or dispersed the data is.
1) The document discusses standard deviation and variance as measures of how dispersed data points are from the mean. It provides formulas to calculate population variance, sample variance, population standard deviation, and sample standard deviation.
2) Examples are given to demonstrate calculating variance and standard deviation from raw data sets and frequency distributions. This helps determine which data set or person is more consistent.
3) The empirical rule is described, stating that approximately 68%, 95%, and 99.7% of values in a bell-shaped distribution fall within 1, 2, and 3 standard deviations of the mean, respectively.
This document provides examples for a statistics lab involving random variables, probability distributions, and confidence intervals.
[1] It asks whether rolling a die is a discrete or continuous random variable and to calculate the mean and standard deviation of rolling a 4-sided die.
[2] The mean of rolling the 4-sided die is calculated as 2.5 and the standard deviation is calculated as 1.118.
[3] It then has the student calculate descriptive statistics like the mean and median of various data samples and compares how centered they are around the true parameter.
MAT 540(Str) Education Organization - snaptutorial.comranga5
This document contains 20 sets of final exam questions and 5 sets of midterm exam questions for the course MAT 540. Each exam set includes multiple choice and short answer questions testing concepts like probability, forecasting, simulation, and decision analysis. Sample questions assess understanding of key terms, calculations, and analyses related to quantitative methods and modeling uncertainty.
1. The standard deviation is a measure of how spread out numbers are from the average value.
2. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
3. When only a sample of data is available rather than the entire population, the sample standard deviation is estimated using N-1 in the denominator rather than N to reduce bias, though some bias still remains for small samples.
This document contains practice exam questions and answers for the MAT 540 class. It includes 20 sets of final exam questions and 5 sets of midterm exam questions. Each exam set contains around 30-40 multiple choice or short answer questions covering topics like probability, forecasting, simulation, and decision analysis. The questions assess understanding of key concepts and ability to perform related calculations.
The document provides an introduction to the ISPCMS project. It will have 4 team members working over 6 weeks. The project uses a Pentium IV processor with 256MB RAM and 40GB hard drive running Windows NT. It will be developed using Visual Basic 6.0 and Oracle 9i. The software engineering paradigm will use a prototype model. The objective of ISPCMS is to provide fast processing of consumer applications, automatic billing, easier payment acceptance, and computerized plan setup with data security. It will have various forms like new connection, disconnection, billing, payment, customer details, and payment details. There is potential to further expand the project into a complete ISPCMS system.
Anthony Plumridge, Principal Lecturer, School of Economics, University of the West of England, Bristol, talks to the SWO Future Skills seminar on key sectors in the region and West of England Area.
The document discusses cloud computing from the perspectives of users, technology, definitions, services, charging models, and business outlook. Technologically, cloud computing evolved from virtualization and the ASP model. For users, the cloud can provide on-demand access to resources and applications. Major cloud services include IaaS, PaaS, and SaaS. The business outlook indicates cloud adoption is growing rapidly and brings benefits to both customers and providers, though risks also exist for customers.
The document provides examples and exercises for solving systems of linear equations by graphing, substitution, and elimination. It explains that when graphing two linear equations, the point of intersection is the solution to the system. For substitution, one equation is solved for one variable in terms of the other and substituted into the other equation. For elimination, like terms are eliminated by adding or subtracting the equations to solve for one variable in terms of the other.
This document provides instructions for a group activity to provide feedback on a descriptive essay draft. Students are assigned different roles - to identify the feeling portrayed, comment on descriptions, identify aspects described in each paragraph, and list metaphors used. It warns that the activity is graded and accurate feedback in the assigned role is required to receive full marks.
This is not your father's Amway! As new players enter the network marketing arena and redefine this distribution channel, which companies will succeed and why? What must we re-invent about the direct selling industry and what tools, products and brands will dominate?
Testing, Reporting, and Analytics... Oh My!Informz
This webinar is perfect for those who are looking to create more effective email marketing programs. Attendees can expect to learn how to create an effective testing program, what to look for in email reporting and analytics, and how to best use analytics to determine success and create emarketing goals.
