| Definition | Write the population, outcome, comparison, or relationship the investigation is meant to illuminate before looking for a calculation. | Name what each row or case represents and what is recorded about it. | Describe how observations entered the dataset, who could be represented, and who may have been missed. | Select a table, graph, center, spread, proportion, or comparison according to the data type and question. | Read the distribution or comparison as a whole, including typical values, spread, shape, clusters, gaps, and unusual observations. | Separate what the observed data show from what remains uncertain because of sampling, measurement, design, or natural variability. | Translate the statistical result into a plain-language statement about the defined variable, group, comparison, and timeframe. | Audit the conclusion, denominator, units, population, timeframe, representation, and uncertainty against the original investigation. |
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| Primary decision question | What would a responsible answer need to describe, compare, estimate, or associate? | Who or what is observed, and which attributes vary across observations? | What process connected the target population to the observed sample? | Which display or summary preserves the feature the question asks about? | What is common, how much do observations differ, and which features qualify the summary? | What could make another sample, measure, or interpretation differ? | What does the evidence support, and what does it not establish? | Would a careful reader know exactly which evidence supports each part of the final claim? |
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| Purpose | A precise question prevents a convenient statistic from replacing the actual evidence need. | Separates the observational unit from the variables, labels, and summaries derived from those observations. | Makes selection, coverage, nonresponse, voluntary-response, and measurement risks visible before interpretation. | A matching representation reveals structure without manufacturing precision or hiding important variation. | Keeps a single average from erasing heterogeneity or a striking outlier from replacing the overall pattern. | Calibrates confidence and protects descriptive evidence from becoming an unsupported causal or universal claim. | Separates calculation from meaning and makes the boundary of the claim auditable. | Catches responsive-looking conclusions that use the wrong variable, wrong group, hidden denominator, or exaggerated certainty. |
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| Time horizon | Before classifying variables or selecting a display. | After stating the question and before choosing arithmetic. | Before treating a sample pattern as evidence about a wider group. | After data and source checks, before drawing a conclusion. | During descriptive analysis, before causal or population claims. | Before writing the final interpretation. | After descriptive or inferential work and before final verification. | Immediately before the learner submits their own analysis. |
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| Typical information | A learner-written sentence names the population or group, the main variable or relationship, and the intended scope. | A compact inventory gives each variable a meaning, unit or category set, and role in the question. | The learner can name the population, sampling frame or available source, observed group, and plausible exclusions. | A one-sentence rationale links the chosen summary to variable type, comparison, and interpretive goal. | The interpretation names both a central pattern and at least one relevant form of variation or shape. | The learner identifies at least one design limitation and states whether it affects measurement, comparison, generalization, or causality. | The conclusion includes context, direction or magnitude when supported, and appropriately limited language. | A claim-to-evidence check confirms every noun, comparison, number, and limitation has a traceable source. |
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| Common confusion | Starting with a formula because it is familiar, then forcing the available data into it. | Calling every number quantitative even when the number is only an identifier or coded category. | Treating a large row count as proof that the sample represents the population. | Reporting every statistic produced by software instead of selecting the evidence that answers the question. | Calling a group consistent because the mean looks stable while the values are widely dispersed. | Using cautious words while still making a claim that reaches beyond the data source. | Repeating a computed value without explaining what it says about the original question. | Checking the arithmetic twice while never checking whether the result answers the question asked. |
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| What does not belong | Do not reproduce a restricted prompt; summarize the statistical decision in your own language. | A label has no numerical meaning merely because digits are used to store it. | Do not invent a random-sampling process or claim representativeness without evidence. | A display is not self-validating; labels, denominators, scale, and source still need examination. | Do not remove an unusual value only because it changes the result; investigate its origin and relevance. | Uncertainty is not a ritual disclaimer; it must be tied to a concrete feature of the evidence. | Association does not by itself prove causation, and a sample result does not automatically describe everyone. | Verification supports responsible reasoning; it does not guarantee a grade or replace current classroom instructions. |
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