Statistical foundations and measurement
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Data and variables
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Population -> group the study concerns.
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Sample -> observed subset of that population.
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Parameter -> describes a population.
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Statistic -> computed from a sample.
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Quantitative data -> measured or counted numerically.
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Qualitative data -> categories.
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Discrete variable -> separate countable values.
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Continuous variable -> values across an interval, subject to measurement precision.
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Binary variable -> two categories; usually nominal.
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Ungrouped data -> retain individual observations.
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Grouped data -> replace observations with class intervals and frequencies.
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Measurement scales
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Nominal -> categories with no order.
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Ordinal -> ordered categories without guaranteed equal spacing.
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Interval -> meaningful differences; no absolute zero.
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Example: Celsius temperature.
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Ratio -> meaningful differences and a meaningful zero.
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Ratios can be interpreted; examples: duration and mass.
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Data collection and sampling
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Basic process -> define question -> collect -> organize -> summarize -> analyze -> interpret.
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Sampling and collection -> shape what conclusions are supported.
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Probability sampling -> can support design-based inference when assumptions and implementation are appropriate.
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Convenience sampling -> useful for exploration; may not represent the population.
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Exploratory data analysis -> pre-model checks
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