Barack Obama was raised by his single mother and grandparents who taught him Midwestern values despite having little money. He put himself through school with loans and later worked for churches in Chicago helping communities affected by plant closures. After law school, Obama turned down lucrative jobs to return to Chicago and lead a voter registration drive while also teaching law and staying active in his community. Obama and his wife Michelle have two daughters. Nearly 14 million women and 13 million children in the U.S. are living in poverty, which Obama and Joe Biden are committed to addressing.
Tags located at the top of report pages on GigaOM Pro can be clicked to search by that tag or browse additional tags. Tags include general topics as well as companies and technologies. Searches can be rerun by selecting the intersection of two tags or a tag can be removed and the search rerun without it. The number next to a tag indicates how many reports match the intersection of the current search results and that tag. RSS entries on GigaOM Pro can also be distributed to other platforms through ifttt.com.
The document discusses the role of culture and its influence on organizations. It defines culture as the shared values, understandings, assumptions, and goals learned from previous generations and passed down over time. Culture is influenced by factors like kinship, education, economy, politics, religion, health, and recreation. It also discusses key cultural value dimensions, differences in cultural perspectives, and the importance of cultural awareness, sensitivity, and avoiding ethnocentrism in organizations.
This document outlines a social media marketing plan for Scholars Academy Tutoring to increase student numbers and revenue. It begins with an overview of the company and research on the tutoring industry, competitors, and target consumers. Segmentation analysis identifies working and stay-at-home moms as the key decision makers. The plan proposes a three phase approach: 1) Updating online presence, 2) Engaging consumers through social media, and 3) Potentially offering online tutoring. The goal is to slowly transition the owners to embracing social media and online opportunities while proving a connection exists between tutoring and the target moms online.
ConnectEDU2.0 is a service that aims to help overseas Filipino parents monitor their children's academic performance in public schools through wireless updates. It provides teachers a website to input student assignments, grades, and activities, and parents receive text alerts about updates. Currently, it relies on basic text messaging, but plans to create its own website and eventually launch a mobile app to provide richer updates with photos and videos. The service targets the estimated 7 million OFW parents spending $1.4 billion annually on communication with their families. It aims to initially capture 3% of this $1.96 billion market, or $58.8 million annually. The service will evolve through three phases - starting as a basic text alert system
Brainstorming is a technique used to generate ideas in a group setting where participants are encouraged to freely propose unconventional solutions. It works best when there is a need to generate many ideas on a given topic from a group. To brainstorm effectively, a facilitator and recorder should be designated, ground rules like no criticism established, and ideas recorded and organized. There are two types - divergent brainstorming aims for quantity of ideas and doesn't require experts, while convergent brainstorming seeks remedies from experts and fewer overall ideas.
Dokumen tersebut merangkum profil Seksi Pemberdayaan Sumber Daya Pendidikan di LPMP Jawa Barat dari tahun 2004-2007. Seksi ini bertugas melakukan fasilitasi sumber daya pendidikan dan peningkatan kompetensi guru, serta direncanakan beberapa kegiatan pelatihan tahunan. Pada tahun 2005, seksi ini berubah nama menjadi Seksi Fasilitasi Sumber Daya Pendidikan sesuai peraturan baru.
This document discusses statistical tests for comparing two independent sample means and two independent sample proportions. It provides steps and examples for conducting large sample z-tests to compare means and proportions. Specifically, it outlines how to test the null hypothesis that there is no difference between population means or proportions using a test statistic, p-value, and conclusion about whether to reject or fail to reject the null hypothesis. Examples are provided using data on time spent on housework by gender and opinions about gender roles over time.
This document discusses statistical tests for comparing two independent sample means or proportions. It provides formulas and assumptions for hypothesis testing when the parameter of interest is the difference between population means or proportions. Examples are provided to demonstrate hypothesis testing to compare means from two samples and proportions from two samples. Steps include stating the null hypothesis, calculating the test statistic, obtaining the p-value, and making a conclusion.
