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Chapter 1:The Nature of Statistics

Lecture PowerPoint Slides

Discovering Statistics

2nd Edition Daniel T. Larose

+ Chapter 1 Overview

1.1 Data Stories: The People Behind the Numbers

1.2 An Introduction to Statistics

1.3 Gathering Data

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+ The Big Picture

Where we are coming from and where we are headed…

Chapter 1 introduces the basic ideas of the field of statistics and the methods for gathering data.

In Chapter 2 we will learn to summarize the data we have gathered using graphs and tables.

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+ 1.1: Data Stories: The People Behind the Numbers

Objectives:

Realize that behind each data set lies a story about real people undergoing real-life experiences.

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1.1: Data Stories: The People Behind the NumbersBehind every data set lies a story about the lives of real people.

+ 1.2: An Introduction to Statistics

Objectives:

Describe what the field of statistics is.

State the meaning of descriptive statistics.

Understand that inferential statistics refers to learning about a population by studying a sample from that population.

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What is Statistics?Statistics are numbers that describe a group of people or things.

The Field of Statistics

The field of statistics is the art and science of:• collecting,• analyzing,• presenting, and• interpreting data

Consider this survey from USA Today.•How did the pollsters arrive at these figures?•Are the figures accurate? •Could they be inaccurate?•Is the difference between men and women meaningful, or could it be due to random chance?

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Case StudyDoes Friday the 13th change human behavior? The following graph displays traffic through a motorway junction on Friday the 6th (green) and on the following Friday, the 13th (yellow).

Discuss the collection, analysis, presentation, and interpretation of these data.

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Descriptive Statistics

In descriptive statistics, we use numbers, graphs, and tables to describe the data set as a first step in data analysis.

Descriptive Statistics

Descriptive statistics refers to the methods for summarizing and organizing the information in a data set.

Elements, Variables, and Observations

•An element is a specific entity about which information is collected.

•A variable is a characteristic of an element that can assume different values for different elements.

•An observation is the set of values of the variables for a given element.

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Descriptive StatisticsVariables

Variable―any characteristic of an element

Qualitative VariableA variable that may be classified into categories. These variables are also called “categorical variables.”

Quantitative Variable A variable that takes on numerical values upon which arithmetic operations may be meaningfully performed.

Discrete Variable Can take either a finite or a countable number of values.

Continuous Variable Can take infinitely many values, forming an interval on the number line.

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Descriptive Statistics

Levels of Measurement

Data may be classified according to the following four levels of measurement.

• Nominal data consists of names, labels, or categories.

• Ordinal data can be arranged in a particular order.

• Interval data are similar to ordinal data, with the property that subtraction may be carried out on interval data.

• Ratio data are similar to interval data, with the property that division may be carried out on ratio data.

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Inferential StatisticsStatistical inference consists of methods for estimating and drawing conclusions about population characteristics based on information contained in a subset (sample) of that population.

Populations, Parameters, Samples, and Statistics

• A population is the collection of all elements of interest in a particular study. A parameter is a characteristic of a population.

• A sample is a subset of the population from which information is collected. A statistic is a characteristic of a sample.

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Inferential Statistics

Population

Sample

Collect data from a Sample.

Perform Data Analysis.

Make an Inference about the Population.

+ 1.3: Gathering Data

Objectives:

Explain what a random sample is, and why we need one.

Identify systematic sampling, stratified sampling, cluster sampling, and convenience sampling.

Explain selection bias and good questionnaire design.

Understand the differences between an observational study and an experiment.

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Random SamplingWe can use the information gathered from a sample to generalize about the population. However, if we get a “bad” sample, the information gleaned from it will be misleading.

The statistician’s remedy is to allow impersonal chance to choose the sample. A sample chosen by chance rules out both favoritism by the sampler and self-selection by respondents.

Random Sample

A random sample (also known as a simple random sample) is a sample for which every element has an equal chance of being selected.

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More Sampling Methods

Systematic SamplingEach element of the population is numbered. The sample is obtained by selecting every kth element where k is some whole number.

Stratified SamplingDivide the population into subgroups, or strata, according to some characteristic, such as race or gender. A random sample is then taken from each stratum.

Cluster SamplingDivide the population into clusters. Select several clusters at random. All elements within the chosen clusters are selected for the sample.

Convenience SamplingSubjects are chosen based on what is convenient for the survey personnel. This method usually does not result in a representative sample.

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Selection BiasSome common pitfalls in the design and implementation of a survey include selection bias and the wording of a questionnaire.

Target Population, Potential Population, and Selection Bias

•The target population is the complete collection of all elements that we are interested in studying.

•The potential population is the collection of elements from the target population that had a chance of being sampled.

•Selection bias occurs when the population from which the actual sample is drawn is not representative of the target population, due to an inappropriate sampling method.

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Good Questionnaire DesignThe wording of questions can greatly affect the responses. Here are several factors to consider when designing a questionnaire.

Five Factors for Good Questionnaire Design

1.Remember: simplicity and clarity

2.When reporting results, include the actual questions asked.

3.Avoid leading questions.

4.Avoid asking two questions in one.

5.Avoid vague terminology.

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Experimental StudiesResearchers can gather data by using survey or sampling methods. However, these methods may not always obtain the information required. In this case, an experimental study may be in order.

Experimental Studies

•In an experimental study, researchers investigate how varying the predictor variable affects the response variable.

•A predictor variable (also called an explanatory variable) is a characteristic intended to explain differences in the response variable.

•A predictor variable that takes the form of a purposeful intervention is called a treatment.

•A response variable is an outcome, a characteristic of the subjects of the experiment presumably brought about by differences in the predictor variable or treatment.

•The subjects in a statistical study represent the elements from which the data are drawn.

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Experimental StudiesThere are three main factors that should be considered when designing an experimental study.

ControlA control group is necessary to compare against the treatment group. In some experiments, members of the control group receive a placebo, a nonfunctioning simulated treatment.

RandomizationMany biases can be introduced into an experiment. To eliminate biases, it is necessary to place subjects into the treatment and control groups randomly.

ReplicationLarger samples are usually better, because they allow for more precise inference. The treatment and control groups each must contain a large enough number of subjects to allow detection of meaningful differences.

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Observational Studies

There are circumstances where it is either impossible, impractical, or unethical for the researcher to place subjects into treatment and control groups.

In an observational study, the researcher observes whether the subjects’ differences in the predictor variable are associated with differences in the response variable. No attempt to manipulate the variables is made.

A sample survey is an example of an observational study.

Random SampleA random sample (also known as a simple random sample) is a sample for which every element has an equal chance of being selected.

+ Chapter 1 Overview

1.1 Data Stories: The People Behind the Numbers

1.2 An Introduction to Statistics

1.3 Gathering Data

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