Some Thoughts About Data Type, Distribution, and Statistical Significance

Although application of statistical methods to biomedical research began only some 150 years ago, statistics is now an integral part of medical research. A knowledge of statistics is also becoming mandatory to understand most medical literature. Data constitute the raw material for statistical work. They are records of measurement or observations or simply counts. A variable refers to a particular character on which a set of data are recorded. Data are thus the values of a variable. It is important to understand the different types of data and their mutual interconversion. Biostatistics begins with descriptive statistics that implies summarizing a collection of data from a sample or population. Categorical data are described in terms of percentages or proportions. With numerical data, individual observations within a sample or population tend to cluster about a central location, with more extreme observations being less frequent. The extent to which observations cluster is summarized by measures of central tendency while the spread can be described by measures of dispersion. The confidence interval (CI) is an increasingly important measure of precision. When we observe samples, there is no way of assessing true population parameters. We can, however, obtain a standard error and use it to define a range in which the true population value is likely to lie with a certain acceptable level of uncertainty. This range is the CI while its two terminal values are the confidence limits. Conventionally, the 95% CI is used. Patterns in data sets or data distributions are important, albeit not so obvious, component of descriptive statistics. The most common distribution is the normal distribution which is depicted as the well-known symmetrical bell-shaped Gaussian curve. Familiarity with other distributions such as the binomial and Poisson distributions is also helpful. Various graphs and plots have been devised to summarize data and trends visually. Some plots, such as the box-and-whiskers plot and the stem-and-leaf plot are used less often but provide useful summaries in select situations.

Linda Shields PhD, FRCNA, Professor of Nursing, University of Limerick, Ireland This is one of a series of short papers on aspects of research by Alison Twycross and Linda Shields The fact that we use statistics as part of everyday life was discussed in a previous paper in this series (Twycross and Shields 2004). This paper will explain the descriptive statistical tests used to give a measure of dispersion. Looking at data in this way allows an indication of the spread or variability of the data to be obtained. For example you might want to compare the spread of pain intensity scores in a child on the days following major surgery. Plotting the scores obtained from a set of data can provide useful information about the dispersion or spread of the data. The graph in Figure 1 shows what is called the normal distribution curve. The normal distribution curve possesses several important mathematical properties: 1 It is symmetrical 2 The mean, median and mode all have the same value 3 The curve descends rapidly at first from the central point but the descent slows down as the tails of the curve are reached (a bell shape) 4 No matter how far you continue the tails of the curve, they never reach the horizontal axis (zero) 5 The normal distribution curve occurs in data drawn from several natural phenomenon – for example, height, IQ, body temperature. Because naturally occurring data are often normally distributed, it is often assumed that all data are normally distributed. Indeed, one of the factors taken into account when choosing which statistical test to use is distribution of the data. It is also possible to describe the spread of data using several simple measures of dispersion. The simplest measure is the range which is the difference between the lowest score and the highest score for a set of data. So if a child reports pain intensity scores over a 24-hour period of: 6, 3, 2, 4, 2, 2, 3, 1, 4, the range is: 6 minus 1 = 5. The range therefore provides information about the spread of scores rather than the typical score. If either the lowest or highest scores are extreme values this will distort the range. The standard deviation is the most common measure used to establish how scores are distributed. The standard deviation is a measure of the dispersion or spread of data scores around the mean value and shows by how much the scores may deviate from the mean. The shape of the curve obtained when the scores are plotted on a graph provides an indication of the value of the standard deviation. If the curve is relatively flat and spread out, the standard deviation will be large, indicating that there is a fairly large variability in the scores. However, if the curve has a steep raise and fall this indicates a small standard deviation and means that all the scores are similar. Another measure sometimes used to ascertain how scores are distributed is variance. The variance measures how far away most scores are from the mean. The smaller the variance, the more similar the scores are; the greater the variance the more disparate the scores are. The statistical methods described in this paper allow the spread or variability of data collected to be ascertained. The most commonly used methods are the range and the standard deviation, which will often be provided in research papers along with the mean score (see Twycross and Shields 2004 for further information about the mean score). These tests are ways of describing the data: descriptive statistics. If you want to establish whether there is a difference between two or more sets of data, or whether there is a relationship between sets of data, inferential statistical tests need to be used PN