IRJET- Analysis of Chi-Square Independence Test for Naïve Bayes Feature Selec...IRJET Journal
This document analyzes using the Chi-Square Independence Test for feature selection in Naive Bayes classification. It uses a student performance dataset to test the Chi-Square Independence Test at different confidence intervals for feature selection. The Chi-Square Test is used to determine whether features are independent or associated with the classification attribute. Features with lower p-values have a stronger association. Naive Bayes models are then built using different feature sets selected at different confidence intervals and evaluated based on their accuracy in 2-class and 5-class classifications of student performance. The results show higher accuracy when using grade features and features selected at higher confidence intervals.
This document provides an overview of econometrics and its application in economic research. It discusses key topics such as:
1. The history and development of econometrics, from linear regression to advanced dynamic models.
2. Statistical issues that can arise in regression like multicollinearity and heteroscedasticity.
3. Model building in econometrics, including partial adjustment models, vector error correction models, and panel data analysis.
4. Examples of econometric analyses using Indonesian economic data to examine relationships between variables like GDP, investment, taxes, and expenditures.
HUDE 225Take Home Directions You are a psychologist working a.docxwellesleyterresa
HUDE 225
Take Home
Directions: You are a psychologist working at a local high-school, and the principal wants to create a pre-assessment of 9th grade students’ algebra ability, in order to identify those in need of remedial instruction.
A team of math teachers constructs the test, and pilots it with one class of students. After these data are collected, the principal asks you to perform an item analysis, in order to provide information about the suitability of the test.
Below is item-response data for 10 participants on 5 selected-response items from the test. All of these items are dichotomous and each are designed to tap the same ability: algebra. Additionally, all of the items feature four possible answer choices.
Your task is to compute all relevant CTT and IRT statistics that we have learned in classfor these particular items. You may use all course materials, and any computer programs (e.g., Excel, SPSS, JMP) or a hand calculator to assist you. Round your answers to two decimal places.
Also—you are the only psychologist in this particular school, so please do your own work. This activity is worth a total of 70 points.
Data:
Examinee
Items
Score
1
2
3
4
5
1
1
1
1
1
1
5
2
1
1
1
0
1
4
3
1
1
1
1
1
5
4
0
0
0
0
0
0
5
1
1
0
1
1
4
6
0
0
0
0
1
1
7
0
1
0
0
0
1
8
1
1
1
1
1
5
9
0
0
1
0
0
1
10
1
0
0
0
0
1
P (5 points)
Q (5 points)
Variance (5 points)
Standard deviation
(5points)
D (5 points)
Point-biserial correlation
(5 points)
Inter-Item Covariance Matrix (5 points: .5 point per covariance)
Item Number
1
2
3
4
5
1
2
3
4
5
Inter-Item Correlation Matrix (5points: .5 point per correlation)
Item Number
1
2
3
4
5
1
1
2
1
3
1
4
1
5
1
Test Statistics (6 points)
Average Score
Composite Variance
Composite SD
Cronbach’s Alpha
Standard Error of Measurement
Standard Error of Estimate
Item-Characteristic Curves (Paste below, 5 points):
(Note: Because of the small sample-size, your principal is only requiring a 1pl IRT model)
Test Information Function (Paste below- 1 point):
Item difficulty parameters (5 points):
Item
b
1
2
3
4
5
Item-Analysis Report: Based on the results of your item analysis, do you think this test is suitable for the purpose for which it was designed? Are there any possible revisions you might recommend? Explain your answer using relevant statistics you calculated above as support. Remember, students may be placed in remedial algebra based on their score on this test, so your report is important. (13 points).
Classical Test Theory and
Item Analysis
1
Review: Why do we measure?
In psychology and education, the
abilities and traits we are interested
in cannot be directly observed
Knowledge, cognitive skills, attitudes,
personality, etc.
So, we use measures to indirectly
assess students on these variables
2
A Classic Discovery
In 1904, Charles Spearman posited the following equation:
X = T ...
