The document provides an overview of a master syllabus for an applied inferential statistics course at Carlos Albizu University. The course introduces students to key concepts in inferential statistics and hypothesis testing through 16 classes involving lectures, assignments, and projects. Students learn various statistical tests including normal distribution, t-test, chi-square, and ANOVA that can be applied to single-group and between-group research designs for psychological research and assessment of minority populations. Evaluation is based on exams, presentations, homework, and exercises.

1. CARLOS ALBIZU UNIVERSITYSAN JUAN CAMPUS<br />MASTER SYLLABUS<br />PSYF-568: APPLIED INFERENTIAL STATISTICS<br />CREDITS: 3CONTACT HOURS: 45<br />COURSE DESCRIPTION<br />The course offers an introduction to inferential statistics in the context of psychological research. The topics covered include: hypothesis testing, statistical inference and research, probability theory, sampling distributions, parametric and non-parametric statistical tests, the normal curve, t and F distributions, Chi square, and the Mann-Whitney’s U test, among others.<br />PRE-REQUISITES<br />The course requires that the student have previous knowledge of basic statistical concepts, including descriptive statistics.<br />COURSE OBJECTIVES<br />The course is intended to empower students with knowledge about inferential statistics and methodology pertaining to psychological research; to enable the student to differentiate among the statistical methods available for hypothesis testing, to evaluate the advantages and disadvantages of such methods, to properly apply inferential statistical procedures with actual research data, and to read and interpret inferential statistical results. Furthermore, the course is intended to help students have a better comprehension of which statistical analysis to utilize when minority populations are assessed.<br />REQUIRED TEXT BOOKS<br />Runyon, R.P., Coleman, K.A., & Pittenger, D.J. (2000). Fundamentals of behavioral statistics (9th ed.). Boston, MA: McGraw Hill.<br />Sánchez-Viera, J.A. (2004). Fundamentos del razonamiento estadístico (3rd ed., revisada). San Juan, PR: Universidad Carlos Albizu.<br />ITINERARY OF CLASS UNITS<br />Unit 1:Introduction to statistical inference concepts<br />Unit 2:Introduction to hypothesis testing<br />Unit 3: Sampling and sampling distributions<br />Unit 4: Use of normal distribution for determining probabilities <br />Unit 5:Inferential statistics for single-group research designs <br />Unit 6: First Partial Exam<br />Unit 7: Inferential statistics for (within-group) repeated-measures research Designs: contrasting means and variances<br />Unit 8: Inferential statistics for (within-group) repeated-measures research designs: Chi square for non-parametric tests<br />Unit 9:Inferential statistics for (within-group) repeated-measures research designs: Wilcoxon’s T and simple One Way ANOVA)<br />Unit 10: Second Partial Exam<br />Unit 11: Inferential statistics for (between-group) independent samples research Designs: Contrasting means and proportions<br />Unit 12: Inferential statistics for (between-group) independent samples research designs: Mann Whitney’s U and one way ANOVA for independent groups<br />Unit 13: Inferential statistics for correlational research designs<br />Unit 14: Final Exam<br />COURSE CONTACT HOURS <br />Professors who teach the course must divide the contact hours the following way:<br />Face-to-face time in the classroom must not be less than 40 hours (16 classes, 2.5 hours each class).<br />For the remaining hours (>5 hours), students will conduct research projects or homework outside the classroom. These projects or homework will include, but are not limited to, practice exercises and assignments to do as homework and hand in for credit. <br />METHODOLOGY<br />The professor who offers the course will select the specific methodology. Teaching methodology for this course can include, among others: conferences by the professor, group discussions, class research projects, in-classroom and assigned problems and exercises involving real and hypothetical research data and situations.