Probability and Statistics Terms Quiz

Probability and Statistics Terms

• Random Experiment: An experiment with unpredictable outcomes. Example: rolling a die can result in any number between 1 to 6.
• Sample Space (S): The complete set of possible outcomes of a random experiment.
  • Tossing a coin: S = {H, T}
  • Rolling a die: S = {1, 2, 3, 4, 5, 6}
• Event: A specific outcome of an experiment. Example: getting heads while tossing a coin.

Population Types

• Infinite Population: An uncountable population where individual units cannot be quantified, e.g., the number of germs in a patient's body.
• Finite Population: A population comprising concrete individuals, such as books or tables.
• Existent Population: Units available in solid form, e.g., physical objects.
• Hypothetical Population: A conceptual population whose units are not tangible; exemplified by theoretical outcomes from experiments like rolling a die or tossing a coin.

Sampling Bias Considerations

• Nonresponse Bias: Occurs when participants drop out or refuse to participate, leading to differences between those who respond and those who do not. Example: study participants with high workloads may be less likely to participate.
• Undercoverage Bias: Happens when some groups are inadequately represented in the sample. Example: national surveys conducted online may overlook elderly and lower-income households.
• Pre-screening or Advertising Bias: Selection methods may skew participant motivation. For instance, those motivated to improve their sleep habits may disproportionately respond to a sleep intervention study.

Sampling Methods

• Convenience Sampling: Gathering data from easily accessible participants, which may lack representativeness. Example: surveying classmates only yields opinions from a narrow demographic.
• Voluntary Response Sampling: Respondents self-select to participate, often attracting those with strong opinions. Example: sending out a survey to all students, but only receiving responses from those with intense views on support services.
• Purposive Sampling: Researcher-selected samples based on specific criteria that fulfill the study’s aims, often used in qualitative research.
• Snowball Sampling: Involves existing participants recruiting new ones, which can lead to representativeness issues as it relies on participant networks.
• Quota Sampling: Dividing a population into subgroups and ensuring a specified number of participants from each subgroup is included in the sample to maintain balance. Example: targeting equal numbers of meat-eaters, vegetarians, and vegans in consumer research.

Sampling Bias in Probability and Non-Probability Samples

• Probability Sampling: Ensures each population member has a known chance of being selected, reducing, but not eliminating bias. Example: using a random number generator for selection.
• Non-Probability Sampling: Based on subjective criteria, leading to the potential for biased results. Example: convenience samples where availability drives selection, compromising representativeness.

This quiz covers essential terms and definitions used in probability and statistics. Test your understanding of concepts like random experiments and more through examples and definitions. Perfect for students looking to solidify their knowledge in these foundational areas.