The document discusses decision trees and ensemble methods. It begins with an agenda that covers the bias-variance tradeoff, generalizations of this concept, the ExtraTrees algorithm, its sklearn interface, and conclusions. It then reviews decision trees, plotting sample data and walking through how the tree would split the data. Next, it covers the general CART algorithm and different impurity measures. It discusses controlling overfitting via tree depth and other techniques. Finally, it delves into explaining the bias-variance decomposition and tradeoff in more detail.
The document discusses score standardization techniques for evaluating information retrieval systems. It presents two main techniques: std-CDF and std-AB. Std-CDF emphasizes moderately high and low performing systems, while std-AB provides a simple linear transformation. Std-AB is shown to have lower within-system variances and more consistent rankings across collections compared to std-CDF. The document also discusses how score standardization can enable topic set size design and comparisons across different test collections. It provides examples applying std-AB to NTCIR-12 tasks, showing it reduces variances and does not change system rankings.
This document provides an overview of regression analysis and compares regression to neural networks. It defines regression as estimating the relationship between variables. The main types covered are linear, nonlinear, simple, multiple and logistic regression. Examples are given to illustrate simple linear regression and least squares methods. The document also discusses best practices like avoiding overfitting and dealing with multicollinearity. Finally, it provides examples comparing regression and deep learning approaches.
The document discusses estimation of multi-Granger network causal models from time series data. It proposes a joint modeling approach to estimate vector autoregressive (VAR) models for multiple time series datasets simultaneously. The key steps are:
1. Estimate the inverse covariance matrices for each dataset using a factor model approach.
2. Use the estimated inverse covariance matrices in a generalized fused lasso optimization to jointly estimate the VAR coefficient matrices for each dataset.
Simulation results show the joint modeling approach improves estimation of the VAR coefficients and reduces forecasting error compared to estimating the models separately, especially when the number of time points is small. The factor modeling approach also provides a better estimate of the inverse covariance than using the empirical estimate.
Extended Analysis of Cauchy’s InequalityIRJET Journal
This paper provides a multivariate generalization of Cauchy's inequality 1 + x ≤ ex, where x can be any non-negative real number. Specifically, it proves the inequality (2) where x1, x2, ..., xn are pairwise non-negative distinct real numbers. It shows this inequality only holds when the sum of x values is 0. The paper also analyzes this inequality using an ordinary differential equation approach and direct proofs based on concepts like monotone functions, divided differences, and the Beppo Levi theorem.
A computational method for system of linear fredholm integral equationsAlexander Decker
This document presents a numerical method for solving systems of linear Fredholm integral equations of the second kind based on cubic spline interpolation. The method involves discretizing the integral equations and approximating the integrals using cubic splines. This produces a system of algebraic equations that can be solved for the unknown functions. The method is demonstrated on an example problem, and results show the method is accurate, with errors improving as the number of subintervals increases. The method performs better than an existing Adomain decomposition method in terms of accuracy.
This document discusses the normal distribution and related concepts. It begins with an introduction to the normal distribution and its properties. It then covers the probability density function and cumulative distribution function of the normal distribution. The rest of the document discusses key properties like the 68-95-99.7 rule, using the standard normal distribution, and how to determine if a data set follows a normal distribution including using a normal probability plot. Examples are provided throughout to illustrate the concepts.
The document discusses the use of the Team Climate Inventory (TCI) questionnaire in general practice settings. It analyzes response rates and reliability when administered to staff in 60 practices in 1998 and 42 practices in 2003. Various multi-level models are used to estimate variance components and calculate reliability and accuracy scores for the TCI subscales. The results show small between-practice variances, affecting reliability scores. However, accuracy scores accounting for sample sizes are still acceptable. While the TCI may not be highly sensitive to practice differences, it can provide a reasonably accurate assessment of workplace climate with sufficient respondent numbers.
This document summarizes the analysis of data from a pharmaceutical company to model and predict the output variable (titer) from input variables in a biochemical drug production process. Several statistical models were evaluated including linear regression, random forest, and MARS. The analysis involved developing blackbox models using only controlled input variables, snapshot models using all input variables at each time point, and history models incorporating changes in input variables over time to predict titer values. Model performance was compared using cross-validation.
