Data, Inference, and Decisions

Unit 1 – Data, Inference, and Decisions: Introduction

Unit 2 – Probability Theory & Distributions

Unit 3 – Sampling and Data Collection Methods

Unit 4 – Descriptive Stats & Data Exploration

Unit 5 – Estimation & Confidence Intervals

Unit 6 – Hypothesis Testing

Unit 7 – Linear Regression & Correlation

Unit 8 – Logistic Regression & Classification

Unit 9 – Time Series Analysis & Forecasting

Unit 10 – Bayesian Inference & Decision Making

Unit 11 – Nonparametric & Robust Methods

Unit 12 – Sampling and Survey Methods

Unit 13 – Data Ethics and Privacy

Unit 14 – Case Studies in Data Analysis

## What do you learn in Data, Inference, and Decisions

You'll get into the nitty-gritty of collecting, analyzing, and interpreting data. It covers probability theory, statistical inference, hypothesis testing, and regression analysis. You'll learn how to make sense of complex datasets, draw meaningful conclusions, and use statistical software to crunch numbers. It's all about turning raw data into useful insights for decision-making.

## Is Data, Inference, and Decisions hard?

It can be pretty challenging, especially if you're not a math whiz. The concepts can get pretty abstract, and there's a lot of statistical theory to wrap your head around. But don't panic - most people find it tough at first. The key is to stay on top of the material, practice a ton, and don't be afraid to ask for help when you need it.

## Tips for taking Data, Inference, and Decisions in college

1. Use [Fiveable Study Guides](https://fiveable.me/cram-mode) to help you cram 🌶️
2. Practice, practice, practice - especially with statistical software like R or SPSS
3. Form study groups to tackle tough concepts like Bayesian inference together
4. Don't just memorize formulas, understand the logic behind them
5. Use real-world examples to make abstract concepts more concrete
6. Stay on top of assignments - they build on each other
7. Attend office hours regularly, especially when stuck on concepts like maximum likelihood estimation
8. Watch "Moneyball" to see how data analysis is applied in sports

## Common pre-requisites for Data, Inference, and Decisions

1. Calculus I: Covers limits, derivatives, and integrals. It's the foundation for understanding many statistical concepts.

2. Introduction to Probability: Introduces basic probability theory and random variables. It's crucial for understanding the probabilistic aspects of statistics.

3. Linear Algebra: Focuses on vector spaces, matrices, and linear transformations. It's essential for understanding multivariate statistics and regression analysis.

## Classes similar to Data, Inference, and Decisions

1. Machine Learning: Explores algorithms that can learn from and make predictions on data. It's like statistics on steroids, with a focus on predictive modeling.

2. Econometrics: Applies statistical methods to economic data. It's similar to Data, Inference, and Decisions but with an economics twist.

3. Experimental Design: Focuses on planning and conducting experiments to collect meaningful data. It's all about setting up studies to get the most reliable results.

4. Data Mining: Digs into large datasets to discover patterns and relationships. It's like being a data detective, using statistical tools to uncover hidden insights.

## Majors related to Data, Inference, and Decisions

1. Statistics: Focuses on the collection, analysis, interpretation, and presentation of data. Students learn to design studies, create models, and draw conclusions from data.

2. Data Science: Combines statistics, computer science, and domain expertise to extract knowledge from data. It's all about using data to solve real-world problems.

3. Economics: Studies how societies allocate scarce resources. Statistical methods are crucial for analyzing economic data and testing economic theories.

4. Psychology: Explores human behavior and mental processes. Statistical analysis is key for interpreting experimental results and understanding psychological phenomena.

## What can you do with a degree in Data, Inference, and Decisions?

1. Data Analyst: Collects, processes, and performs statistical analyses on large datasets. They turn numbers into insights that help businesses make better decisions.

2. Biostatistician: Applies statistical methods to biology and health-related fields. They might design clinical trials or analyze public health data to inform medical decisions.

3. Market Research Analyst: Studies market conditions to examine potential sales of products or services. They use statistical techniques to forecast future trends and consumer behavior.

