Statistics

Course Outline:

• Chapters 1, 2, 3, 4
• Chapters 5, 6, 7 (omit joint continuous distributions)
• Chapter 8 (focus on the o(weird symbol) unknown cases)
• Chapters 9, 12 (time permitting)

We will be applying statistical methods to the analysis of scientific data

Also, we will be using R!!

Homework will be assigned every class but not collected

There will be graded homework also (mostly involving R)

Beginning Jan 25, 5-10 minute quizzes (over homework mostly) are going to be every Thursday class (which there is no exam)

2 lowest quizzes will be dropped.

We will have three 50 minute exams:

• Feb 27
• April 12
• May 3

NO FINAL EXAM

Take advantage of extra credit work.

Up to 20 percentage points will be added to your lowest exam score for completed R projects.

Can be worked on with a team of 3

Introduction to Statistics

In statistics you:

1. Design experiments to collect data
• Random sampling is very important
2. Extracting information from data
• Plots should use equal scales on the axes
3. Making decisions and predictions in the presence of uncertainty and variation
• These decisions would be like verifying that a machine has the efficiency that it is supposed to

Populations, Samples, and Processes

A census is a complete enumeration of a population

A sample is a subset of the population selected in some prescribed manner

A variable is a characteristic of the objects chosen. This is often a numeric measurement, but can also be a category.

Univariate data is where there is only one variable measured (this is the focus of the course)

Bivariate = 2 variables measured

Multivariate = 3 or more

Branches of Statistics

Descriptive Statistics

Using data to describe

Stem-and-leaf display is a way to line up data

Inferential Statistics

Using data to infer

Using sample sizes to make inferences about a population

1. Point estimates
• One estimate
2. Hypothesis tests
• Directly test point estimate against a hypothesis
3. Confidence intervals
• Interval of plausible values for p

Probability and Statistics

Conclusions must be phrased as probabilistic statements

Enumerative Versus Analytic Studies

A sampling frame may contain serial numbers of all furnaces manufactured by a particular company during a certain time period

Analytical study takes some study and extrapolates the next step for improvement

• Sample students preference for soda and try to infer if a change in can color would make beverage more popular

Enumerative studies dont look for extrapolation used mostly to describe

• Sample students and just see what proportion prefer coke or pepsi

Data Collection

Random Sample - truly random: will skew toward the population distribution

Stratified Sample - picking portions of the population to try and match the distribution

Convenience Sample - based on people that happen to see it or just is around. usually does not reflect the population

Designed experiments are where the conditions are manipulated.

Observational study is where the condition is not controlled, we can only learn correlation