Introduction to Statistical Analysis

Introduction to Statistical Analysis

By Jenette Pangilinan

During the earlier times, statistics was associated with compilation of data such as births and deaths. Later on, it included data of unemployment, inflation rates, index rates and so on. Over the years, applied mathematics stimulated theoretical and practical work.

​History of Statistics

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​History of Statistics

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Sir Ronald Fisher

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• British mathematician  who developed a design to improve the interpretation of results in experimental studies.

Open Ended

WHY STUDY STATISTICS?

Why Study Statistics?

•Statistical theories is applied in business and industry, psychology, education, in military intelligence, and in other fields that has benefited humanity.

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•Statistics improves skills in critical analysis of information, thus making one less susceptible to misleading or deceptive claims.

Why Study Statistics?

•It provides bases for important and intelligent decisions to be made. A manufacturer’s decision to increase or decrease production of items depends on careful analyses of collected information regarding consumer reactions to such item.

•It is the key to quality control in industry thereby reducing manufacturing costs immensely.​

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Why Study Statistics?

•Students study the course for different reasons. Some undertake statistics as a requirement while others study it recognizing its value and application in any field they wish to pursue.

•Knowledge of statistical principles and techniques is needed in research.​

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Open Ended

What are the uses of statistics in business?

As a businessperson, you may find yourself involved with statistics in at least one of the following ways:

• as a practitioner collecting, analyzing, and presenting findings based on statistical data

• as a consumer of statistical claims and findings offered by others, some of whom may be either incompetent or unethical.

​Descriptive vs Inferential

​Descriptive Statistics

• Concerned with techniques that are used to describe or characterize the obtained data.

​Descriptive Statistics

Example:

​Upon looking around your class, you may find that 35% of your fellow students are wearing Casio watches. If so, the figure “35%” is a descriptive statistic. You are not attempting to suggest that 35% of all college students in the United States, or even at your school, wear Casio watches. You’re merely describing the data that you’ve recorded.

Inferential Statistics

· Involves techniques that use the obtained sample data to infer to

populations.

· Embraces techniques that allow one to use obtained sample data to

make inferences or draw conclusions about populations.

· It allows you to make predictions or inferences and draw conclusion

from a collected data.

Inferential Statistics

Example:

​Based partially on an examination of the viewing behavior of several thousand television households, the ABC television network may decide to cancel a prime-time television program. In so doing, the network is assuming that millions of other viewers across the nation are also watching competing programs.

​Activity 1:

Descriptive vs Inferential

Fill in the Blanks

According to the Bureau of the Census, there are 2.2 million U.S. households with a single father and one or more children younger than 18.

Fill in the Blanks

In observing a sample of nurses and other healthcare workers who were likely infected with the swine flu, researchers found that only half routinely wore gloves when dealing with patients.

Fill in the Blanks

Survey results revealed that 26% of thirsty golfers order a sports drink when they finish their round and head for the clubhouse.

Fill in the Blanks

There have been 82 confirmed or suspected suicides among active-duty service personnel this year, compared to 51 for the same period in 2008.

Fill in the Blanks

The number of mutual funds peaked at 8305 in 2001, but the combination of bear markets and mergers and acquisitions has driven the number of funds down to 8011.

​KEY TERMS IN STATISTICS

Sometimes referred to as the universe, this is the entire set of people or objects of interest.​

Population

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​This is a smaller number (a subset) of the people or objects that exist within the larger population. It is said to be representative if its members tend to have the same characteristics as the population from which they were selected.

Sample

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Statistic vs Parameter

​STATISTIC

This is a measured characteristic of the sample.

For example, our retailer may find that 73% of the sample members rate the store as having higher-quality merchandise than the competitor across the street. The sample statistic can be a measure of typicalness or central tendency, such as the mean, median, mode, or proportion, or it may be a measure of spread or dispersion,such as the range and standard deviation.

Statistic vs Parameter

​Parameter

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This is a numerical characteristic of the population. If we were to take a complete census of the population, the parameter could actually be measured.

Quantitative vs Qualitative Variable

​Qualitative Variable

• allow for classification of  individuals based on some attribute or characteristic.

• In expressing results involving qualitative variables, we describe the percentage or the number of persons or objects falling into each of the possible categories.

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Quantitative vs Qualitative Variable

​Quantitative Variable

• enable us to determine how much of something is possessed, not just whether it is possessed.

• provide numerical measures of individuals. Arithmetic operations such as addition and subtraction can be performed on the values of a quantitative variable and will provide meaningful results.

