ECI - Estimation and Confidence Module Overview

Introduction

Responses of individuals from a sample are used to infer some conclusion about a wider population. Probability is used to express the "strength" of the conclusion by taking chance variation into account. STATISTICAL INFERENCE provides methods for drawing conclusions about a population parameter from a sample statistic. There are two types of inference: estimation using confidence intervals and hypothesis testing using probability and logic.

CONFIDENCE INTERVALS estimate the value of a population parameter and how accurate it is. A 95% confidence interval corresponds with plus and minus 2 standard deviations in a Normal distribution. Recall that Normal distributions follow the empirical 68-95-99.7 rule. This thinking can extend to any desired level of certainty such as 90%, 99%, and others. This unit focuses exclusively on confidence intervals for both mean and proportion statistics.

TESTS OF SIGNIFICANCE will be addressed in the next unit. This procedure focuses on assessing the evidence for a claim about a population. The claim can be made by others or it can be the result of our own data collection. These tests use elaborate vocabulary BUT the basic idea is simple and logical. An outcome that would rarely happen if a claim were true is evidence enough that the claim is NOT TRUE. Interpreting the results of these tests is the final step needed for data driven decision making using statistical analysis.

Essential Questions

How confident can we be about the conclusions resulting from data analysis?
Given that statistics is not a perfect science, how much error is acceptable?
What is meant by margin of error?
Are there any basic assumptions that need to be made before generalizing from our sample results to the broader population?

Key Terms

The following key terms will help you understand the content in this module.

Interval- set of values bounded at both ends

Confidence interval- a level-C confidence interval for a model parameter is an interval of values of the form estimate +/- margin of error

Confidence level- assigns a probability that the confidence interval cited covers the true population parameter...typical confidence levels are 90%, 95%, 99% among others

Margin of error- the extent of the confidence interval on either side of the observed statistic value...calculated as the product of the C level critical value and the standard error of the data

Critical value- the number of standard deviations away from the mean of the sampling distribution to correspond to the specified level of confidence

Assumptions- every model is based on necessary assumptions that we assume and cannot necessarily verify

Conditions- conditions can be checked to see whether an assumption is at least reasonable

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