The Indonesian Government introduced rice farm insurance scheme (Asuransi Usaha Tani Padi – AUTP program) to protect rice farm from loss caused by flood, drought and pest and disease infestations. It has been discussed the method to calculate pure premium of the rice farm insurance scheme in Indonesia with assume that the distribution of rice yield data is normal distribution, gamma distribution, or normal mixture distribution. The normal distribution can be used for the case of distribution of rice yield data in the form of symmetry. The gamma distribution can be used for the case of distribution of rice yield data in the form of skewed to the right or positively skewed. In addition, the normal and gamma distributions are categorized as unimodal distributions. It has also been discussed the method of calculating pure premium of the rice farm insurance scheme in Indonesia with the assumption that the rice yield data is normal mixture distribution. The normal mixture distribution can be categorized as multimodal distribution. Characteristic of the normal mixture distribution is suitable for rice yield data in Indonesia that contain rice yield data from several provinces. On the other hand it is also known that the 4-parameter beta mixture distribution can be applied to rice yield data in Indonesia. This distribution is more flexible than the normal mixture distribution in terms of the tail shape of the distribution. In this paper, pure premium calculation method of the AUTP program is formulated with assume that the distribution of rice yield data is the 4-parameter beta mixture distribution.Monte Carlo simulation is used to evaluate performance of the method. The Monte Carlo simulation results show that the proposed method has higher accuracy and precision when increasing sample size. The method is applied to the rice productivity data in several provinces in Indonesia for the period 1970 to 2016.

1. Probability Models. 1.1 Discrete Probability Models. 1.2 Conditional Probability and Independence. 1.3 Random Variables. 1.4 Expectation. 1.5 The Variance. 1.6 Covariance and Correlation. 2. Special Discrete Distributions. 2.1 The Binomial Distribution. 2.2 The Hypergeometric Distribution. 2.3 The Geometric and Negative Binomial Distributions. 2.4 The Poisson Distribution. 3. Continuous Random Variables. 4.1 Continuous RV's and Their Distributions. 4.2 Expected Values and Variances. 4.3 Transformations of Random Variables. 4.4Joint Densities. 4 Special Continuous Distributions. 4.1 The Normal Distribution. 4.2 The Gamma Distribution. 5. Conditional Distributions. 5.1 The Discrete Case. 5.2 Conditional Expectations for the Discrete Case. 5.3 Conditional Densities and Expectations for Continuous RV's. 6. Limit Laws. 6.1 Moment Generating Functions. 6.2 Convergence in Probability and in Distribution. 6.3 The Central Limit Theorem. 6.4 The Delta-Method. 7. Estimation. 7.1 Point Estimation. 7.2 The Method of Moments. 7.3 Maximum Likelihood. 7.4 Consistency. 7.5 The OMEGA-Method. 7.6 Confidence Intervals. 7.7 Fisher Information, The Cramer-Rao Bound, and Asymptotic Normality of MLE's. 7.8 Sufficiency. 8. Testing Hypotheses. 8.1 Introduction. 8.2 The Neyman-Pearson Lemma. 8.3 The Likelihood Ratio Test. 8.4 The p-Value and the Relationship Between Tests of Hypotheses and Confidence Intervals. 9. The Multivariate Normal, Chi-square, t, and F-Distributions. 9.1 The Multivariate Normal Distribution. 9.2 The Central and Noncentral Chi-Square Distributions. 9.3 Student's t-Distribution. 9.4 The F-Distribution. 10.3 Nonparametric Statistics. 10.1 The Wilcoxon Test and Estimator. 10.2 One Sample Methods. 10.3 The Kolmogorov-Smirnov Tests. 11. Linear Models. 11.1 The Principle of Least Squares. 11.2 Linear Models. 11.3 F-Tests for H0. 11.4 Two-Way Analysis of Variance. 12. Frequency Data. 12.1 Logistic Regression. 12.2 Two-Way Frequency Tables. 12.3 Chi-Square Goodness of Fit Tests. 13. Miscellaneous Topics. 13.1 Survival Analysis. 13.2 Bootstrapping. 13.3 Bayesian Statistics. 13.4 Sampling.