<br />EDUCATIONAL TECHNIQUES<br />The professor who offers the course will select the specific educational techniques. The techniques could include, but will not be limited to: practical demonstrations, providing printed materials (handouts), slide shows and simulations, among others.<br />EVALUATION<br />The professor who offers the course will select the specific evaluation criteria. These criteria could include, but would not be limited to: projects, exams, class presentations, homework assignments, and exercises.<br />RESEARCH COMPETENCIES<br />Utilizing inferential statistics to develop and evaluate research hypotheses in various research designs.<br />Performing statistical analyses that are relevant to the evaluation of research hypotheses in the context of various research designs.<br />Presenting and interpreting the results of inferential statistical analyses competently.<br />ATTENDANCE POLICY<br />Class attendance is mandatory for all students. After two unexcused absences, the student will be dropped from the class, unless the professor recommends otherwise. When a student misses a class, he/she is responsible for the material presented in class. <br />AMERICANS WITH DISABILITIES ACT (ADA)<br />Students that need special accommodations should request them directly to the professor during the first week of class.<br />COURSE UNITS<br />UNIT 1: INTRODUCTION TO STATISTICAL INFERENCE CONCEPTS<br />Upon completion of this unit, students will understand the basic concepts pertaining to statistical inference, as well as the role of inferential statistics in behavioral research.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit, students will be able to:<br />Distinguish between inferential and descriptive statistics<br />Discuss the role of statistical inference in behavioral research<br />Identify the limitations of statistical inference in behavioral research<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004)<br />Chapter 1 – Introducción (Introduction)<br />Chapter 10 - Inferencia estadística (Statistical Inference)<br />Runyon, Coleman & Pittenger (2000)<br />Chapter 11 – Introduction to statistical inference<br />UNIT 2: INTRODUCTION TO HYPOTHESIS TESTING<br />Upon completion of this unit, students will understand the concepts and process of hypothesis testing, as well as describe the steps involved in scientific hypothesis testing.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit, students will be able to:<br />Identify the steps associated with hypothesis testing in psychological research and in assessment and diagnosis of ethnic minority clients.<br />Discuss the concepts of research hypothesis and statistical hypothesis<br />Distinguish between Type I and Type II errors<br />Explain the concepts of significance level and statistical power<br />Discuss the concept of one-tailed vs. two-tailed tests in relation to research hypotheses.<br />Discuss the basic concepts of probability theory in its relation to statistical inference<br />REQUIRED READINGS:<br />Sánchez-Viera (2004)<br />Chapter 10 - Inferencia estadística (Statistical Inference)<br />UNIT 3: SAMPLING AND SAMPLING DISTRIBUTIONS<br />Upon completion of this unit, students will understand the concepts of sampling and sampling distributions in psychological research and in assessment of minority populations.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit, students will be able to:<br />Explain the concept of sampling distribution<br />Identify different types of sampling distributions commonly used in statistical tests<br />Discuss the theory underlying sampling distributions<br />Understand the use of probability models in statistical tests<br />Describe different sampling methods and their differences<br />Explain the concept of sampling error<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 17 – Sobre muestras y muestreo: Nociones Basicas (On samples and sampling: Basic concepts)<br />Runyon, Coleman & Pittenger (2000) <br />Chapter 11 – Introduction to statistical inference (pp. 266-277)<br />Section 11.3 – The concept of sampling distributions<br />Section 11.4 – Applications of the sampling distribution<br />UNIT 4: USE OF THE NORMAL DISTRIBUTION FOR DETERMINING <br /> PROBABILITIES<br />Upon completing this unit, students will acquire knowledge about the normal distribution, its characteristics and its use to determine probabilities and test for significance.