...of observed variables and a set of continuous latent variables. When the observed variables are categorical, CFA is also referred to as item response theory (IRT) analysis (Baker & Kim, 2004; du Toit, 2003). CFA with covariates (MIMIC) includes models where the relationship between factors and a set of covariates are studied to understand measurement invariance and population heterogeneity. These models can include direct effects, that is, the regression of a factor indicator on a covariate in order to study measurement non-invariance. Structural equation modeling (SEM) includes models in which regressions among the continuous latent variables are estimated (Bollen, 1989; Browne & Arminger, 1995; Joreskog & Sorbom, 1979). In all of these models, the latent variables are continuous. Observed dependent variable variables can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types. CFA is a measurement model. SEM has two parts: a measurement model and a structural model. The measurement model for both CFA and SEM is a multivariate regression model that describes the relationships between a set of observed dependent variables and a set of continuous latent variables. The observed dependent variables are referred to as factor indicators and the continuous latent variables are referred to as factors. The relationships are described by a set of linear regression equations for continuous factor indicators...
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...One One-Variable Statistics 1.0 Statistic Terminology Key Concepts Population vs. Sample Population: the entire group about which data are being collected. Sample: part of a population selected so as to gain information about the whole population. Data Data: information providing the basis of a discussion form which conclusions may be drawn. Primary vs. Secondary data Primary data * data gathered directly by the researcher in the act of conducting research or an experiment. • gathered by surveys or experiments Secondary data * data gathered by someone other than the researcher / organization. • found on the internet, books or magazines Observational vs. Experimental data Observational data • data gathered by observation of the subject • For example, the subject is recorded and the behaviours are noted on a period of time. Experimental data • data gathered through experimentation. Categorical (qualitative) vs. Numerical (quantitative) data Categorical data • data that is grouped by specific categories • categories may be ordered naturally (ordinal variables) or have no order (nominal variables) • For example, for ordinal variables height can be naturally ordered using short, average, tall. • For example, for nominal variables hair colour cannot be naturally ordered since no order occurs to their colours. Numerical data * data that are in real number values * can be either discrete or continuous Variable Variable:...
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...share program in Washington, D.C. 3. Data Analysis/ explanation of data set: We are taking hourly data over the span of 2years .Then we split the data into 2 sets: Training data set which comprises of 10000 records and Testing Data set comprises of 6000 records. Training Data set: It is comprised of 1-19th days of each month Testing Data set: It is comprised of 19th to end of month So, we will predict the total bike demand in training data set for each hour and then we will test it on the testing data. 4. Attribute Explanation: Date time hourly date + timestamp Continuous Variable Season 1 = spring, 2 = summer, 3 = fall, 4 = winter Categorical Variable Holiday whether the day is considered a holiday whether the day is neither a weekend nor holiday Categorical Variable Working day Categorical Variable Weather 1: Clear, Few clouds, Partly Categorical Variable cloudy, Partly cloudy 2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist 3:...
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...Date : October 10th 2013 QUESTION 1 Explain the following variables with their categories. For example: categorical, continuous, discrete or qualitative or quantitative. 1. Nominal 2. Ordinal 3. Dichotomous 4. Interval 5. Ratio Answer: We need to grasp the different types of variables we may discover while doing our dissertation. Categorical variables and Continuous variables are the main types of variables. Categorical variables are also known as qualitative or discrete variables while continuous variables are known as quantitative variables. Categorical variables can be differentiated as: * Nominal * Dichotomous * Ordinal Categorical variables have categories or rates/level that is used to describe how the variables should be controlled, measured or presented. Continuous variables can be differentiated as: * Interval * Ratio Continuous variables are always within the form of numerical value which is used to describe how variables should be controlled, measured or presented. 1. Nominal Nominal variables cannot be ordered which is meant they cannot be measured by levels (e.g. a scale from 1 to 5) but by two or more categories (e.g. blue, black, brown or blonde hair). Nominal variables can answer questions such as: a. Gender : Male or Female b. Type of property : a house, apartment or bungalow c. Hair colors : blond, brown, red hair, black, etc d. Blood type: A, B, AB or O For example: Question ...
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...Inferential statistics C. Analytical statistics D. All of the above 2. The _________________ random variables yield categorical responses so that the responses fit into one category or another. A. Quantitative B. Discrete C. Continuous D. Qualitative 3. Which of the following is a qualitative/categorical variable? A. The number of pets owned by a family. B. The number of doors on a car. C. Your favourite TV show. D. Your IQ score. 4. Which of the following is a quantitative variable? A. The make of a TV. B. A person's gender. C. The distance from one city to another (in km). D. A person’s educational background. 5. The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a DVD player made by the company over the past 12 months are satisfied with their products, the possible responses to the question "How much time do you use the DVD player every week on the average?" are values from a A. discrete numerical random variable. B. continuous numerical random variable. C. categorical random variable. D. Cannot answer because of lake of information 6. The classification of student major (accounting, economics, management, marketing, other) is an example of A. a categorical random variable. B. a discrete random variable. C. a continuous random variable. D. Cannot answer because of lake of information 7. Quantitative data refers to: A. any data you present...
