Use descriptive statistics to summarize the observations you collected. Use inferential statistics when you want to estimate a population value or assess a specific claim about a population—and only when the sample and method support that step. First decide what your question is about: the data in front of you, or a wider group.
Start with the question you need to answer
A sample is the set of observations you collected; the population is the larger group you want to understand. A statistic summarizes a sample, while a parameter describes a population. Inferential statistics use sample statistics to draw conclusions about population parameters. Penn State STAT 200 defines inference in those terms.
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- If you need to describe only the observations collected, use descriptive statistics.
- If you need to estimate an unknown population quantity, use inferential estimation.
- If you need to evaluate a stated claim about a population quantity, use an inferential hypothesis test.
Inference does not make a sample representative. The population must be defined, and the way the sample was selected must justify extending results beyond the observations.
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When descriptive statistics are the right choice
Descriptive statistics organize and summarize the data you have. They answer questions such as how many observations fall into each category, what the typical value is, how widely values vary, and whether a pattern is visible in a graph.
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- Use counts and proportions for categorical data.
- Use a mean or median to describe a typical value, choosing the measure that fits the data and question.
- Use measures of spread and graphs to show variability and shape, not just a single average.
Keep the scope of the wording clear: “In this survey, 42% of respondents chose option A” describes the respondents. It does not establish that 42% of the broader population would choose it unless the sampling design supports that conclusion.
When to estimate a population value with a confidence interval
Use inferential estimation when the goal is to learn about an unknown population quantity from sample data. A point estimate gives one sample-based value; a confidence interval gives a range of reasonable estimates while expressing uncertainty. Penn State’s confidence-interval lesson explains this sample-to-population purpose.
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- This guide is a perfect overview for the topics covered in introductory statistics courses.
A confidence interval is not a range expected to contain a specified percentage of individual observations. It describes uncertainty in estimating a population parameter. Interpret it alongside the sample design and the assumptions of the procedure used to calculate it.
When to test a specific population claim
Use a hypothesis test when you have a defined claim about a population parameter and want to assess how compatible the sample evidence is with that claim. The test starts with a specified null hypothesis; it is not a general-purpose way to summarize a dataset. Penn State distinguishes the roles directly: confidence intervals estimate a population parameter, while tests evaluate a specified hypothesis.
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A p-value is not the probability that the null hypothesis is true. It measures how unusual the observed result, or one more extreme, would be under the null hypothesis and the test’s assumptions. Statistical significance alone does not establish practical importance or prove that one variable caused another.
Choose an inferential procedure that fits the design
There is no single test or interval suitable for every dataset. The research question, outcome type, number of groups, and whether observations are independent or paired all affect the choice. Procedures also differ in their assumptions, so check the conditions for the particular method rather than applying a generic rule.
- Target: identify the parameter or claim you want to estimate or test.
- Variable: determine whether the outcome is categorical or quantitative.
- Groups and design: establish how many samples or groups there are and whether observations are independent, paired, or otherwise related.
- Assumptions: assess the sampling process and the conditions required by the chosen procedure.
- Alternative methods: if a normal approximation is unsuitable, an exact, bootstrap, or randomization method may be appropriate, depending on the design and question.
Penn State’s one-sample lesson and two-sample lesson illustrate method-specific assumptions and alternatives. Their classroom conditions are guidance for those procedures, not universal guarantees for every dataset.
A practical decision sequence
- Define the target. State the population you care about, if the question concerns more than the collected observations.
- Name the goal. Decide whether you are describing the dataset, estimating a population parameter, or evaluating a specific population claim.
- Identify the data structure. Note the variable type, number of groups, and study design, including whether observations are dependent.
- Check whether inference is justified. Consider how the sample was obtained and whether the procedure’s assumptions are plausible.
- Report only what the design permits. Present sample summaries as sample summaries; describe population conclusions as estimates or test results with their uncertainty and limitations.
What neither approach can establish on its own
A calculation cannot repair a poorly defined population or a biased sample. Even a correctly calculated interval or test may give a misleading population conclusion if the data collection process does not support generalization. Likewise, an association in observational data does not by itself show causation; causal claims require an appropriate design and additional support.
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