<br />LEARNING OBJECTIVES:<br />Upon completion of this unit, students will be able to:<br />Explain the characteristics of the normal distribution.<br />Use the normal distribution to determine probabilities.<br />Define the concepts of “probability”, “sampling distribution”, “normal curve”. <br />Determine probabilities using the formula (Z) as a significance test. <br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 11 – La curva normal: Teoría y aplicaciones (The normal curve: Theory and applications)<br />UNIT 5: INFERENTIAL STATISTICS FOR SINGLE-GROUP RESEARCH<br /> DESIGNS<br />Upon completion of these units, students will understand the process of statistical inference with one-sample research designs, as well as the appropriate use of these tests for behavioral research, including: normal distribution, t-test, and Chi square.<br />LEARNING OBJECTIVES:<br />Upon successful completion of these units, students will be able to:<br />Discuss the assumptions of statistical tests for single-group research designs<br />Identify real and hypothetical research situations where these designs are applicable<br />Identify the limitations of statistical tests for single-group research designs<br />Compute statistics for the comparison of sample vs. population means using the normal and the Student-t distributions.<br />Compute statistics for the comparison of sample vs. population proportions using the normal distribution.<br />Solve one-sample statistical tests through the Chi square distribution to compare sample vs. population variances.<br />Solve one-sample statistical tests through the binomial distribution to compare sample vs. population proportions.<br />Competently interpret results from single-group statistical tests<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 11, section 11.5 – Diseño de una muestra: Contraste de medias (Single-group research design: Contrasting means)<br />Chapter 11, section 11.7 - Diseño de una muestra: Contraste de proporciones (Single-group research design: Contrasting proportions)<br /> Chapter 12, section 12.3 – Diseño de una muestra: Contraste de medias (Single-group research design: Contrasting means)<br />Chapter 13, Section 13.2 – Chi cuadrado para contrastes de varianzas: Diseño de una muestra (Chi Square for comparing variances: Single-group research designs <br />Chapter 13, Section 13.3 – Aplicaciones de Chi cuadrado en pruebas noparametricas (Applications of Chi square for non-parametric tests)<br />Chapter 14, section 14.4 – Diseño entre grupos: Prueba H de Kruskal=Wallis (Independent group research designs: Kruskal-Wallis H test) <br />Runyon, Coleman & Pittenger (2000)<br />Chapter 12 – Statistical inference: Single samples<br />UNIT 6: FIRST PARTIAL EXAM<br />UNIT 7: INFERENTIAL STATISTICS FOR (WITHIN-GROUP) REPEATED-MEASURES RESEARCH DESIGNS: CONTRASTING MEANS AND VARIANCES<br />Upon completion of this unit, students will understand the processes of inferential statistics for correlated-samples (repeated-measures) research designs. Students will discuss the applications and proper use of these tests in psychological research, including: t-test, Chi Square, normal distribution, Wilcoxon’s T.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit, students will be able to:<br />Discuss the assumptions of statistical tests for (within-group) repeated-measures research designs.<br />Identify real and hypothetical research situations where these tests are applicable<br />Identify the limitations of statistical tests for repeated-measures research designs<br />Compute statistics for the comparison of correlated-samples’ means, and variances using the Student-t distribution.<br />Compute statistics for the comparison of correlated-samples’ means, and variances using the normal distribution.<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 12, section 12.4 – Diseño intragrupos: Contraste de medias (Within-group research designs: Comparing means) <br />Chapter 12, section 12.9 – Diseño intragrupos: Contraste de 2 varianzas (Within-group research designs: Comparing variances) <br />Runyon, Coleman & Pittenger (2000)<br />Chapter 13 – Statistical inference: Two-sample cases<br />UNIT 8: INFERENTIAL STATISTICS FOR (WITHIN-GROUP) REPEATED-MEASURES RESEARCH DESIGNS: CHI SQUARE FOR NON-PARAMETRIC TESTS<br />Upon completion of this unit, students will understand the processes of inferential statistics for correlated-samples (repeated-measures) research designs. Students will discuss the applications and proper use of these tests in psychological research, including Chi Square.