Applied Statistics Lesson 1: Basics of Statistics Review

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What is the term given to the analysis of data that helps describe, show, or summarize data in a meaningful way?

Descriptive statistics

What are properties of samples, such as the mean or standard deviation, called?

Statistics

What type of statistics allows us to make generalizations about populations from samples?

Inferential statistics

What is the process called that aims to ensure the sample accurately represents the population?

Sampling strategy

Why are descriptive statistics important in presenting data?

To visualize and interpret data more meaningfully

What does inferential statistics arise from due to the nature of sampling?

Sampling error

What is one limitation of descriptive statistics?

Descriptive statistics cannot be used to generalize to other people or objects.

What is one limitation of inferential statistics?

One limitation of inferential statistics is that you are providing data about a population that you have not fully measured, leading to uncertainty in the results.

What is an independent variable?

An independent variable is a variable that is being manipulated in an experiment.

What is a dependent variable?

A dependent variable is the result of an experiment.

Explain one limitation of using descriptive statistics in generalizing results.

Descriptive statistics cannot be used to claim that a treatment or intervention will work in other individuals.

Why can inferential statistics lead to uncertainties in the calculated values?

Inferential statistics involve providing data about a population that has not been fully measured, leading to uncertainties in the results.

What are measures of central tendency in descriptive statistics?

The mode, median, and mean.

What are measures of spread in descriptive statistics?

The range, quartiles, absolute deviation, variance, and standard deviation.

What is the difference between a population and a sample in inferential statistics?

Population includes all the data of interest, while a sample is just a portion of the population.

What are the similarities between descriptive and inferential statistics?

Both rely on the same set of data.

What is a parameter in statistics related to descriptive statistics?

The mean or standard deviation of a population.

What is a sample used for in inferential statistics?

It is used when it is impossible to study the entire population.

What are examples of Interval Variables?

Exam Score, Income, Time

List examples of Ratio Variables.

Height, Mass, Distance, Weight

What are some data collection methods mentioned in the text?

Telephone survey, Mailed Questionnaire, Personal Interview

Name a type of Probability Sampling technique.

Simple Random

What is a type of Non-Probability Sampling?

Convenient

What is a categorical variable also known as?

Qualitative variable

How are continuous variables defined?

Variables whose values are obtained by measuring

What distinguishes interval variables from ratio variables?

The presence of a true zero point in ratio variables

Explain why temperature measured in degrees Celsius or Fahrenheit is not a ratio variable.

0°C does not represent the absence of temperature

What does a ratio variable have that an interval variable does not?

A true zero point

Can you give an example of a ratio variable?

Temperature measured in Kelvin

Study Notes

Properties of Samples and Statistics

  • Properties of samples, such as the mean or standard deviation, are called statistics, not parameters.
  • Parameters are properties of populations, such as the mean or standard deviation.

Descriptive Statistics

  • Descriptive statistics analyze data to describe, show, or summarize it in a meaningful way.
  • Descriptive statistics help identify patterns in data, but do not allow for conclusions beyond the data or hypotheses.
  • They are used to present data in a more meaningful way, enabling simpler interpretation.
  • Examples of descriptive statistics include measures of central tendency (mean, median, mode) and measures of spread (range, quartiles, variance, standard deviation).

Inferential Statistics

  • Inferential statistics use samples to make generalizations about the populations from which the samples were drawn.
  • It is essential for the sample to accurately represent the population.
  • Sampling strategy is critical to achieve this.
  • Inferential statistics arise from sampling error, which naturally occurs when sampling.

Limitations of Descriptive and Inferential Statistics

  • Descriptive statistics are limited to making summations about the data actually measured, and cannot be used to generalize to other people or objects.
  • Inferential statistics have two main limitations:
  • Uncertainty about the values calculated due to incomplete measurement of the population.
  • Educated guesses required to run inferential tests, which introduce uncertainty.

Types of Variables

  • Independent variable: a variable being manipulated in an experiment (also called experimental or predictor variable).
  • Dependent variable: the result of an experiment (also called outcome variable).
  • Types of continuous variables:
  • Interval variables: can be measured, but have no intrinsic zero (e.g., exam score, income, time, generation age range).
  • Ratio variables: interval variables with an intrinsic zero (e.g., height, mass, distance, weight).

Data Collection and Sampling

  • Data collection methods:
  • Telephone survey
  • Mailed questionnaire
  • Personal interview
  • Sampling techniques:
  • Probability sampling:
  • Simple random sampling
  • Stratified random sampling
  • Cluster sampling
  • Systematic sampling
  • Non-probability sampling:
  • Convenient sampling
  • Snowball sampling
  • Quota sampling
  • Purposive sampling

Categorical and Continuous Variables

  • Categorical variable (also called qualitative variable): a variable with a limited, usually fixed, number of categories (e.g., nominal, ordinal, dichotomous).
  • Continuous variable (also called quantitative variable): a variable whose value is obtained by measuring along a continuum, with a numerical value (e.g., temperature, height, mass).

Explore the fundamental concepts of statistics including properties of samples, descriptive statistics, and limitations of reaching conclusions beyond analyzed data. Test your knowledge with this quiz.

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