The document describes a simple and effective approach to score standardization called std-AB. It begins by discussing existing standardization methods like std-CDF and their limitations. It then proposes the std-AB method, which linearly transforms raw scores to have a range of 0 to 1. The document evaluates std-AB using several IR test collections and measures like nDCG and nERR. It finds that std-AB performs comparably to std-CDF in terms of ranking systems, handles new systems fairly in a leave-one-out test, and has fewer swaps between topic sets than std-CDF. The document concludes std-AB is a simple and effective alternative to existing standardization methods.
The Spearman rank correlation coefficient is a nonparametric measure of statistical dependence between two variables. It assesses how well the relationship between ranked variables can be described using a monotonic function. The Spearman correlation ranks the data values and then applies the Pearson correlation coefficient to the ranks. It is calculated by finding the differences between the ranks of corresponding data points, squaring these differences, summing them, and normalizing. The Spearman correlation ranges from -1 to 1, with -1 indicating a perfect negative correlation and 1 indicating a perfect positive correlation. Examples are provided to demonstrate calculating Spearman's rho from ranked data and testing for correlation using the test statistic and critical values.
This document defines key concepts in probability, including:
- Probability is a numerical measure of the likelihood of an event occurring. It is measured on a scale from 0 to 1.
- A random experiment is any process with uncertain outcomes that can be repeated. It has a sample space of all possible outcomes.
- Sample outcomes are the potential results of an experiment. The sample space is the set of all sample outcomes.
- An event is any subset of sample outcomes, such as a specific outcome or group of outcomes.
- Probability rules include that the probability of an event must be between 0 and 1, the probability of two mutually exclusive events sums to their individual probabilities, and conditional probability is the probability of one
CA in Patna is a team of professional Chartered Accountant which are providing best services like Company Registration, Income Tax Return, Sales Tax Consultants, Bank Audit and other services specially in Patna.
CA in Dwarka is a team of professional Chartered Accountant which are providing best services like Company Registration, Income Tax Return, Sales Tax Consultants, Bank Audit and other services specially in Dwarka and Delhi NCR.
CA in Dwarka is a team of professional Chartered Accountant which are providing best services like Company Registration, Income Tax Return, Sales Tax Consultants, Bank Audit and other services specially in Dwarka and Delhi NCR.
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This document provides steps for designing a website. It begins by explaining the purpose of a website and identifying key considerations like audience and goals. It then lists rules for website design, such as understanding the user perspective and respecting interface conventions. The document outlines the website design process, including planning, following design rules, using website building tools to create pages, and types of pages. It also lists common website development languages and tools. The document concludes by encouraging the use of templates and pre-designed elements to efficiently build a website.
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
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A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
2. Sociology 601 Class 8: September 24, 2009
6.6: Small-sample inference for a proportion
7.1: Large sample comparisons for two
independent sample means.
7.2: Difference between two large sample
proportions.
2
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3. 7.1 Large sample comparisons for two independent
means
So far, we have been making estimates and
inferences about a single sample statistic
Now, we will begin making estimates and inferences
for two sample statistics at once.
many real-life problems involve such comparisons
two-group problems often serve as a starting point for
more involved statistics, as we shall see in this class.
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4. Independent and dependent samples
Two independent random samples:
Two subsamples, each with a mean score for some other
variable
example: Comparisons of work hours by race or sex
example: Comparison of earnings by marital status
Two dependent random samples:
Two observations are being compared for each “unit” in
the sample
example: before-and-after measurements of the same
person at two time points
example: earnings before and after marriage
husband-wife differences
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5. Comparison of two large-sample means
for independent groups
Hypothesis testing as we have done it so far:
Test statistic: z = (Ybar - o) / (s /SQRT(n))
What can we do when we make inferences about a
difference between population means (2 - 1)?
Treat one sample mean as if it were o ?
(NO: too much type I error)
Calculate a confidence interval for each sample mean
and see if they overlap?
(NO: too much type II error)
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6. Figuring out a test statistic
for a comparison of two means
Is Y2 –Y1an appropriate way to evaluate 2 - 1?