Chapter 3 - Statistical methods in bioinformatics

INTRODUÇÃO: O envelhecimento é um processo natural de redução progressiva da reserva funcional dos indivíduos e o fator que determina saúde dos idosos é a independência nas suas atividades habituais, que consiste em sua funcionalidade e quando acometidos por alguma enfermidade tendem a ter uma recuperação mais lenta, em comparação aos pacientes jovens, devido ao declínio funcional inerente ao processo de senescência, o que pode resultar em maior risco de morte. OBJETIVO: Avaliar o impacto da capacidade funcional na mortalidade de idosos após seis meses de alta da Unidade de Terapia Intensiva. MÉTODOS: Trata-se de um estudo de coorte, ambispectivo, realizado em uma Unidade de Terapia Intensiva de um hospital público de grande porte, localizado na cidade de Salvador, Bahia em 2018. A amostra foi composta por pacientes idosos admitidos na UTI, com idade igual ou superior a 60 anos, onde foram aplicadas as Escalas de Mobilidade em UTI (EMU) e Estado Funcional (FSS) para avaliar a capacidade funcional no dia da alta da UTI e através de contato telefônico, foi observado a ocorrência de óbito após 6 meses da alta. Foram excluídos pacientes com instabilidade hemodinâmica, desordens congnitivas. e aqueles onde houve impossibilidade de contato telefônico. Para análise estatística dos dados de variáveis contínuas foram avaliados com medidas de tendência central e dispersão, variáveis categóricas avaliadas com medidas de frequência e para relacionar a capacidade funcional e mortalidade foi utilizado o teste não paramétrico de Mann-Whitney com o uso do software SPSS. RESULTADOS: A amostra foi composta por 30 pacientes, sendo a maior parte composta por indivíduos do sexo masculino (60,0%), com média de idade 68,0(±6,7) anos, com perfil diagnóstico predominantemente clínico (70,0%), média de tempo de internamento de 3,2 (±1,8) dias, capacidade funcional aferida pela escala do estado funcional (FSS) da alta de 29,3(±8,5) e pela escala de mobilidade em UTI (EMU) da alta de 8,8 (± 2,6) . Dos pacientes inicialmente avaliados, 08 (21,1%) foram excluídos por impossibilidade de contato por telefônico após a alta, tendo completado o estudo com 30 pacientes, destes 11 (28,9%), evoluíram a óbito em até seis meses após a alta da UTI. Um dado que chama atenção é a taxa de mortalidade nos pacientes estudados, que chegou a 36,6% CONCLUSÃO: O status funcional, de pacientes idosos, no momento da alta da UTI está relacionado com uma maior taxa de mortalidade em seis meses após a alta da unidade de terapia intensiva.

This article reviews and compares different existing statistical tests utilized in significance analysis of gene expression from DNA microarray data. Microarray gene expression study facilitates the investigation of genes that are differentially expressed with respect to different classes of samples. Many gene expression studies also aim to find groups of genes that do something together, or to find out molecular similarities among a group of samples. In all respects, it is very important to know whether there is a difference between two sets of results, and whether that difference is likely to occur due to random variations of the datasets. Hence instead of simple data analysis, statistical tests are the proper way to check statistical relevance. Basically, the statistical significance test is compulsory for yielding an ordered list of relevant genes in terms of differential expression to the investigator. This article surveys a few important statistical tests which include both parametric and nonparametric tests and compares those statistical tests with respect to different performance metrics. The statistical tests have been applied on several artificial and real-life microarray gene expression datasets. Most of the time, real-life datasets contain noise and noisy data can have undesirable effect on the results of any data mining analysis. Therefore, performance analysis on noisy datasets for different statistical tests has also been performed to facilitate the comparative study. Furthermore, correlation analysis of the resultant genes from different statistical methods has been accomplished. Keywords: Analysis, correlation analysis, eigenvector, nonparametric tests, P-value, parametric tests, principal component, statistical tests.

SPC (Statistic Process Control) Control charts are widely used to establish and maintain statistical process control in many domains for process performance shift detection. But the assumption of process data distribution is a potential risk to cause unexpected alarm ratio when we use inadequate control limit setting method. In manufactory practice, we found many engineering data are not following normal distribution. So one by one to analyzes and data transmit is hard to execute in practice, special for large amount of engineering data in semiconductor manufactory. Therefore, in this paper we propose to use different control methods or control chart for the different data types. Basically, 4 types of data distribution are mainly focused: fix valued data (just only one constant value occurs in normality), discrete distribution, normal distribution and continuous non-normal distribution. We design to use data level counts and normal distribution test to split them base on some statistical methods. Depending on the result of classification, we assign the suitable quality control method or control chart type for each class. Of course, the false alarm rate is considered to balance all data types into comparable level.

