Quantitative Variables & Statistics Basics

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Questions and Answers

Which of the following variables is an example of a quantitative variable?

  • Type of waste (dried leaves, recyclables, food scraps)
  • Social class (poor, middle, rich)
  • Number of cups of rice consumed per meal (correct)
  • Satisfaction level on a conservation program (unsatisfied, satisfied, highly satisfied)

A variable measured on an ordinal scale has a true zero point.

False (B)

What level of measurement is exemplified by 'Birth order (First born, second born, etc.)'?

Ordinal

In statistics, the process of determining the value or label of a particular variable for a particular element is known as ______.

<p>measurement</p> Signup and view all the answers

Match the level of measurement with the appropriate example:

<p>Nominal = Sex of students (Male, Female) Ordinal = UP student classification (Fr, So, Jr, Sr) Interval = Daily maximum temperature (in Celsius) Ratio = Household size</p> Signup and view all the answers

Which level of measurement is characterized by categories that are distinct, non-overlapping, exhaustive, and of equal importance?

<p>Nominal (D)</p> Signup and view all the answers

Which of the following is NOT a characteristic of interval level of measurement?

<p>There is a true zero point. (D)</p> Signup and view all the answers

Provide an example, not from the given text, of data measured at the ratio level.

<p>Height</p> Signup and view all the answers

Which of the following best characterizes statistics as a field?

<p>A science dealing with the collection, organization, analysis, presentation, and interpretation of data. (D)</p> Signup and view all the answers

Statistics is primarily useful for analyzing past events and has limited application in predicting future trends.

<p>False (B)</p> Signup and view all the answers

Give an example, not provided in the text, of how statistics might be used to compare different subpopulations within a society.

<p>Comparing the average income of college graduates versus those with only a high school diploma to evaluate the economic impact of higher education.</p> Signup and view all the answers

The use of statistics to understand how absences in a lecture class affects final grades is an example of studying ______ relationships.

<p>cause-and-effect</p> Signup and view all the answers

What is the primary role of statistics in social sciences?

<p>To describe population characteristics and relationships between them. (B)</p> Signup and view all the answers

Which example illustrates how statistics can be used to explain social phenomena?

<p>Identifying key attributes considered by voters when choosing a presidential candidate. (A)</p> Signup and view all the answers

Match the statistical use with its respective application.

<p>Describe population characteristics = Determining the average daily time spent online by Filipinos Compare subpopulations = Analyzing the obesity rate difference between Filipino men and women Explain a phenomenon = Identifying the most important attributes for millennial voters Predict future phenomena = Estimating the likelihood of prostate cancer based on finger length</p> Signup and view all the answers

If a study finds a strong correlation between ice cream sales and crime rates, which conclusion is most appropriate?

<p>There maybe confounding variable affecting both ice cream sales and crime rates. (D)</p> Signup and view all the answers

Which level of measurement possesses a true zero point, indicating the complete absence of the characteristic being measured?

<p>Ratio (B)</p> Signup and view all the answers

The daily maximum temperature measured in Celsius is an example of ratio scale.

<p>False (B)</p> Signup and view all the answers

What is the level of measurement for categorizing types of waste (e.g., dried leaves, recyclables, food scraps)?

<p>Nominal</p> Signup and view all the answers

A summary measure describing a specific characteristic of the population is known as a ________.

<p>Parameter</p> Signup and view all the answers

Which of the following levels of measurement allows for all algebraic operations (addition, subtraction, multiplication, division) to be performed?

<p>Ratio (B)</p> Signup and view all the answers

In a statistical study, what does the term 'population' refer to?

<p>A collection of all elements under consideration. (B)</p> Signup and view all the answers

Match each level of measurement with the appropriate operation that can be performed:

<p>Nominal = Equality Ordinal = Greater than or less than Interval = Difference or sum Ratio = All algebraic operations</p> Signup and view all the answers

A sample always includes every member of the population being studied.

<p>False (B)</p> Signup and view all the answers

If you are analyzing 'satisfaction level' (unsatisfied, satisfied, highly satisfied), which level of measurement are you working with?