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...statistical inference. b. deductive reasoning. c. descriptive statistics. d. statistical thinking. A pie chart showing the party preferences of a sample voters in the northeast is an example of Select one: a. a population. b. descriptive statistics. c. deductive reasoning d. statistical inference The flight time of an airplane going from London to Paris is an example of a Select one: a. categorical variable. b. continuous numerical variable. c. discrete numerical variable. d. constant. Respondents whose telephone numbers have been selected from a directory of all telephone listings in a particular geographical area can be considered a Select one: a. population. b. constant. c. universe. d. sample. The portion of a population that has been selected for analysis is called the Select one: a. variable. b. sample. c. universe. d. data. Response to the question "What is your favorite leisure time activity?" is an example of a Select one: a. numerical variable. b. population. c. constant. d. categorical variable. The process of using the results of a sample to describe the characteristics of the sample is called Select one: a. sampling. b. deductive reasoning. c. statistical inference. d. descriptive statistics. Using a survey of a sample of consumers to draw conclusions about an entire group of consumers is an example of Select one: a. descriptive statistics. b. deductive reasoning. c. statistical...
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...are considered a variable which in this case is a whole number between 0-25. Another variable is the amount of time the students took to study for the test. In this case, the variable varies between a second, minute, hour, or maybe even a tenth of a second. So, variables can differ depending on the situation or the information which is given. Now two types of numerical variables2 are discrete and continuous. Discrete3 is like IQ scores, SAT scores, a person’s shoes size, and so on. Continuous4 is more along the lines of height, weight, and age. Sometimes in the real world the distinction between continuous and discrete variables can be a blur. Height, weight, and age are considered continuous in theory, but they always seem to be rounded off to the nearest inch, ounce, or year, at which point they become discrete. On the other hand, money, which in theory is a discrete variable (because the difference between two values can’t be less than a penny), is mostly thought as a continuous variable because in most real life situation a penny can be thought of as an insignificantly small amount of money. Variables can also be used to describe gender, hair color, nationality, and so on. These variables are called categorical (or qualitative) variables5. Now in some situations categorical variables must be treated differently from numerical variables. They can’t be added, multiplied, or averaged up. In other ways, you can say that both categorical and discrete variables can be treated similarly...
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...to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data. There are two general types of statistic that are used to describe data: Measures of central tendency and Measures of spread. Description of variables and types of data given are as follows: StartSal – Numerical and can be treated as continuous. OnRoad Pct – Numerical and continuous StateU – Categorical and can be treated as nominal CISDegree – categorical and can be treated as nominal Stayed3yrs – Categorical, ordinal and coded Tenure – Numerical and continuous With the given variables, here are the descriptive statistics: Note for non numeric data variables, the descriptive analysis could not be computed. These are: StateU, CISDegree and Stayed3yrs. Variable | Mean | StDev | Variance | Sum | Minimum | Maximum | Range | StartSal | 37986.36 | 1927.05 | 3713503.50 | 2507100.00 | 33800.00 | 42300.00 | 8500.00 | OnRoadPct | 0.5206 | 0.1783 | 0.0318 | 34.3600 | 0.1600 | 1.1100 | 0.9500 | Tenture | 15.294 | 6.622 | 43.850 | 520.000 | 5.0 | 31.000 | 26.000 | The central tendencies for the two variables (StartSal and OnRoadPct) are as follows: StartSal: Mean = 37986.36, Mode = 36100.00 and Median = 37700.00. OnRoadPct : Mean = 0.5206, Mode = 36100.00 and...
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...of California, Los Angeles Abstract Treating Likert scale data as continuous outcomes in confirmatory factor analysis violates the assumption of multivariate normality. Given certain requirements pertaining to the number of categories, skewness, size of the factor loadings, etc., it seems nevertheless possible to recover true parameter values if the data stem from a single homogenous population. It is shown in a multi-group and a latent class context that analyzing Likert data under the assumption of multi-variate normality may distort the factor structure differently across groups or classes. Hence, investigating measurement invariance, which is a necessary requirement for a meaningful comparison of observed groups or latent classes, is problematic. Analyzing subscale scores computed from Likert items does not necessarily solve the problem. Based on a power study, some conditions are established to obtain acceptable results. Questionnaires designed to measure latent variables such as personality factors or attitudes typically use Likert scales as a response format. In response to statements such as ‘does the student yell at others’, participants are asked to choose one of a given number of ordered response categories which run for instance from ‘almost never’ to ‘almost always’. In case the interest of a study focuses on the latent variables underlying the items, data analysis will include fitting latent variable models such as confirmatory factor models. A special type of factor...