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Types of Quantitative Variables

• Discrete Variables

• Continuous Variables​

Discrete Variables

• are those with a finite range of values or a potentially infinite, but countable, range of values.

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Example:

The number of employees on the payroll of a manufacturing firm, the number of patrons attending a theatrical performance, or the number of defectivesin a production sample.

Continuous Variables

• are those that have infinite ranges and really cannot be counted and they are measured with scales.

Example:

The volume of liquid in a water tower could be any quantity between zero and its capacity when full. ​

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​Activity 2:

Qualitative vs Quantitative​

Multiple Choice

Gender

• Qualitative

• Quantitative

Multiple Choice

Temperature

• Qualitative

• Quantitative

Multiple Choice

Number of days during the past week  that a college student aged 21 years   or older has had at least one drink.

• Qualitative

• Quantitative

Multiple Choice

Zip code

• Qualitative

• Quantitative

Multiple Choice

Class rank

• Qualitative

• Quantitative

​Activity 3:

Discrete vs Continuous Variables​

Multiple Choice

The number of heads obtained after flipping a coin five times.

• Discrete

• Continuous

Multiple Choice

The number of cars that arrive at a  McDonald’s drive–through between 12:00PM and 1:00PM.

• Discrete

• Continuous

Multiple Choice

The distance a 2007 Toyota Prius can travel in city driving conditions with a full tank of gas.

• Discrete

• Continuous

Multiple Choice

Age of subjects in an experiment

• Discrete

• Continuous

Multiple Choice

Number of bar presses by a rat in a Skinner

    box.

• Discrete

• Continuous

​Level of Measurements

Nominal Scale/Level

• The simplest form of measurement.

• Most often used with variables that are qualitative in nature rather than quantitative.

• It is important to note that the units of a nominal scale are categories, there is no magnitude relationship between the units of a nominal scale. Thus, there is no quantitative relationship between the categories.

Nominal Scale/Level

Example:

Entergy Corporation lists four types of domestic electric customers. In its computer records, the company might use “1” to identify residential customers, “2” for commercial customers, “3” for industrial customers, and “4” for government customers. Aside from identification, these numbers have no arithmetic meaning.

Ordinal Scale/Level

• In this scale, in addition to identity, there is the property of rank order, which means that the elements in a set can be lined up in a series from lowest to highest or vice versa.

• Ordinal scales imply nothing about how much greater one ranking is than another. Even though ordinal scales may employ numbers or “scores” to represent the rank ordering, the numbers do not indicate units of measurement.

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Ordinal Scale/Level

Example:

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The performance difference between the first-ranked job applicant and the second ranked applicant may be small while the difference between the second and third ranked applicants may be large. There is a classification and ranking, however, it implies nothing about how much greater one ranking is than another.​​

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Interval Scale/Level

• The interval scale not only includes “greater than” and “less than” relationships, but also has a unit of measurement that permits us to describe how much more or less one object possesses than another.

• It has the property of equal intervals between adjacent units but does not have an absolute zero point.

Interval Scale/Level

​Example:

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The Celsius scale of temperature measurement is a good example of the interval scale. Zero on the Celsius scale is the temperature at which water freezes; therefore it does not have absolute zero point. It has the property of equal intervals between adjacent units but does not have an absolute zero point.

Ratio Scale/Level

• Highest, level of measurement is called a ratio scale.

• It has an absolute zero point.

• In the physical sciences, the use of this type of measurement scale is common; times, distances, weights, and volumes can be expressed as ratios in a meaningful and logically consistent way.

Ratio Scale/Level

Example:

​Election votes, natural gas consumption, return on investment, the speed of a production line, and FedEx Corporation’s average daily delivery of 6,900,000 packages during 2008.

​Activity 4: Levels of Measurement

Multiple Choice

Number of bicycles ridden by students in the

     freshman class.

• Nominal

• Ordinal

• Interval

• Ratio

Multiple Choice

Types of bicycles ridden by students in the

    freshman class.

• Nominal

• Ordinal

• Interval

• Ratio

Multiple Choice

Number of days during the past week that a

   college student aged 21 years or older has had

   at least one drink.

• Nominal

• Ordinal

• Interval

• Ratio

Multiple Choice

Proficiency in mathematics graded in the categories

    of poor, fair, and good.

• Nominal

• Ordinal

• Interval

• Ratio

Multiple Choice

Temperature in Celsius.

• Nominal

• Ordinal

• Interval

• Ratio

​- Karl Pearson

"Statistics is the grammar of science."