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit, students will be able to:<br />Perform correlated–sample statistical tests through the Chi square distribution to compare proportions in repeated measures designs.<br />Competently interpret and present the results from statistical tests for repeated-measures research designs, including Chi Square.<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 13, section 13.3 – Aplicaciones de Chi Cuadrado en pruebas no paramétricas (Chi square for non-parametric tests)<br />Runyon, Coleman & Pittenger (2000)<br />Chapter 13 – Statistical inference: Two-sample cases<br />UNIT 9: INFERENTIAL STATISTICS FOR (WITHIN-GROUP) REPEATED-MEASURES RESEARCH DESIGNS: WILCOXON’S T AND SIMPLE ONE WAY ANOVA<br />Upon completion of this unit, students will understand the processes of inferential statistics for correlated-samples (repeated-measures) research designs. Students will discuss the applications and proper use of these tests in psychological research, including: Wilcoxon’s T and the F statistic.<br />LEARNING OBJECTIVES:<br />Upon successful completion of these units, students will be able to:<br />Discuss the assumptions of statistical tests for (within-group) repeated-measures research designs.<br />Identify real and hypothetical research situations where these tests are applicable<br />Perform correlated samples statistical tests using the Wilcoxon’s T test and the signs test. <br />Perform correlated samples statistical tests using the F statistic <br />Competently interpret results from statistical tests for repeated-measures research designs, including the signs test, Wilcoxon’s T and the F statistic.<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 14, section 14.6 – Diseño intragrupos: Prueba de los signos (Within group research designs: the signs test)<br />Chapter 14, section 14.7 – Diseño intragrupos: Prueba T de Wilcoxon (Within group research designs: Wilcoxon’s T test)<br />Chapter 15, Section 15.7 – Análisis de varianza simple para un diseno intragrupos (Simple oneway ANOVA for within-group research designs)<br />Runyon, Coleman & Pittenger (2000)<br />chapter 13 – Statistical inference: Two-sample cases<br />Chapter 18 (section 18.3) – Statistical inference: Ordinally scaled variables<br />UNIT 10: SECOND PARTIAL EXAM<br />UNIT 11: INFERENTIAL STATISTICS FOR (BETWEEN-GROUP) TWO INDEPENDENT SAMPLES RESEARCH DESIGNS: CONTRASTING MEANS AND PROPORTIONS<br />Upon completion of these units, students will understand the processes of statistical inferences for designs with two independent samples (between group designs), as well as the appropriate use of these tests in psychological research, including: the normal distribution, t-test, Chi Square and Mann-Whitney’s U test.<br />LEARNING OBJECTIVES:<br />Upon successful completion of these units, students will be able to:<br />Discuss the assumptions of statistical tests for between-group research designs<br />Identify real and hypothetical research situations where these tests are applicable<br />Identify the limitations of statistical tests for research designs comparing two independent samples.<br />Compute statistics for the comparison of two independent samples’ means and proportions using the Student–t distribution.<br />Compute statistics for the comparison of two independent samples’ means and proportions using the normal distribution.<br />Solve independent–samples statistical tests through the Mann-Whitney’s U test (for variables in ordinal scale).<br />Solve independent–samples statistical tests through the Chi-square distribution (tests of independence, median test, etc.).<br />Competently interpret results from statistical tests for two-independent-samples research designs.