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...2 Broad Study in Statistics Descriptive (mô tả) : provides simple summaries about the data collected & about the preliminary observations that have beed made. Such summaries maybe either quantitative (numerical measures) or visual (e.g. simple-to-understand graphs) e.g. Present a summary report of this year business result to management Inferential (suy luận) : are systems of procedures that can be used to draw conclusions from datasets arising from systems affected by random variation. The type of inferential statistical procedure used depends upon the type of data collected as well as the distribution of the data. The procedures are usually used to test hypotheses and establish probability. e.g. Estimate the IQ score of Kaplan students by observing a small group of students Population : e.g. A population is a collection of all individuals, objects, or measurement of interest Sample : e.g. A sample is a portion or part of the population of interst MCQ 1. The process of using sample statistics to draw conclusions about true population parameters is called Statistical inference. Keywords: inferential statistics 2. Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called Descriptive statistics. 3. The collection characteristics of the employees of a particular firm is an example of Descriptive statistics. 4. The estimation of the population...
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...------------------------------------------------- Ch 1 Introduction 1.1 Why Learn Statistics? * Statistics is the branch of mathematics that transforms numbers into useful information for decision makers. Statistics lets you know about the risks associated with making a business decision and allows you to understand and reduce the variation in the decision-making process. * Statistics provides you with methods for making better sense of the numbers used every day to describe or analyze the world we live in. * Statistical methods help you understand the information contained in “the numbers” and determine whether differences in “the numbers are meaningful or just due to chance. * Why learn statistics? First and foremost, statistics helps you make better sense of the world. Second, statistics helps you make better business decisions. 1.2 Statistics in Business * In the business world, statistics has these important specific uses: 1. To summarize business data 2. To draw conclusions from those data 3. To make reliable forecasts about business activities 4. To improve business processes * The statistical methods you use for these tasks come from one of the two branches of statistics: descriptive statistics and inferential statistics. * Descriptive statistics are the methods that help collect, summarize, present, and analyze a set of data. * Inferential statistics are the methods that...
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...Data Analysis in SPSS Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 February 21, 2004 If you wish to cite the contents of this document, the APA reference for them would be DeCoster, J. (2004). Data Analysis in SPSS. Retrieved from http://www.stat-help.com/notes.html Heather Claypool Department of Psychology Miami University of Ohio 136 Benton Hall Oxford, OH 45056 All rights to this document are reserved Table of Contents Introduction ...................................................................................................................................................................1 Interactive Mode versus Syntax Mode ..........................................................................................................................2 Descriptive Statistics .....................................................................................................................................................4 Transformations.............................................................................................................................................................5 Compute ....................................................................................................................................................................5 Recode ............................................................................................................................
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...12777 −Summer 2008 (Prof. Latham) 1. For each of the variables described below, indicate whether the variable is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible. Indicate your choice for each by circling the appropriate answer. Variable Type of variable Level of measurement 2. Which of the following variables are best thought of as continuous, which discrete? Indicate your choice for each by circling the appropriate answer. (a) The number of personal telephone calls made tomorrow at Bingley Corporation. Discrete Continuous (b) The number of defective compact discs in a batch of discs. Discrete Continuous (a) Distance (in miles) Nominal from home to the Quantitative Ordinal nearest all−night Categorical Interval Ratio convenience store (b) Temperature (in degrees Celsius) Nominal Quantitative Ordinal Categorical Interval Ratio Nominal Quantitative Ordinal Categorical Interval Ratio (c) The time for a participant to identify the color of the letters when the word red is shown in green letters on a computer screen. Discrete Continuous (c) Closing price (in dollars) of a stock (d) The number of tickets purchased by a caller on a Rose Bowl ticket hotline. Discrete Continuous (d) Letter grade (A, B, Nominal C, D, or F) Quantitative Ordinal Categorical Interval Ratio 3. In a recent phone survey, people were...
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...and Discrete Probability Distributions Simple Probability To develop an understanding of basic probability concepts To introduce conditional probability To use Bayes’ Theorem to revise probabilities in light of new information To provide an understanding of the basic concepts of discrete probability distributions and their characteristics To develop the concept of mathematical expectation for a discrete random variable To introduce the covariance and illustrate its application in finance To present applications of the binomial distribution in business To present applications of the Poisson distribution in business 02 Counting Techniques 03 Continued 04 Conditional Probability 05 Discrete probability distribution. 06 Mathematical Expectation of Discrete Random Variable 07 Properties of mean and variance of a discrete random Variable. 08 Binomial Distribution. 09 Poisson Distribution. 10. The Normal Distribution and Sampling Distribution Introduction Mathematical Models of Continuous Random Variables To...
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...psycholinguistics) is wrong. Because the often significant correlation between data coming from one speaker or experimental item is not modeled, the standard error estimates, and hence significances are invalid. Any conclusion may only be true of your random sample of items, and not of another random sample. • Modeling random effects as fixed effects is not only conceptually wrong, but often makes it impossible to derive conclusions about fixed effects because (without regularization) unlimited variation can be attributed to a subject or item. Modeling these variables as random effects effectively limits how much variation is attributed to them (there is an assumed normal distribution on random effects). • For categorical response variables in experimental situations with random effects, you would like to have the best of both worlds: the random effects modeling of ANOVA and the appropriate modeling of categorical response variables that you get from logistic regression. GLMMs let you have both simultaneously (Jaeger 2007). More specifically: – A plain ANOVA is inappropriate with a...
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