• Answer: Yes. We can appropriately define (2 - 1) as a
parameter of interest and estimate it in an unbiased way
with (Y2 – Y1) just as we would estimate with Y.
• This line of argument may seem trivial, but it becomes
important when we work with variance and standard
deviations.
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7. Figuring out a standard error for a comparison of two
means
Comparing standard errors:
A&F 213: formula without derivation
Is s2
Ybar2 - s2
Ybar1an appropriate way to estimate
2
(Ybar2-Ybar1)?
No!
2
(Ybar2-Ybar1)= 2
(Ybar2) - 2(Ybar2,Ybar1) + 2
(Ybar1)
Where 2(Ybar2,Ybar1) reflects how much the observations
for the two groups are dependent.
For independent groups, 2(Ybar2,Ybar1) = 0,
so 2
(Ybar2-Ybar1)= 2
(Ybar2) + 2
(Ybar1)
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8. Step 1: Significance test for 2 - 1
The parameter of interest is 2 - 1
Assumptions:
the sample is drawn from a random sample of some sort,
the parameter of interest is a variable with an interval
scale,
the sample size is large enough that the sampling
distribution of Ybar2 – Ybar1 is approximately normal.
The two samples are drawn independently
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9. Step 2: Significance test for 2 - 1
The null hypothesis will be that there is no
difference between the population means. This
means that any difference we observe is due to
random chance.
Ho: 2 - 1 = 0
(We can specify an alpha level now if we want)
Q: Would it matter if we used
Ho: 1 - 2 = 0 ?
Ho: 1 = 2 ?
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10. Step 3: Significance test for 2 - 1
The test statistic has a standard form:
z = (estimate of parameter – Ho value of parameter)
standard error of parameter
Y Y
( )
0
2 1 2
2
2
1
s
s
Q: If the null hypothesis is that the means are the
same, why do we estimate two different standard
deviations?
10
2
1
n
n
z
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11. Step 4: Significance test for 2 - 1
P-value of calculated z:
• Table A
• Stata: display 2 * (1 – normal(z) )
• Stata: testi (no data, just parameters)
• Stata: ttest (if data file in memory)
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12. Step 5: Significance test for 2 - 1
Step 5: Conclusion.
Compare the p-value from step 4 to the alpha level
in step 1.
If p < α, reject H0 If p ≥ α, do not reject H0
State a conclusion about the statistical significance
of the test.
Briefly discuss the substantive importance of your
findings.
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13. Significance test for 2 - 1: Example
Do women spend more time on housework than
men?
Data from the 1988 National Survey of Families and
Households:
sex sample size mean hours s.d
men 4252 18.1 12.9
women 6764 32.6 18.2
The parameter of interest is 2 - 1
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14. Significance test for 2 - 1: Example
1. Assumptions: random sample, interval-scale variable,
sample size large enough that the sampling distribution of
2 - 1is approximately normal, independent groups
2. Hypothesis: Ho: 2 - 1= 0
3. Test statistic:
z = ((32.6 – 18.1) – 0) / SQRT((12.9)2/4252 + (18.2)2/6764) = 48.8
4. p-value: p<.001
5. conclusion:
a. reject H0: these sample differences are very unlikely to occur if men
and women do the same number of hours of housework.
b. furthermore, the observed difference of 14.5 hours per week is a
substantively important difference in the amount of housework.
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15. Confidence interval for 2 - 1:
2
2
2
1
s
s
c i Y Y z
housework example with 99% interval:
c.i….
= (32.6 – 18.1) +/- 2.58*( √((12.9)2/4252 + (18.2)2/6764))
= 14.5 +/- 2.58*.30
= 14.5 +/- .8, or (13.7,15.3)
By this analysis, the 99% confidence interval for the
difference in housework is 13.7 to 15.3 hours.
15
2
1
2 1 . .
n
n
School.edhole.com
16. Stata: Large sample significance test for
2 - 1
Immediate (no data, just parameters)
ttesti 4252 18.1 12.9 6764 32.6 18.2, unequal
• Q: why ttesti with large samples?