Objective To evaluate the performance of serum small dense low-density lipoprotein cholesterol(sdLDL-C)kit using enzymic method and investigate the clinical value in coronary heart disease(CHD). Methods According to the standard of Clinical and Laboratory Standards Institute(CLSI ), evaluae the precision, linearity ranges, reportable range and accuracy of sdLDL-C kit. The 683 patients with coronary heart disease ( CHD, 423 men and 260 women, age 35-79 years) who were diagnosed at the people′s hospital of Peking university from October 2015 to October 2016 were divided into two groups. The treated group include 571 patients( CHD1, 342 men and 229 women, age 40-79 years) which taking lipid-lowering drugs and the other include 112 cases ( CHD2, 81 men and 31 women, age 35-70 years ) without Lipid-lowing treatment. Besides, the Control group contains 472 healthy persons(274 men and 198 women, age 41-75 years), were collected from the people′s hospital of Peking university between April and August 2016. The liver function, renal function, blood glucose and blood lipid in CHD group(CHD1, CHD2) and healthy control group were detected. The new enzyme assay kit was used for the determination of sdLDL-C. The data of normal distribution were compared by independent t test between the two groups. The Mann-Whitney U nonparametric test was used for comparison between two groups. Results The precision of sdLDL-C kit examination was in compliance with manufacturer′ statement. The linearity was good in 0.11-2.42 mmol/L(Y=1.008 9X+ 0.024 8, R2=0.998 2), the scope of the report is 0.11-4.84 mmol/L. The level of sdLDL-C in CHD group was significantly higher than that in healthy control group, it has a statistical significance[0.824(0.443) mmol/L, 0.609(0.361) mmol/L; Z=-5.603, P<0.001]. The level of sdLDL-C in (CHD 1) was lower than (CHD 2)[0.761(0.479) mmol/L, 0.888(0. 426) mmol/L; Z=-2.304, P<0.021]. After additional adjustment for various tradition cardiovascular risk factor, including ages, sex, CHO, TG, Hs-CRP, Lp(a), and GLU, the highest quartile of sdLDL-C comparison to the bottom quartile, the OR was 3.02, (95% CI, 1.15-9.05)for CHD. Conclusions Experiment data demonstrated that sdLDL-C kit using enzymic method has good performance in the precision, linearity ranges, reportable range and accuracy, sdLDL-C serum level was significantly higher in CHD group.(Chin J Lab Med, 2017, 40: 716-720) Key words: Coronary disease; Lipoproteins, LDL; Reagent kits, diagnostic; Reproducibility of results

1. Introduction. Statistics and the Life Sciences. Examples and Overview. 2. Description of Populations and Samples. Introduction. Frequency Distributions: Techniques for Data. Frequency Distributions: Shapes and Examples. Descriptive Statistics: Measures of Center. Boxplots. Measures of Dispersion. Effect of Transformation of Variables (Optional). Samples and Populations: Statistical Inference. Perspective. 3. Random Sampling, Probability, and the Binomial Distribution. Probability and the Life Sciences. Random Sampling. Introduction to Probability. Probability Trees. Probability Rules (Optional). Density Curves. Random Variables. The Binomial Distribution. Fitting a Binomial Distribution to Data (Optional). 4. The Normal Distribution. Introduction. The Normal Curves. Areas Under a Normal Curve. Assessing Normality. The Continuity Correction (Optional). Perspective. 5. Sampling Distributions. Basic Ideas. Dichotomous Observations. Quantitative Observations. Illustration of the Central Limit Theorem (Optional). The Normal Approximation to the Binomial Distribution (Optional). Perspective. 6. Confidence Intervals. Statistical Estimation. Standard Error of the Mean. Confidence Interval. Planning a Study to Estimate. Conditions for Validity of Estimation Methods. Confidence Interval for a Population Proportion. Perspective and Summary. 7. Comparison of Two Independent Samples. Introduction. Standard Error of (y1 - y2). Confidence Interval. Hypothesis Testing: The t-test. Further Discussion of the t-test. One-Tailed Tests. More on Interpretation of Statistical Significance. Planning for Adequate Power (Optional). Student's t: Conditions and Summary. More on Principles of Testing Hypotheses. The Wilcoxon-Mann-Whitney Test. Perspective. 8. Statistical Principles of Design. Introduction. Observational Studies. Experiments. Restricted Randomization: Blocking and Stratification. Levels of Replication. Sampling Concerns (Optional). Perspective. 9. Comparison of Paired Samples. Introduction. The Paired-Sample t-Test and Confidence Interval. The Paired Design. The Sign Test. The Wilcoxon Signed-Rank Test. Further Considerations in Paired Experiments. Perspective. 10. Analysis of Categorical Data. Inference for Proportions: The Chi-Squared Goodness-of-Fit Test. The Chi-Squared Test for a 2 X 2 Contingency Table. Independence and Association in a 2 X 2 Contingency Table. Fisher's Exact Test (Optional). The r x k Contingency Table. Applicability of Methods. Confidence Interval for a Difference Between Proportions. Paired Data and 2 X 2 Tables (Optional). Relative Risk and the Odds Ratio (Optional). Summary of Chi-Squared Tests. 11. Comparing the Means of Many Independent Samples. Introduction. The Basic Analysis of Variance. The Analysis of Variance Model (Optional). The Global F-Test. Applicability of Methods. Two-Way ANOVA (Optional). Linear Combinations of Means (Optional). Multiple Comparisons (Optional). Perspective. 12. Linear Regression and Correlation. Introduction. The Fitted Regression Line. Parametric Interpretation of Regression: The Linear Model. Statistical Inference Concerning B1. The Correlation Coefficient. Guidelines for Interpreting Regression and Correlation. Perspective. Summary of Formulas. 13. A Summary of Inference Methods. Introduction. Data Analysis Samples. Appendices. Chapter Notes. Statistical Tables. Answers to Selected Exercises. Index. Index of Examples.

