To perform a hypothesis test in Python, state a null and alternative hypothesis, match a statistical test to your outcome and study design, check its assumptions, then interpret the test statistic and p-value alongside an effect estimate and uncertainty interval. For two independent groups with a numeric outcome, SciPy’s Welch independent-samples t-test is a practical starting point when equal variances are not assumed.
1. Define the question before choosing a Python test
A hypothesis test evaluates data against a specified null model. Start by identifying the population quantity or relationship you want to learn about, then state:
- Null hypothesis (H₀): the reference claim, such as equal population means or no association.
- Alternative hypothesis (H₁): the difference or relationship you are looking for.
- Direction: decide whether the alternative is two-sided or directional before examining the result.
For example, a two-sided test might ask whether two population means differ; a directional test might ask whether one is greater than the other. Choose the direction based on the question and analysis plan, not on which direction the observed data happen to favor.
2. Match the test to the outcome and study design
The right test depends on what was measured, how observations were collected, and which population quantity is being tested. Identify the unit of observation and whether measurements are independent, paired, or repeated. Repeated measurements on the same people or items are not independent observations.
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| Question or data structure | Possible approach | Key consideration |
|---|---|---|
| Compare means from two independent numeric samples | Independent-samples t-test, such as Welch’s test | Each observation should be independent across groups; choose variance handling deliberately. |
| Compare a numeric outcome measured on paired or repeated units | A paired or repeated-measures procedure appropriate to the design | Preserve the pairing; do not treat paired measurements as independent samples. |
| Test association between categorical variables or count data | A suitable contingency-table procedure, such as chi-square independence or Fisher’s exact test | Check whether the method’s assumptions or approximation suit the table and sample. |
| Test a proportion | Proportion methods documented by Statsmodels, including a z-test or confidence interval where appropriate | Select a method that fits the proportion question and data conditions. |
These are options for different questions, not interchangeable remedies for a poorly specified design. SciPy organizes its available tests by use and documents procedures such as chi-square and Fisher exact tests in its hypothesis-testing tutorial and statistics reference. Statsmodels documents proportion tests and confidence intervals in its statistics reference.
3. Run a two-independent-group test in SciPy
For two independent numeric samples, scipy.stats.ttest_ind returns a test statistic, p-value, and degrees of freedom. Its default equal_var=True requests the conventional pooled-variance test. Set equal_var=False to request Welch’s t-test, which does not assume equal population variances. The example below uses Welch’s test and requests a 95% confidence interval for the population mean difference.
from scipy import stats
# group_a and group_b should contain independent observations
# of the same numeric outcome.
result = stats.ttest_ind(
group_a,
group_b,
equal_var=False, # Welch's t-test
alternative="two-sided",
nan_policy="omit",
)
print(f"t = {result.statistic:.3f}")
print(f"df = {result.df:.1f}")
print(f"p = {result.pvalue:.4g}")
print(result.confidence_interval(confidence_level=0.95))Install SciPy in the Python environment where you will run the analysis if it is not already available. The code assumes group_a and group_b have already been prepared as numeric samples. Check their contents, units, and sample sizes before testing. The confidence-interval method and returned fields are documented in the SciPy ttest_ind reference.
Missing values and pairing
nan_policy="omit" excludes missing observations from the calculation. Use it only when excluding those values is substantively appropriate; omission should not conceal why data are missing or whether missingness could affect the conclusion. If the observations are paired or repeated on the same units, use a paired procedure instead of this independent-samples call.
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Choosing the alternative
Use alternative="two-sided" when either direction would count as evidence relevant to your question. Use "greater" or "less" only when that directional alternative was selected in advance and matches the question. Changing the direction after seeing the data changes the test being performed.
4. Check assumptions and analysis choices
Before interpreting a result, verify that the procedure matches the data-generating design and that its assumptions and implementation options are defensible. At minimum, review:
- Independence: determine whether observations are independent or linked by person, site, time, or another unit.
- Outcome and target: confirm the test addresses the measured outcome and target quantity, such as a mean, proportion, association, or distributional difference.