4. Financial Analyst: Evaluates investment opportunities and provides financial guidance. They use statistical models to assess risk and predict financial performance.

## Data, Inference, and Decisions FAQs

1. How much programming is involved? You'll likely use statistical software like R or SAS, but it's not a coding-heavy course. The focus is more on understanding and applying statistical concepts.

2. Can I use a graphing calculator on exams? It depends on your professor, but many allow it. Some might even provide formula sheets, so focus on understanding rather than memorization.

3. How does this course differ from an intro stats class? This course goes deeper into theory and covers more advanced topics. You'll deal with more complex datasets and learn to choose appropriate statistical methods for different scenarios.

Statistics

Theory

1.4 Introduction to data visualization and exploration

1.3 Types of data and their characteristics

1.2 The role of data in decision-making processes

1.1 Overview of the course and its objectives

2.4 Expectation, variance, and moments

2.3 Discrete and continuous probability distributions

2.2 Conditional probability and Bayes' theorem

2.1 Basic probability concepts and rules

2.5 Joint, marginal, and conditional distributions

3.1 Sampling techniques and their applications

3.2 Sample size determination and power analysis

3.3 Experimental design and randomization

3.4 Surveys, questionnaires, and measurement scales

3.5 Dealing with missing data and outliers

4.1 Measures of central tendency and dispersion

4.2 Correlation and association measures

4.3 Data visualization techniques (histograms, box plots, scatter plots)

4.4 Exploring multivariate relationships

4.5 Introduction to data preprocessing and transformation

5.1 Point estimation and properties of estimators

5.2 Interval estimation and confidence intervals

5.4 Bootstrap and resampling methods

5.3 Estimating means, proportions, and variances

6.1 Formulation of null and alternative hypotheses

6.2 Type I and Type II errors, significance level, and power

6.3 One-sample and two-sample tests (t-tests, z-tests)

6.5 Chi-square tests for goodness-of-fit and independence

6.4 Analysis of variance (ANOVA)

6.6 Nonparametric tests (rank-based methods)

7.2 Least squares estimation and interpretation of coefficients

7.1 Simple linear regression model and assumptions

7.4 Coefficient of determination and model evaluation

7.5 Multiple linear regression and model selection

7.6 Dealing with multicollinearity and heteroscedasticity

7.3 Inference for regression parameters

8.2 Maximum likelihood estimation and interpretation of coefficients

8.1 Binary logistic regression model and assumptions

8.5 Multinomial and ordinal logistic regression

8.4 Model evaluation and performance metrics (confusion matrix, ROC curve)

8.3 Odds ratios and confidence intervals

9.1 Components of time series (trend, seasonality, cycles)

9.2 Stationarity and autocorrelation

9.3 Moving averages and exponential smoothing

9.4 ARIMA models and Box-Jenkins methodology

9.5 Forecasting and model evaluation

10.1 Bayesian probability and Bayes' rule

10.2 Prior and posterior distributions

10.3 Bayesian estimation and credible intervals

10.4 Bayesian hypothesis testing and model selection

10.5 Decision theory and loss functions

10.6 Value of information and optimal decision-making

11.1 Nonparametric density estimation (kernel methods)

11.2 Nonparametric regression (local polynomial, splines)

11.3 Robust estimation and M-estimators

11.4 Rank-based methods and permutation tests

12.1 Simple random sampling and stratified sampling

12.2 Cluster sampling and multistage sampling

12.3 Ratio and regression estimators

12.4 Survey design and questionnaire construction

12.5 Nonresponse and bias in surveys

13.1 Ethical considerations in data collection and analysis

13.2 Privacy and confidentiality issues

13.3 Informed consent and data protection regulations

13.4 Bias and fairness in data-driven decision-making

14.1 Application of statistical methods in real-world scenarios

14.2 Case studies from various domains (e.g., healthcare, finance, marketing)

14.3 Interpretation and communication of results to non-technical audiences

14.4 Limitations and challenges in data-driven decision-making

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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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