This article analyses the activities related to measures of central tendency (MCT), measures of dispersion (MD), and their relationships in Brazilian mathematics textbooks intended for the final years of elementary school (6th to 9th grades) approved by PNLD 2020, with the proposed statistical literacy by Gal (2002) as a basis. A page-by-page document analysis was carried out on all 11 collections. We found 1.237 activities. The arithmetic mean and amplitude were the most frequently measured. The nature of the quantitative variable stands out in relation to the qualitative one, and fictitious data is quantitatively greater than real data. The connection between MCTs and MDs is scarcely explored in textbooks. Understanding their link is fundamental for decision making, forming critical citizens, and promoting statistical literacy.

The development of sustainability assessment and sustainability reporting tools (SRTs) for infrastructure is pivotal because they serve to inform on progress towards achieving sustainability goals. However, the assessment of sustainability can be improved. The purpose of this paper is to draw attention to the deficiencies and limitations of existing SRTs and offer an alternative framework that is intended as a guide to enhancing assessment and reporting, and addressing current deficiencies. The alternative framework proposed encompasses six elements: (1) systems-based criteria selection; (2) quantitative measurement scales for criteria; (3) characterizing each criterion by a measure of central tendency and dispersion; (4) the distinction of additionality; (5) criteria weighting; and (6) combining criteria to give an overall score characterized by a measure of central tendency and a measure of dispersion. This is based on infrastructure project comparison. It is contended that, within the alternative framework offered, overall sustainability scores obtained provide an improved characterization of sustainability, because of the acknowledgement of the different elements and their combination. The paper offers a rational way by which the sustainability of infrastructure projects can be gauged and compared.

Interlaboratory results obtained by recommended methods for seed germination testing of 25 native forest species were subjected to different statistical tools. The pre-testing and re-testing methods for the preparation of germination were conducted at the Federal University of Uberlândia. In order to validate these methods, seed lots of different physiological qualities and their randomization diagrams of lots and seeds, and the repetitions in completely randomized design (CRD), were sent to laboratories. Among the various statistical methods in the validation process, data outliers were identified by the study of Boxplots and measure DFFITS. After elimination of the outliers, discrepancies in variances were studied by the methods of Cochran and Levene for the mean and median. The consistency and accuracy of results obtained by the laboratories for each lot was done by the study of repeatability and reproducibility (R&R) by the method of analysis of variance, which estimated the variance components of these measures and the their percentage contribution in relation to the total variation. Where it was possible to identify eventual superestimation of these estimates, the same was done using the tools of control charts for mean and range, excluding the results from laboratories identified outside the expected standards. The remaining sets of observations were used to calculate Mandel's h and k measures. The data obtained from the study of R&R were subjected to analysis of variance in CRD evaluating the effect of factors: laboratories, lots and their interaction (laboratory*lots), and their assumptions tested, and another study by the grouped analysis method. In addition to these, a comparison between the classical analysis of variance, using the Normal distribution, with variance analysis by generalized linear models for the Binomial distribution was done. It was observed that the measure DFFITS found a greater number of outlier points in relation to Boxplot. In general, most species had homogeneous variances. The study of R&R by the method of analysis of variance identified, with the aid of control charts, lots tending to overestimate the variance of repeatability and reproducibility, resulting in a set of consistent information. There were no major differences between the choice of experiment analysis by the classic or grouped analysis of variance. However, the same was not observed when using the Binomial distribution to model the original variable number of normal seedlings, in which this distribution was best suited for most species in contrast with the normal distribution. Therefore, the method was validated for 20 species, from a total of 25, and 18 of these using the Binomial distribution. Moreover, the study of R&R by the method of analysis of variance was more interesting than the statistics Mandel's h e k.