For the immediate command, you need the following:
sample size for group 1 (n = 4252)
mean for group 1
standard deviation for group 1
sample size for group 2
mean for group 2
standard deviation for group 2
instructions to not assume equal variance (, unequal)
16
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17. Stata: Large sample significance test for
2 - 1, an example
. ttesti 4252 18.1 12.9 6764 32.6 18.2, unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | 4252 18.1 .1978304 12.9 17.71215 18.48785
y | 6764 32.6 .221294 18.2 32.16619 33.03381
---------+--------------------------------------------------------------------
combined | 11016 27.00323 .1697512 17.8166 26.67049 27.33597
---------+--------------------------------------------------------------------
diff | -14.5 .2968297 -15.08184 -13.91816
------------------------------------------------------------------------------
Satterthwaite's degrees of freedom: 10858.6
Ho: mean(x) - mean(y) = diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
t = -48.8496 t = -48.8496 t = -48.8496
P < t = 0.0000 P > |t| = 0.0000 P > t = 1.0000
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18. Large sample significance test for 2 - 1: command for a
data set (#1)
. ttest YEARSJOB, by(nonstandard) unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
0 | 980 9.430612 .2788544 8.729523 8.883391 9.977833
1 | 379 7.907652 .3880947 7.555398 7.144557 8.670747
---------+--------------------------------------------------------------------
combined | 1359 9.005887 .2290413 8.443521 8.556573 9.4552
---------+--------------------------------------------------------------------
diff | 1.522961 .4778884 .5848756 2.461045
------------------------------------------------------------------------------
diff = mean(0) - mean(1) t = 3.1869
Ho: diff = 0 Satterthwaite's degrees of freedom = 787.963
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.9993 Pr(|T| > |t|) = 0.0015 Pr(T > t) = 0.0007
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19. Large sample significance test for 2 - 1: command for a
data set (#2)
. ttest conrinc if wrkstat==1, by(wrkslf) unequal
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
self-emp | 190 48514.62 2406.263 33168.05 43768.03 53261.2
someone | 1263 34417.11 636.9954 22638 33167.43 35666.8
---------+--------------------------------------------------------------------
combined | 1453 36260.56 648.5844 24722.9 34988.3 37532.82
---------+--------------------------------------------------------------------
diff | 14097.5 2489.15 9191.402 19003.6
------------------------------------------------------------------------------
diff = mean(self-emp) - mean(someone) t = 5.6636
Ho: diff = 0 Satterthwaite's degrees of freedom = 216.259
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000
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20. 7.2: Comparisons of two independent
population proportions
In 1982 and 1994, respondents in the General Social Survey
were asked: “Do you agree or disagree with this statement?
‘Women should take care of running their homes and leave
running the country up to men.’”
Year Agree Disagree Total
1982 122 223 345
1994 268 1632 1900
Total 390 1855 2245
Do a formal test to decide whether opinions differed in the
two years.
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21. Step 1: Significance test for π2 - π1
The parameter of interest is π2 - π1
Assumptions:
the sample is drawn from a random sample of some sort,
the parameter of interest is a variable with an interval
scale,
the sample size is large enough that the sampling
distribution of Pihat2 – Pihat1 is approximately normal.
The two samples are drawn independently
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22. Step 2: Significance test for π2 - π1
The null hypothesis will be that there is no
difference between the population proportions. This
means that any difference we observe is due to
random chance.
Ho: π2 - π1 = 0
(State an alpha here if you want to.)
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23. Step 3: Significance test for π2 - π1
The test statistic has a standard form:
z = (estimate of parameter – Ho value of parameter)
standard error of parameter
( ˆ
ˆ )
2 1
1 1
Where pihat is the overall weighted average
This means we are assuming equal variance in the two
populations.
Q: why do we use an assumption of equal variance to
estimate the standard error for the t-test?
23
1 2
ˆ 1 ˆ
n n
z
School.edhole.com
24. Step 4: Significance test for π2 - π1
P-value of calculated z:
• Table A, or
• Stata: display 2 * (1 – normal(z) ), or
• Stata: testi (no data, just parameters)
• Stata: ttest (if data file in memory)
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25. Step 5: Significance test for π2 - π1
Conclusion:
Compare the p-value from step 4 to the alpha level
in step 1.
