How Collected Data Tells The Truth - AP Statistics

1. Define 'frequency distribution.'

   A summary of how often different values occur in a dataset. Shows how frequently each value appears in the data.

2. What is the purpose of a control group?

   To serve as a baseline for comparison in an experiment. Shows what happens without the treatment for comparison.

3. What is cluster sampling?

   Dividing the population into clusters and randomly selecting entire clusters. Takes whole groups instead of individual members.

4. Define 'quantitative data.'

   Data that can be measured and expressed numerically. Represents measurable quantities with numerical values.

5. Identify the term for 'a variable that can take on different values.'

   Random variable. Its value changes randomly according to some probability distribution.

6. What is the term for 'a study that observes individuals and measures variables without controlling them'?

   Observational study. Researchers watch and record but don't manipulate variables.

7. What is the purpose of a pilot study?

   To test the feasibility of a full-scale study. Small-scale trial run to identify potential problems before full study.

8. What is a statistic in the context of a sample?

   A numerical summary of a sample. It describes characteristics of the sample data collected.

9. Define 'experiment' in statistics.

   A study where conditions are controlled to determine cause and effect. Researchers actively manipulate variables to test causation.

10. What is a lurking variable?

    A variable not included in the study that affects the variables studied. Hidden variables can create false associations between studied variables.

11. What is the purpose of random sampling?

    To reduce bias and ensure each member has an equal chance of selection. Randomness prevents systematic selection patterns that create bias.

12. Identify the term for 'the mistaken belief that random events can be predicted.'

    Gambler's fallacy. Past random events don't influence future random outcomes.

13. What is a parameter in the context of a population?

    A numerical summary of a population. It's a fixed value describing the entire population.

14. What is the term for 'a graphical representation of the distribution of data'?

    Histogram. Shows frequency patterns using bars of different heights.

15. Define 'confounding variable.'

    A variable that influences both the dependent and independent variables. Makes it hard to determine which variable causes the effect.

16. What is a sample in statistics?

    A subset of the population used to collect data. We study the subset to make inferences about the whole population.

17. What is the primary goal of descriptive statistics?

    To summarize and describe the main features of a dataset. Organizes and presents data patterns without making predictions.

18. What is response bias?

    Bias introduced by anything in a survey design that influences responses. Survey design itself affects how people answer questions.

19. What is 'external validity'?

    The extent to which the results of a study can be generalized to other situations. Measures how well findings apply beyond the specific study conditions.

20. What does 'systematic sampling' entail?

    Selecting every $k^{th}$ individual from a list of the population. Uses a regular interval pattern to choose subjects systematically.

21. Define 'simple random sample.'

    Each member of the population has an equal chance of selection. No individual is more likely to be chosen than another.

22. What is a population in statistics?

    The entire group of individuals or instances about whom we hope to learn. It's the complete set we want to study, not just a portion.

23. Identify the term for 'data collected over a period of time.'

    Longitudinal data. Tracks changes in the same subjects over time.

24. Identify the concept of 'interquartile range (IQR).'

    The difference between the first and third quartiles in a dataset. Measures the spread of the middle $50\%$ of data values.

25. Define 'qualitative data.'

    Data that describes qualities or characteristics. Describes categories or attributes that can't be measured numerically.

26. What is the placebo effect?

    Changes in participants' behavior due to their expectations of treatment. Believing you're treated can cause real changes in response.

27. What is 'randomization' in an experiment?

    The process of randomly assigning subjects to different treatment groups. Chance assignment prevents systematic differences between groups.

28. What is the definition of 'census'?

    A complete enumeration of a population. Attempts to collect data from every individual in the population.

29. Identify the term for 'data collected at a single point in time.'

    Cross-sectional data. Like a snapshot - captures one moment in time.

30. What is voluntary response bias?

    Bias from individuals who self-select into the survey. Self-selected participants often have strong opinions, creating bias.

31. What is a stratified sample?

    A sample that divides the population into strata and samples each stratum. Groups similar individuals together, then samples from each group.

32. What is the term for 'a method of data collection where the researcher does not interfere'?

    Naturalistic observation. Observing in natural settings without researcher intervention.

33. Define 'sampling error.'

    The difference between a sample statistic and the corresponding population parameter. Natural variation between sample results and true population values.

34. What is the importance of replication in experiments?

    To ensure results are consistent and not due to chance. Repeated trials help distinguish real effects from random variation.

35. What is a 'sampling frame'?

    A list of individuals from which a sample is actually selected. The actual source from which researchers can select participants.

36. Define 'nonresponse bias.'

    Bias introduced when a large fraction of sampled individuals fail to respond. Missing responses can skew results if non-responders differ systematically.

37. Define bias in data collection.

    Systematic error introduced into sampling or testing. It skews results in a particular direction consistently.

38. What does 'inferential statistics' involve?

    Making predictions or inferences about a population based on a sample. Uses sample data to draw conclusions about the larger population.

39. Define 'double-blind experiment.'

    An experiment where neither the subjects nor the experimenters know who receives the treatment. Prevents bias from expectations of both subjects and researchers.

40. Identify the term for 'the chance of a particular outcome occurring in an experiment.'

    Probability. Numerical measure of likelihood, ranging from $0$ to $1$.

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