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# Applied Mathematics & Statistics

#### AMS 315, Data Analysis

Catalog Description: Statistical analysis of data. Exploratory data analysis. Estimation. Parametric and nonparametric hypothesis tests. Power. Robust techniques. Use and interpretation of statistical computer packages, such as SPSS.

PrerequisiteAMS 310

3 credits

Textbook (recommended):
"An Introduction to Statistical Methods and Data Analysis", by Ott and Longnecker, 7th Edition, Cengage Learning; 2015; ISBN# 9781305269477.  (Please note earlier editions of this textbook will also be acceptable.)

Actuarial Exam: A student receiving a B- or better in this course and in  AMS 316 satisfies the Actuarial Exam test in Applied Statistics, through the  Society of Actuaries Validation by Educational Experience program. For more details about actuarial preparation at Stony Brook see  Actuarial Program

AMS 315 IS ALSO OFFERED DURING SUMMER SCHOOL. CHECK THE SUMMER SCHOOL BULLETIN FOR TIMES.

Topics
1.  Overview of basic statistics-- hypothesis testing, regression, chi-square test, confidence intervals (This material was previously covered in AMS 310, Survey of Probability and Statistics) –  4 class hours.
2.  Probability and Probability Distributions (Ott&L  §4.7-4.12) –  5 class hours.
3.  Inferences about Populataion Central Value (Ott&L  §7.1-7.3) – 3 class hours
4.  Inferences Comparing 2 Populations’ Central Values (Ott&L  §6.1,2,4,6,7) –  5 class hours.
5.  Categorical Data (Ott&L  §10.1-10.6)  – 6 class hours.
6.  Linear Regression and Correlation (Ott&L  §11.1-11.8) – 9 class hours.
7.  Multiple Regression and Correlation (Ott&L  §12.1-12.9) – 6 class hours.
8.  Examinations and Review – 4 class hours.

Learning Outcomes for AMS 315, Data Analysis

1.) Review topics from the prerequisite course (AMS 310 or any one semester college level introduction to statistics).
*Basic probability distributions; i.e., binomial, Poisson, normal, and exponential distributions;
*Probability calculations; e.g., probability of an event for a random variable following one of the basic distributions, use of Bayes’ Theorem, finding expected value and variance of a random variable;
*Vocabulary of statistical procedures; e.g., confidence intervals, tests of hypotheses, Type I and Type II error rates;
*One sample Student t procedures.

2.) Demonstrate skill using the following methods of probability theory:
*Central chi-square and central F-distributions;
*Bonferroni’s inequality applied to multiple tests of hypotheses;
*Logic of multiple comparison procedures;
*Decomposing chi-square sums of squares;
*Expected value and variance of multiple linear combinations of random variables.

3.) Develop proficiency using intermediate level statistical procedures.
*Two sample tests and confidence intervals;
*Tests and confidence intervals for the variance of a normally distributed random variable;
*Tests comparing the variances of two independent normal random variables;
*Tests and confidence intervals for the one way analysis of variance;
*Statistical procedures for multiple comparisons;
*Categorical variable tests using the chi-squared distribution;
*One predictor linear regression;
*Multiple predictor linear regression.

4.) Review scientific studies that use the techniques of the course.
*Read papers posted on class blackboard.
*Reference to papers as techniques studied in lecture.

5.) Learn the statistical computing package of the student’s choice and apply it to obtain the statistical model that generated a set of synthetic data.
* One predictor linear regression group project using synthetic data that requires students to merge separate files.
* Multiple predictor linear regression group project using synthetic data to recreate statistical model that generated the data. Model includes non-linear predictors and interactions of two predictors. 