3 - Measures of Central Tendency

Preface Section One: Introduction to Statistical Analyses 1. Using Statistics to Conduct Quantitative Research A World of Statistics Why Do Quantitative Research? Typical Steps Involved in Quantitative Research 2. Collecting Data on Variables Variables and Hypotheses Measurement of Variables Sampling Section Two: Descriptive Statistics 3. Central Tendency Doing a Study and Reporting Descriptive Information Typical Measures of Central Tendency Relations among Mean Median and Mode 4. Looking at Variability and Dispersion Assessing Dispersion The Relationship Between Measures of Central Tendency and Variability Examining Distributions 5. Correlations The Notion of Correlation Elements of the Correlation Computing the Pearson Product-Moment Correlation Matters Affecting Correlations Methods of Correlations Alternative Forms of Association 6. Ensuring Reliability and Validity The Notion of Measurement Acceptability How to Do a study of Measurement Adequacy Reliability Validity The Relation of Validity to Reliability Section Three: Inferential Statistics 7. Statistical Significance Hypothesis Testing when Comparing Two Means Doing a Study that Tests a Hypothesis of Differences Between Means Assumptions in Parametric Hypothesis Testing Comparing Sample and Population Means Comparing the Means of Two Sample Groups: The Two-Sample t Test Comparing Means Differences of Paired Scores: The Paired Difference t Assessing Power 8. Comparing More than Two Means: One-Way Analysis of Variance Hypothesis Testing for More than Two Means The Analysis of Variance Hypothesis Test What after ANOVA? Multiple Comparison Tests Extensions of Analysis of Variance 9. Factorial Analysis of Variance Doing a Study that Involves More than One Independent Variable Types of Effect to Test Computing the Fixed-Effect ANOVA Random and Mixed-Effects Designs Section Four: Nonparametric Tests 10. Nonparametric Tests for Categorical Variables The Notion of Distribution-Free Statistics Conducting a Study that Requires Nonparametric Tests of Categorical Data The Chi-Square Test Alternatives to Chi-Square for Frequency Data 11. Nonparametric Tests for Rank Order Dependent Variables Doing a Study Involving Ordinal Dependent Variables Comparing Ranks of One Group to Presumed Populations Characteristics: Analogous Tests to One-Sample t Tests Comparing Ranks from Two Sample Groups Comparing Ranks from More than Two Sample Groups: Analogous Tests to One-Way ANOVA Section Five: Advanced Statistical Applications 12. Meta-Analysis Meta-Analysis: An Alternative to Artistic Literature Reviews Conducting the Meta-Analysis Study Using Computer Techniques to Perform Meta-Analysis 13. Multiple Regression Correlation Contrasting Bivariate Correlation and Multiple Regression Correlation Components of Multiple Correlations How to Do a Multiple Regression Correlation Study 14. Extensions of Multiple Regression Correlation Using Categorical Predictors Contrasting Full and Reduced Models: Hierarchical Analysis Interaction Effects Examining Nonlinear Effects 15. Exploratory Factor Analysis Forms of Factor Analysis The Notion of Multivariate Analyses Exploratory Factor Analysis 16. Confirmatory Factor Analysis Through the AMOS Program The Notion of Confirmatory Factor Analysis Using the AMOS Program for Confirmatory Factor Analysis 17. Modeling Communication Behavior The Goals of Modeling How to Do a Modeling Study Path Models Using the AMOS Program Appendix A: Using Excel XP to Analyze Data Getting Ready to Run Statistics With Excel Handling Data Using the Menu Bar Toolbars How to Run Statistics From the Analysis ToolPak Using Functions Appendix B: Using SPSS 12 for Windows How to enter and Screen Your Own Data in SPSS How to Enter Data From a Word Processor How to Create Indexes From Scales Commands in the SPSS System Dealing With Output Alternative Editing Environments Appendix C: Tables References Index About the Author