- Variance handling: for an independent t-test, decide whether the pooled equal-variance assumption is appropriate or whether Welch’s option is preferable.
- Missing data: establish how missing values are handled and whether that choice could change the analyzed sample or conclusion.
- Alternative and threshold: specify the direction of the test and the significance threshold as part of the analysis plan.
- Approximation: for tests based on approximations, consider whether the data conditions make that approximation suitable.
There is no single test that becomes valid merely because Python can calculate it. SciPy’s test reference and tutorial describe distinct procedures; consult the entry for the selected test rather than treating all p-values as equivalent.
5. Interpret the p-value without overclaiming
A p-value is conditional on the null model: it measures how likely data at least as extreme as those observed would be if that model were true. SciPy describes the independent t-test p-value as quantifying “the probability of observing as or more extreme values assuming the null hypothesis” that the samples come from populations with the same means. It is not the probability that the null hypothesis itself is true.
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Compare the p-value with a significance threshold chosen before examining the result. If it is below the threshold, describe the result as evidence against the stated null under the selected model—not proof that the null is false. If it is above the threshold, say the analysis did not provide sufficient evidence to reject the null. That outcome does not establish equality or prove that an effect is absent.
For the example, the reported confidence interval is for the difference in population means, with the sign determined by the order of group_a and group_b. Read it together with the p-value: the estimated magnitude and plausible range help show whether the result matters in context. Statistical significance alone does not describe practical importance.
6. Report enough context to make the result useful
A result is interpretable only when readers can see what was tested and how the data support the conclusion. Report:
- The test and the question it addresses, including the null and alternative where relevant.
- The group sizes and useful descriptive summaries for each group.
- The estimated difference or other effect estimate, with a confidence interval where available.
- The test statistic, degrees of freedom when returned, and p-value.
- Material choices such as Welch versus pooled variance, missing-value handling, and a directional alternative.
7. Troubleshoot common problems
The test raises an error or the result is not numeric
Check that both inputs contain numeric observations and are in the expected format. Inspect data preparation for strings, invalid values, or empty groups before calling the function.
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The result has fewer observations than expected
Review missing values in both samples and the chosen nan_policy. With "omit", observations containing missing values are excluded from the calculation. Confirm the exclusions are justified and report the analyzed group sizes.
The test compares the wrong observations
Check the study design. If each value in one group corresponds to a value in the other group, or the same units are measured more than once, an independent-samples test may not answer the intended question. Choose a paired or repeated-measures method that preserves that structure.
The conclusion changes when the alternative changes
The alternative specifies which departures from the null count as evidence. Choose two-sided or directional testing before looking at results, and do not select the direction afterward to obtain a preferred conclusion.
A non-significant p-value is being read as proof of no effect
It is not proof of equality. Report the estimated effect and its uncertainty, and describe the finding as insufficient evidence to reject the null under the chosen analysis.
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8. Or skip the browser setup
Hypothesis testing itself needs a statistical library, not a browser screenshot. If your Python workflow also needs a clean capture of a web page—for documentation, a report, or an AI-assisted workflow—ScreenshotNeo offers a one-request screenshot API. Its capture options include PNG, JPEG, WebP, or PDF output; use the documented parameters for the output you need. See the ScreenshotNeo API documentation.
import requests
r = requests.get(
"https://api.screenshotneo.com/v1/shot",
params={"access_key": "YOUR_API_KEY", "url": "https://stripe.com"},
timeout=90,
)
open("shot.webp", "wb").write(r.content)ScreenshotNeo removes cookie and consent banners, newsletter popups, and chat widgets before the shot; bot checks, blank pages, and failed loads are not billed. Its MCP server lets AI agents take screenshots, and the free plan includes 1,000 screenshots a month with no card; paid plans start at $5 for 3,000. Sign up for free ScreenshotNeo access.
Frequently Asked Questions
Does a p-value tell me the probability that the null hypothesis is true?
No. It is calculated assuming the null model and describes how extreme the observed data are under that model.
Does a result above the significance threshold prove two groups are equal?
No. It means the analysis did not provide sufficient evidence to reject the stated null; it does not establish equality.
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