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Use descriptive statistics to summarize the observations you collected; use inferential statistics when you want to estimate or test a claim about a wider population. Before choosing a calculation, define the question and population you care about, then check whether your sampling method and the procedure’s assumptions support that conclusion.
Start with the question: describe, estimate, or test
The choice depends on what you want to learn—not simply on how large or complicated your dataset is. A sample is the set of observations you collected; a population is the full group your question concerns. A statistic summarizes a sample, while a parameter describes a population. Penn State STAT 200 defines inferential statistics as procedures that use data from an observed sample to reach a conclusion about a population (Penn State STAT 200: Collecting Data).
- Describe: What do the observations in this dataset look like?
- Estimate: What value is plausible for a population quantity we cannot directly observe?
- Test: How compatible are these data with a specific claim about a population quantity?
Those are different goals. An estimate and a test are both inferential, but they answer different questions.
Use descriptive statistics to report the data you have
Descriptive statistics organize observed data without extending the result to a larger group. They are the right choice when your audience needs a clear account of the dataset itself—for example, the number of records, the share in each category, a typical value, or how much values vary.
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- Use counts and proportions for categorical variables, such as device type or survey response.
- Use a mean or median to summarize a numerical variable; the better choice depends on the shape of the data and the question.
- Use measures of spread and suitable graphs to show variability and distribution, rather than letting one average stand in for the whole dataset.
State the scope explicitly: “Among the 120 customers surveyed, 42% chose option A” describes those respondents. It does not, by itself, establish that 42% of all customers would choose option A.
Use inferential statistics to estimate a population quantity
If the question concerns an unknown population parameter, use an inferential estimate. A point estimate gives one sample-based value. A confidence interval gives a range of estimates together with a method for expressing uncertainty. Penn State describes confidence intervals as sample-based estimates of population parameters (Penn State STAT 200: Confidence Intervals).
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Interpret an interval as uncertainty about the population quantity under the method’s assumptions—not as a range that contains a stated percentage of individual observations. The interval’s usefulness depends on the design and procedure behind it, as well as the data.
Use a hypothesis test only for a specified population claim
A hypothesis test evaluates evidence against a defined claim about a population parameter. It is not a general-purpose way to summarize data. Specify the null hypothesis—the claim being assessed—and select a test that matches the variable, groups, and study design. Penn State distinguishes the purposes directly: “Confidence intervals use data from a sample to estimate a population parameter. Hypothesis tests use data from a sample to test a specified hypothesis” (Penn State STAT 200: Hypothesis Testing, Part 2).
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A p-value is not the probability that the null hypothesis is true. It describes how unusual data at least as incompatible with the null would be under that hypothesis and the test’s assumptions. Statistical significance alone does not show that an effect is practically important, nor does it establish causation.
Check the sample and method before generalizing
Inference cannot repair a biased sample or an unclear target population. A calculation may be correct while its conclusion is too broad. Before reporting a population estimate or test result, make the intended population and sample-selection process clear, then examine the assumptions of the particular procedure.
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- Define the population: Specify who or what the conclusion is meant to cover.
- Describe how observations were selected: Explain the sampling or recruitment process and relevant limitations.
- Match the method to the design: Identify the variable type, number of groups or samples, and whether observations are independent or paired.
- Check procedure-specific conditions: Distributional and approximation requirements vary by method; do not treat one test’s classroom rule as universal.
Observational association also does not, by itself, show that one variable caused another. Causal conclusions require an appropriate design and additional support.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Choose a method that fits the data and design
Once you have decided to make an inference, the research question, variable, number of samples, and dependence structure guide the procedure. Different methods have different assumptions; the labels “one sample” or “two samples” are not enough on their own to select a valid test.
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| Situation | What to establish | Possible direction |
|---|---|---|
| One sample, estimating or testing a quantity | Identify the parameter, variable, sampling design, and conditions for the chosen procedure. | Depending on the question and conditions, a z or t procedure, bootstrap, or randomization method may be considered. See Penn State STAT 200: Inference for One Sample. |
| Two samples or groups | Determine whether samples are independent or paired, what is being compared, and whether the procedure’s conditions are plausible. | Choose a method for that design; when normal-approximation conditions are unsuitable, an exact, bootstrap, or randomization alternative may be appropriate. See Penn State STAT 200: Inference for Two Samples. |
These are examples of method choices, not universal guarantees. If conditions are not met, do not silently proceed as though they were: consider a suitable alternative for the design and question, or limit the conclusion to descriptive reporting.
Quick Recap
A practical decision sequence
- Write the question in plain language. Is it about the collected records, an unknown population value, or a specific population claim?
- Name the target population. If you cannot define the group the conclusion should describe, do not present a sample result as representative of it.
- Choose the purpose. Summarize observed data descriptively; use an interval to estimate a population quantity; use a test to assess a specified hypothesis.
- Describe the data and design. Note the variable type, number of groups or samples, and whether observations are independent or paired.
- Check sampling and procedure assumptions. Select a method whose requirements are plausible, and consider an appropriate alternative if they are not.
- Report only what the design supports. Distinguish the sample result from the population conclusion and state relevant uncertainty and limitations.
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