<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 11, Section 11.6 - Diseño entregrupos: Contrastes para 2 medias muestrales (Independent samples research designs: comparing means)<br />Chapter 11, Section 11.8 - Diseño entregrupos: Contrastes para 2 proporciones muestrales (Independent samples research designs: comparing proportions)<br />Chapter 12, section 12.5 – Diseño entregrupos: Contrastes para 2 medias muestrales (Independent samples research designs: comparing means)<br />Chapter 12, Section 12.8 – Diseño entregrupos: Contrastes para 2 proporciones muestrales (Independent samples research designs: comparing proportions)<br />Runyon, Coleman & Pittenger (2000)<br />Chapter 13 – Statistical inference: Two-sample cases<br />UNIT 12: INFERENTIAL STATISTICS FOR (BETWEEN-GROUP) TWO INDEPENDENT SAMPLES RESEARCH DESIGNS: MANN WHITNEY’S U AND ONE WAY ANOVA FOR INDEPENDENT GROUPS<br />Upon completion of this unit, students will understand the processes of statistical inferences for designs with two independent samples (between-group designs), as well as the appropriate use of these tests in psychological research, including Mann-Whitney’s U test and one way ANOVA.<br />LEARNING OBJECTIVES:<br />Upon successful completion of these units, students will be able to:<br />Perform independent–samples statistical tests using the Mann-Whitney’s U test (for variables in ordinal scale).<br />Perform independent–samples statistical tests using the Chi-square distribution (tests of independence, median test, etc.).<br />Perform independent–samples statistical tests using oneway ANOVA for comparing means.<br />Competently present and interpret results from statistical tests for two-independent-samples research designs, including Mann-Whitney’s U and oneway ANOVA.<br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 14, section 14.3 – Diseño entregrupos: Prueba U de Mann-Whitney (Independent samples research designs: Mann-Whitney’s U test )<br />Chapter 15, section 15.5 – Análisis de varianza simple para un diseño entregrupos (Simple oneway ANOVA for between-group research designs)<br />Chapter 15, section 15.8 – Contrastes de varianzas para muestras independientes (Comparing variances in between-group research designs)<br />Runyon, Coleman & Pittenger (2000)<br />Chapter 13 – Statistical inference: Two-sample cases<br />UNIT 13: CORRELATIONAL STATISTICS<br />Upon completion of this unit, students will understand the process through which correlation coefficients are computed and tested for significance, as well as the different statistical methods available and their significance tests.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit, students will be able to:<br />Discuss the assumptions of statistical tests for correlation coefficients<br />Identify the different methods through which correlation coefficients can be tested for significance (normal curve, t-test, chi square, tables of critical values, etc.) and their applications.<br />Compute correlation coefficients for interval- and ratio- scaled variables (Pearson’s r) <br />Competently interpret results from statistical tests for correlational analysis <br />ASSIGNED READINGS:<br />Sánchez-Viera (2004) <br />Chapter 9 – Correlación y regresión simple lineal (Correlation and simple linear regression) <br />Chapter 16- Pruebas de hipótesis para índices de correlación (tests of significance for correlation indexes) <br />Runyon, Coleman & Pittenger (2000)<br />Chapter 8 - Correlation<br />UNIT 14: FINAL EXAM<br />REFERENCES<br />Bordens, K.S., & Abbot, B.B. 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Professional Psychology: Research and Practice, 27 (1), 79-77.<br />Ritchey, F. J. (2002). Estadística para las ciencias sociales: El potencial de la imaginación estadística. México: McGraw Hill. <br />Rosenthal, R., & Rosnow, R.L. (1991). Essentials of behavioral research: Methods and data analysis (2nd ed.). New York: McGraw-Hill.<br />Runyon, R.P., Coleman, K.A., & Pittenger, D.J. (2000). Fundamentals of behavioral statistics (9th ed.). Boston, MA: McGraw Hill.<br />Sánchez-Viera, J.A. (2004). Fundamentos del razonamiento estadístico (3ra ed., revisada). San Juan, PR.: Universidad Carlos Albizu.<br />Visauta-Vinacua, B. (1997). Análisis estadístico con SPSS para Windows: Estadística básica. México: McGraw Hill. <br />Vogt, P.W. (1999). Dictionary of statistics and methodology (2nd ed.). Thousand Oaks, CA: Sage.<br /> <br />Revised by: María C. Vélez-Pastrana, Ph.D. (December, 2000; October, 2003)<br />Revised by: Sean K. Sayers Montalvo, Ph.D. (June, 2006)<br />Revised by: María C. Vélez-Pastrana, Ph.D. (August, 2008)<br />