<p>Ordinal (A)</p> Signup and view all the answers

Why is the level of measurement an important consideration when choosing a statistical tool?

<p>Different levels of measurement allow for different types of statistical analysis.</p> Signup and view all the answers

Define what a 'variable' is in the context of statistics.

<p>A characteristic or attribute that can assume different values for different elements.</p> Signup and view all the answers

The actual value that a variable takes for a particular element is known as an ______.

<p>observation</p> Signup and view all the answers

Which of the following is the best example of a qualitative variable?

<p>The brand of laptops used by students in a class. (A)</p> Signup and view all the answers

In a study examining the effects of a new fertilizer on crop yield, researchers collect data from 500 randomly selected farms across the country. Which of the following is the sample in this study?

<p>The 500 selected farms. (A)</p> Signup and view all the answers

Which of the following is the best example of a research question that aims to understand a population?

<p>What is the average income of software engineers in Silicon Valley based on a survey of 200 engineers? (A)</p> Signup and view all the answers

Match the following statistical terms with their definitions:

<p>Population = Entire group under study Sample = Subset of the population Variable = Characteristic that can vary Observation = Realized value of a variable</p> Signup and view all the answers

In a study examining the percentage of students who own laptops at a university, what would be considered a parameter?

<p>The exact percentage of laptop owners among all students at the university. (C)</p> Signup and view all the answers

Descriptive statistics involves making predictions or generalizations about a population based on data from a sample.

<p>False (B)</p> Signup and view all the answers

A researcher collects data from a sample of voters to predict the outcome of an election. Is this an example of descriptive or inferential statistics?

<p>inferential statistics</p> Signup and view all the answers

A __________ is a numerical summary of a sample, while a __________ is a numerical summary of a population.

<p>statistic; parameter</p> Signup and view all the answers

Which of the following scenarios best illustrates the use of inferential statistics?

<p>Using the results of a poll to predict the voting preferences of an entire electorate. (C)</p> Signup and view all the answers

In a study, a researcher finds that 70% of the sampled patients respond positively to a new drug. What statistical term best describes this value?

<p>Statistic (D)</p> Signup and view all the answers

If a university reports the average age of all its students, is this value considered a parameter or a statistic?

<p>Parameter (C)</p> Signup and view all the answers

Flashcards

Statistics

A body of knowledge dealing with the collection, organization, presentation, analysis, and interpretation of data.

Statistics (Numerical)

Numerical figures or facts systematically collected and presented.

Descriptive Statistics

To summarize and describe the main features of data from a population.

Describe Population

To observe the characteristics of a group.

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Compare Subpopulations

To identify similarities and differences between groups.

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Explain a Phenomenon

To provide reasons and explanations for events or trends in a population.

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Predict Future Phenomena

To estimate or forecast future events or trends within a population.

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Population

The entire group of individuals, objects, or events of interest in a statistical study.

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Sample

A subset of the population from which data is actually collected.

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Variable

A characteristic or attribute that can vary among elements in a collection.

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Observation

The specific value of a variable that is observed or recorded.

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Data

The complete set of observations collected for analysis.

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Qualitative Variable

A variable with categories or labels rather than numerical values.

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Population (voting example)

All registered Filipino voters.

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Sample (voting example)

Registered Filipino voters.

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IQ Score

A score representing a person's level of intelligence.

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Nominal Level

A level of measurement where data is categorized into distinct groups with no inherent order.

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Ordinal Level

A level of measurement where data is categorized into ordered groups, but the intervals between ranks aren't equal or meaningful.

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Interval Level

A level of measurement where there are equal intervals between values, but no true zero point.

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Ratio Level

A level of measurement with equal intervals and a true zero point, allowing for ratio comparisons.

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Measurement

The process of assigning a value or label to a variable for an element, based on observation.

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Parameter

A summary measure describing a characteristic of the entire population.

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Interval Level

Categories are distinct, magnitude matters, fixed unit of measurement, no true zero.

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Level of Measurement: Importance

The level of measurement affects which statistical tools can be used to analyze the data.

