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Chapter 1 Introduction to Statistics. 1-1 Overview 1-2 Types of Data 1-3 Critical Thinking 1-4 Design of Experiments. Section 1-1 Overview. Overview.

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Chapter 1Introduction to Statistics

1-1 Overview

1-2 Types of Data

1-3 Critical Thinking

1-4 Design of Experiments


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Section 1-1Overview


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Overview

A common goal of studies and surveys and other data collecting tools is to collect data from a small part of a larger group so we can learn something about the larger group.

In this section we will look at some of the ways to describe data.


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population

Definitions

parameter

  • Data:observations (such as measurements, genders, survey responses) that have been collected

  • Statistics:a collection of methods for planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data


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  • Population:the complete collection of all elements (scores, people, measurements, and so on) to be studied; the collection is complete in the sense that it includes all subjects to be studied

  • Census:Collection of data from every member of a population

  • Sample:Sub collection of members selected from a population


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Chapter Key Concepts

  • Sample data must be collected in an appropriate way, such as through a process of random selection.

  • If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them.


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Section 1-2 Types of Data


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Key Concept

The subject of statistics is largely about using sample data to make inferences (or generalizations) about an entire population. It is essential to know and understand the definitions that follow.


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sample

statistic

  • Parameter:a numerical measurement describing some characteristic of a population.

  • Statistic:a numerical measurement describing some characteristic of a sample.

  • Quantitative data: numbers representing counts or measurements.

  • Qualitative (or categorical or attribute) data…can be separated into different categories that are distinguished by some nonnumeric characteristic.


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Working with Quantitative Data

Quantitative data can further be described by distinguishing between discrete and continuous types.


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  • Discretedata result when the number of possible values is either a finite number or a ‘countable’ number (i.e. the number of possible values is 0, 1, 2, 3, . .)

  • Continuous (numerical) data

    result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps


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4 Levels of Measurement: another way to classify data

  • Nominal level of measurement: characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in an ordering scheme (such as low to high)

  • Ordinal level of measurement involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless

  • Interval level of measurement: like the ordinal level, with the additional property that the difference between any two data values is meaningful, however, there is no natural zero starting point (where none of the quantity is present)

  • Ratio level of measurement: the interval level with the additional property that there is also a natural zero starting point (where zero indicates that noneof the quantity is present); for values at this level, differences and ratios are meaningful


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Summary - Levels of Measurement

  • Nominal- categories only

  • Ordinal- categories with some order

  • Interval- differences but no natural starting point

  • Ratio- differences and a natural starting point


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Extra Example

The following are the finishing positions of a sample of drivers in a NASCAR race: 3, 8, 12, 15, 27 (3rd place, 8th place, etc.)

  • What is the level of measurement of these data?

  • Are these data discrete or continuous?

  • Are the data qualitative or quantitative?


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Class Survey

Please complete the survey and submit. Do not sign your name.

  • ___Female ___Male

  • Randomly select four digits and enter them here:__ __ __ __

  • Your eye color:

  • Your height in inches:

  • Total value of the coins now in your possession:

  • Number of keys in your possession right now:

  • Number of credit cards in your possession right now:

  • Enter the last four digits of your social security number: ___ ___ ___ ___

  • Record your pulse rate by counting the number of heartbeats for one minute.

  • Do you exercise vigorously for at least 20 minutes twice a week (running, swimming, cycling, tennis, basketball, etc.)? YES/NO

  • How many classes are you taking this semester?

  • Are you currently employed? YES/NO

    If yes, how many hours do you work each week?

    13) During the past 12 months, have you been the driver of a car that was involved in a crash? YES/NO

    14) Do you smoke? YES/NO

    15) Are you: Left-handed Right-handed Ambidextrous


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Section 1-3

Critical Thinking


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Key Concepts

  • Success in the introductory statistics course typically requires more common sense than mathematical expertise.

  • This section is designed to illustrate how common sense is used when we think critically about data and statistics.


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Misuses of Statistics

  • Voluntary response sample (or self-selected sample)

    One in which the respondents themselves decide whether to be included.

    In this case, valid conclusions can be made only about the specific group of people who agree to participate.

    2) Small sample

    Conclusions should not be based on samples that are far too small.


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Misuse # 3- Graphs

To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the graph’s shape.


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Misuse # 4- Pictographs

Part (b) is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption.


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Misuse # 5- Percentages

Misleading or unclear percentages are sometimes used. For example, if you take 100% of a quantity, you take it all. 110% of an effort does not make sense.


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Other Misuses of Statistics

  • Loaded Questions

  • Order of Questions

  • Refusals

  • Correlation & Causality

  • Self Interest Study

  • Precise Numbers

  • Partial Pictures

  • Deliberate Distortions


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During a broadcast of a show on MTV, the host asks viewers to call in and vote for or against a new song, with the result that 74% of 12, 335 viewers favor it. Given that the sample is so large and the percentage is so far above 50%, is it valid to conclude that the majority of Americans favor the song? Why or why not?


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