If p < α, reject H0 If p ≥ α, do not reject H0
State a conclusion about the statistical significance
of the test.
Briefly discuss the substantive importance of your
findings.
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26. Significance test for π2 - π1: Example
1. Assumptions: random sample, interval-scale variable,
sample size large enough that the sampling distribution of
2 - 1is approximately normal, independent groups
2. Hypothesis: Ho: π2 - π1= 0
3. Test statistic:
z = (122/345 – 268/1900) /
SQRT[(390/2245)*(1 - 390/2245)*(1/345 + 1/1900)]
= 9.59
4. p-value: p<<.001
5. conclusion:
a. reject H0: attitudes were clearly different in 1994 than in 1982.
b. furthermore, the observed difference of .21 is a substantively
important change in attitudes.
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27. Comparisons of two independent population proportions:
Confidence Interval
confidence interval:
P P
2 2
P P
1 1
Notice that there is no overall weighted average
Pihat, as there is in a significance test for
proportions.
Instead, we estimate two separate variances from the
separate proportions.
Why?
27
2
1
2 1
(1 ) (1 )
. .
n
n
c i P P z
School.edhole.com
28. STATA: Significance test for π2 - π1:
immediate command
. prtesti 345 .3536 1900 .1411
STATA needs the following information:
sample size for group 1 (n = 345)
proportion for group 1 (p = 122/345)
sample size for group 2 (n = 1900)
proportion for group 2 (p = 268/1900)
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29. STATA: Significance test for π2 - π1:
immediate command
. prtesti 345 .3536 1900 .1411
Two-sample test of proportion x: Number of obs = 345
y: Number of obs = 1900
------------------------------------------------------------------------------
Variable | Mean Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x | .3536 .0257393 .3031518 .4040482
y | .1411 .0079865 .1254467 .1567533
-------------+----------------------------------------------------------------
diff | .2125 .0269499 .1596791 .2653209
| under Ho: .0221741 9.58 0.000
------------------------------------------------------------------------------
Ho: proportion(x) - proportion(y) = diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
z = 9.583 z = 9.583 z = 9.583
P < z = 1.0000 P > |z| = 0.0000 P > z = 0.0000
Note the use of one standard error (unequal variance) for the
confidence interval, School.and another edhole.(equal com
variance) for the
significance test. 29
30. STATA command for a data set (#1)
. prtest nonstandard if (RACECEN1==1 | RACECEN1==2), by(RACECEN1)
Two-sample test of proportion 1: Number of obs = 1389
2: Number of obs = 260
------------------------------------------------------------------------------
Variable | Mean Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1 | .2800576 .0120482 .2564436 .3036716
2 | .3538462 .0296544 .2957247 .4119676
-------------+----------------------------------------------------------------
diff | -.0737886 .0320084 -.1365239 -.0110532
| under Ho: .0307147 -2.40 0.016
------------------------------------------------------------------------------
diff = prop(1) - prop(2) z = -2.4024
Ho: diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(Z < z) = 0.0081 Pr(|Z| < |z|) = 0.0163 Pr(Z > z) = 0.9919
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31. STATA command for a data set (#1)
. gen byte wrkslf0=wrkslf-1
(152 missing values generated)
. prtest wrkslf0 if wrkstat==1, by(sex)
Two-sample test of proportion male: Number of obs = 874
female: Number of obs = 743
------------------------------------------------------------------------------
Variable | Mean Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
male | .8272311 .0127876 .8021678 .8522944
female | .9044415 .0107853 .8833027 .9255802
-------------+----------------------------------------------------------------
diff | -.0772103 .0167286 -.1099978 -.0444229
| under Ho: .0171735 -4.50 0.000
------------------------------------------------------------------------------
diff = prop(male) - prop(female) z = -4.4959
Ho: diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(Z < z) = 0.0000 Pr(|Z| < |z|) = 0.0000 Pr(Z > z) = 1.0000
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