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Example of Ordinal Variable

Social class (poor, middle, rich)

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Example of Quantitative Variable

Household size is what type of variable?

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Example of Nominal Variable

"Yes" or "No" on marijuana legalization.

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Inferential Statistics

Techniques for generalizing from a sample to a population.

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90% and 80% in the example.

The value 90% is a parameter, and 80% is a statistic.

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Staff used descriptive statistics?

Staff member who organized, summarized, and presented collected data.

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Study Notes

Definition of Statistics

  • Statistics is a body of knowledge and science.
  • It deals with collection, organization, presentation, interpretation, and analysis methods.

Uses of Statistics

  • Describe the general characteristics of a population, for example Filipinos spend 10 hours on average online.
  • Compare different subpopulations, such as Filipino women outliving their male counterparts by six years.
  • It explains phenomena in a population, for example the political experience of a presidential candidate is the most important attribute for 25% of Filipino millennial voters
  • Statistics predicts future phenomena in the population.
  • For example, a male with a longer index finger than ring finger is 33% less likely to develop prostate cancer.
  • Statistics can describe relationships between characteristics of elements in a population.
  • For example, a strong positive relationship exists between divorce rates and margarine consumption in Maine, U.S.A
  • Study the cause-and-effect, such as a six-point decrease in STAT 166 final standing for each lecture absence.
  • Statistics is a useful took in decision making

Population vs Sample

  • Population: A collection of all elements under consideration in a statistical study.
  • Sample: A part or subset of the population from which information is collected.
  • Example: A study on voting behavior and preferences in the Philippines:
    • Population is all registered Filipino voters
    • Sample is a subset of registered Filipino voters

Variable, Observation and Data

  • Variable: A characteristic or attribute of elements in a collection that can assume different values.
  • Observation: The realized value of a variable.
  • Data: A collection of observations.
  • Examples of Values:
    • Sex of students.
    • Household size.
    • Favorite color of women.
    • Support for Marijuana legalization.
    • Number of cups of rice per meal.
    • Length of service in years of employees.

Types of Variables

  • Qualitative Variable: Variables that have labels or names assigned to categories.
    • Examples: Sex of students, favorite color of women, support for marijuana legalization.
  • Quantitative Variable: Variables that are measured or counted in numbers.
    • Examples: Household size, number of cups of rice consumed, length of service.

Levels of measurement

  • Measurement is the determination of the value or label of a variable for an element based on observations.
  • Levels of measure include, nominal, ordinal, interval, and ratio.
  • Nominal: Numbers classify elements into distinct, non-overlapping and equal categories.
    • Example: Sex of students (1 for male, 2 for female)
  • Ordinal: Numbers classify elements into distinct categories arranged by magnitude.
    • Example: UP student classification (Freshman, Sophomore, Junior, Senior)
  • Interval: Numbers classify elements into distinct categories, arranged by magnitude, with a fixed unit of measurement but no true zero
    • Example: Daily maximum temperature in Celsius.
  • Ratio: Numbers classify elements, arranged by magnitude, with a fixed unit and an absolute zero.
    • Example: Number of cups of rice per meal.
  • The level of measurement influences the choice of statistical tool for data analysis
    • Statistical tools include equality for nominal data, greater than or less than for ordinal data, difference or sum for interval data, and all algebraic operations for ratio data

Parameter vs Statistic

  • Parameter: A summary measure describing a population characteristic.
  • Statistic: A summary measure describing a sample characteristic.
  • Example: If 60 of 100 STAT 166 students own an android phone, the parameter is 60%.
  • If a random sample of 10 students shows that 8 own an android phone, the statistic is 80%.

Major areas in Statistics

  • Descriptive Statistics: Uses techniques to organize, summarize, and present data collected from a sample or population.
    • Example: Observing a change in Filipino immigrants to the US between 2014-2019 using US Census Bureau data.
  • Inferential Statistics: Uses techniques to analyze sample data, leading to generalizations about the population.
    • Example: Concluding that rats are smart and comparable to humans in decision-making based on a random sample of rats. Samples can be descriptive statistics to characterize the samples, but no generations can be made for the entire population

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