Empirical Data

Examples of Empirical Data in the following topics:

• Lab: Probability Topics

  • Record the results in the "Without Replacement" column section of the "Empirical Results" table.
  • Use the data from the "Empirical Results" table to calculate the empirical probability questions.
  • Convert P(no yellows) to decimal format for both Theoretical "With Replacement" and for Empirical "With Replacement".
  • Empirical "With Replacement": P(no yellows) = c.

• Empirical Formulas

  • Empirical formulas describe the simplest whole-number ratio of the elements in a compound.
  • Empirical formulas are the simplest form of notation.
  • Empirical formulas can be determined using mass composition data.

• Measures of the Spread of the Data

  • An important characteristic of any set of data is the variation in the data.
  • In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean.
  • In a data set, there are as many deviations as there are items in the data set.
  • The data value 11.5 is farther from the mean than is the data value 11.
  • For ANY data set, no matter what the distribution of the data is:

• Sociology and Science

  • Early sociological studies were thought to be similar to the natural sciences due to their use of empiricism and the scientific method.
  • The effect of employing the scientific method and stressing empiricism was the distinction of sociology from theology, philosophy, and metaphysics.
  • This early sociological approach, supported by August Comte, led to positivism, an idea that data derived from sensory experience and that logical and mathematical treatments of such data are together the exclusive source of all authentic knowledge.
  • While there are some individuals who begin analyzing data without a theoretical orientation to guide their analysis, most begin with a theoretical idea or question and gather data to test that theory.
  • The second step is the collection of data, and this is really where the two approaches differ.

• Rationalism

  • This is commonly called continental rationalism, because it was predominant in the continental schools of Europe, whereas in Britain empiricism, or a theory that knowledge comes only or primarily from a sensory experience, dominated.
  • Although rationalism and empiricism are traditionally seen as opposing each other, the distinction between rationalists and empiricists was drawn at a later period and would not have been recognized by philosophers involved in Enlightenment debates.
  • On the other hand, Leibniz admitted in his book Monadology that "we are all mere Empirics in three fourths of our actions."
  • In his views, a priori concepts do exist, but if they are to lead to the amplification of knowledge, they must be brought into relation with empirical data.
  • Immanuel Kant (1724–1804) rejected the dogmas of both rationalism and empiricism and tried to reconcile rationalism and religious belief, individual freedom and political authority, as well as map out a view of the public sphere through private and public reason.

• Z-scores

  • The z-score allows us to compare data that are scaled differently.
  • If X is a random variable and has a normal distribution with mean µ and standard deviation σ then the Empirical Rule says (See the figure below)

• References

  • The role of anomalous data in knowledge acquisition: A theoretical framework and implications for science instruction.
  • Niedderer (Eds.), Research in Physics Learning: Theoretical Issues and Empirical Studies (pp. 310-329).

• Logic

  • Empiricism is rooted in the inductive process and is based on empirical observations.
  • The application of inference and inductive methods requires judgment and caution in the interpretation of data.

• Tradition vs. Science

  • By employing the scientific method and emphasizing empiricism, sociology established itself as an empirical science and distinguished itself from other disciplines that tried to explain the human condition, such as theology, philosophy, or metaphysics.
  • This approach to doing science is often termed positivism or empiricism.
  • Both positivist and verstehen approaches employ a scientific method as they make observations and gather data, propose hypotheses, and test their hypotheses in the formulation of theories.

• Introduction

  • We use sample data to make generalizations about an unknown population.
  • The sample data help us to make an estimate of a population parameter.
  • The interval of numbers is a range of values calculated from a given set of sample data.
  • The Empirical Rule, which applies to bell-shaped distributions, says that in approximately 95% of the samples, the sample mean, x, will be within two standard deviations of the population mean µ.