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Introduction to Statistics - Key Concepts

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  • What is statistics?

    Statistics is the science of collecting, organizing, analyzing, and interpreting data to make informed decisions.

  • Define population and sample in statistics.

    Population is the entire set of data or all individuals of interest. A sample is a subset of the population.

  • What is a parameter versus a statistic?

    A parameter is a numerical value describing a population, while a statistic describes a sample.

  • What is qualitative data?

    Qualitative data are non-numerical and describe qualities or categories, such as eye color or favorite music genre.

  • What is quantitative data? Differentiate discrete and continuous data.

    Quantitative data are numerical. Discrete data can be counted and are whole numbers; continuous data can take any value within a range.

  • Give an example of qualitative and quantitative data.

    Qualitative: Favorite color. Quantitative discrete: Number of students in a class. Quantitative continuous: Temperature.

  • What are the four levels of measurement?

    Nominal, Ordinal, Interval, and Ratio levels classify data based on order, meaningful differences, and presence of a true zero.

  • Describe nominal level of measurement.

    Nominal data are categories or labels with no order or ranking, e.g., hair color.

  • Describe ordinal level of measurement.

    Ordinal data have a meaningful order but differences are not meaningful, e.g., letter grades.

  • Describe interval level of measurement.

    Interval data have meaningful differences but no true zero, e.g., temperature in °F.

  • Describe ratio level of measurement.

    Ratio data have a true zero and meaningful ratios, e.g., height or weight.

  • What is the difference between an experiment and an observational study?

    An experiment applies a treatment and can imply causation; an observational study only measures without intervention and cannot imply causation.

  • What is simple random sampling (SRS)?

    SRS means every subject and every possible group has an equal chance of being selected.

  • What is a representative sample?

    A representative sample reflects the characteristics of the population proportionally.

  • Describe systematic sampling.

    Systematic sampling selects every kth subject from a list or sequence.

  • Describe cluster sampling.

    Cluster sampling divides the population into groups (clusters) and randomly selects entire clusters.

  • Describe stratified sampling.

    Stratified sampling divides the population into strata with similar characteristics, then randomly samples from each stratum.

  • Why can't you say water at 80°F is twice as hot as at 40°F?

    Because temperature in °F is interval level data with no true zero, ratios like 'twice as hot' are meaningless.

  • Can causation be assumed from an observational study?

    No, observational studies do not control variables, so causation cannot be assumed.

  • Can causation be assumed from an experiment?

    Yes, because experiments apply treatments and control variables, causation can be inferred.