Introduction

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Do curso por Duke University

Inferential Statistics

1295 classificações

Duke University

Inferential Statistics

1295 classificações

Curso 2 de 5 em Specialization Statistics with R

This course covers commonly used statistical inference methods for numerical and categorical data. You will learn how to set up and perform hypothesis tests, interpret p-values, and report the results of your analysis in a way that is interpretable for clients or the public. Using numerous data examples, you will learn to report estimates of quantities in a way that expresses the uncertainty of the quantity of interest. You will be guided through installing and using R and RStudio (free statistical software), and will use this software for lab exercises and a final project. The course introduces practical tools for performing data analysis and explores the fundamental concepts necessary to interpret and report results for both categorical and numerical data

Na lição

Central Limit Theorem and Confidence Interval

Welcome to Inferential Statistics! In this course we will discuss Foundations for Inference. Check out the learning objectives, start watching the videos, and finally work on the quiz and the labs of this week. In addition to videos that introduce new concepts, you will also see a few videos that walk you through application examples related to the week's topics. In the first week we will introduce Central Limit Theorem (CLT) and confidence interval.

Introduction4:25

Sampling Variability and CLT20:59

CLT (for the mean) examples10:52

Conheça os instrutores

Mine Çetinkaya-Rundel
Associate Professor of the Practice
Department of Statistical Science

This unit is a formal introduction to statistical inference where you will see

building blocks from the previous units come together in commonly used statistical

inference methods just as confidence, intervals and hypothesis tests.

In this until will also introduce the central limit theorem

which provides the basis for these methods.

Let's start with an example for a survey conducted by the Pew Research Center.

The study is titled Young, Underemployed, and

Optimistic, Coming of Age, Slowly, in a Tough Economy.

Young adults hit hard by the recession.

A plurality of the public.

41% believes young adults rather than middle aged or

older adults are having the toughest time in today's economy.

Tough economic times, altering young adults daily lives and long term plans.

While, negative trends in the labor market have been felt most acutely by

the youngest workers.

Many adults in their late 20s and

early 30s have also felt the impact of the weak economy.

Among all 18 to 34 year olds, fully half,

49%, say they have taken a job they didn't want just to pay the bills

with 24% saying they have taken an unpaid job to gain work experience.

We're also told that the general public survey is based on telephone interviews

conducted between December 6 and 19 2011 with a nationally representative sample

of 2,048 adults aged 18 and older living in the continental United States.

Margin of sampling error is plus or minus 2.9% points for

results based on the total sample and 4.4% points for

adults ages 18 to 34 at the 95% confidence level.

With all sorts of studies the margin of error is often recorded and

this information can often be found in the fine print.

So, what does this mean?

Remember, the study had estimated that 41% of the public believes that young adults,

rather than middle aged or older adults,

are having the toughest time in today's economy.

Meaning that, 41 plus or minus 2.9.

We are 95% confident that 38.1% to 43.9% of

the public believe young adults rather than middle-aged or

older adults are having the toughest time in today's economy.

We were also told that 49% of the public had taken a job they didn't want

just to pay the bills.

Meaning that 49 plus or minus, 4.4%,

we are 95% confident that 44.6 to 53.4%

of 18 to 34 year olds have taken a job they didn't want, just to pay the bills.

The 41 and 49% we have on hand, come from the sample data.

But we're often interested in population parameters.

Since compete populations are difficult, or impossible to collect data on.

That would mean collecting data from the entire US population for this study for

example, we use sample statistics as point estimates for

the unknown population parameters of interest.

But these samples statistics vary from sample to sample.

Other random samples of Americans would yield

slightly different estimates, for example.

Quantifying how sample statistics vary provides a way to

estimate the margin of error associated with our point estimate.

Discussion on sampling variability, in other words, how

estimates vary from one sample to another, will be the first focus of this unit.

Within that discussion, we're going to introduce the central limit theorem

which describes shapes, centers and spreads of sampling distributions when

certain conditions about the population, as well as the sampling scheme are met.

This unit is also going to serve as a formal introduction to

statistical inference.

And we're going to highlight techniques that are considered to be

pillars of statistical inference, such as confidence intervals and hypothesis tests.

We will wrap up the unit with a discussion of statistical versus practical

significance.

We're going to consider the effect of sample size, confidence, and

significance levels in our conclusions.

And finally we're going to discuss statistical power.

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