P Value for Median and IQR Calculator

Test medians and spread differences using practical inputs. Choose Mann Whitney or permutation style analysis. Download clean tables and summaries for review later easily.

Calculator

Example Data Table

Observation Sample A Sample B
11210
21411
31513
41715
51816
62018
72119
82320
92522
102824

Formula Used

This calculator uses two robust statistics. The median is the 50th percentile. The interquartile range equals Q3 minus Q1. These measures resist extreme outliers better than the mean and standard deviation.

The p value is estimated with a permutation test. First, the observed difference is computed. Then both samples are pooled. The pooled values are repeatedly shuffled and split into new groups. A new median difference and IQR difference are recorded each time.

For a two sided test, the p value is:

p = (count of permuted differences at least as extreme as observed + 1) / (iterations + 1)

For one sided tests, the calculator counts shuffled differences in the chosen direction only. This approach works well when data are skewed, non normal, or contain outliers.

How to Use This Calculator

  1. Enter Sample A values in the first box.
  2. Enter Sample B values in the second box.
  3. Choose the number of permutation iterations.
  4. Select a two sided, greater, or less hypothesis.
  5. Set the alpha level for significance.
  6. Press the calculate button.
  7. Review the median and IQR p values shown above the form.
  8. Download the summary as CSV or PDF if needed.

About This Median and IQR P Value Tool

Why this calculator is useful

This calculator helps compare two independent samples with robust methods. It focuses on median and interquartile range. These measures work well when data are skewed. They also help when outliers make mean based testing less reliable.

What the tool calculates

The tool reports sample size, mean, standard deviation, median, and IQR for both groups. It then estimates p values for the difference in medians and the difference in IQR values. The result appears immediately above the form after submission.

Why permutation testing is used

There is no single simple closed form p value for every IQR comparison. A permutation approach solves this problem well. It creates many shuffled versions of the pooled data. Then it checks how often the shuffled statistic is as extreme as the observed statistic.

When to use median and IQR

Use the median when you want the central location without heavy influence from outliers. Use the IQR when you want the spread of the middle fifty percent. Together, they describe the center and variability of non normal data clearly.

Reading the output

A small p value suggests a meaningful difference under the selected hypothesis. A large p value suggests the observed gap may happen by random group assignment. Statistical significance does not measure practical importance, so always review the actual differences too.

Data entry tips

You can enter values with commas, spaces, or line breaks. Each group should contain at least four values, because quartiles need enough data for stable interpretation. More observations and more iterations usually improve stability of the estimated p values.

Export options

The calculator includes CSV and PDF export buttons. These help with documentation, classroom work, and reports. The exported summary contains the main result table, which keeps the workflow simple and easy to share.

Frequently Asked Questions

1. What does this calculator test?

It tests whether two independent samples differ in median and IQR. It uses permutation based p values, which are useful for skewed or non normal data.

2. Why not use a t test here?

A t test focuses on means. This tool focuses on medians and spread. It is better when outliers or skewness make mean based testing less suitable.

3. What is the IQR?

The interquartile range is Q3 minus Q1. It measures the spread of the middle half of the data and is less sensitive to extreme values.

4. What does a small p value mean?

A small p value suggests the observed difference is less likely under random reassignment of data between groups. It supports evidence of a real difference.

5. How many iterations should I use?

At least 5000 iterations is a solid starting point. Larger values usually give a more stable estimate, though they may take longer to process.

6. Can I use unequal sample sizes?

Yes. The calculator accepts different group sizes. It preserves each sample size during every permutation split when estimating the p value.

7. Does significance prove practical importance?

No. A significant result only suggests statistical evidence. You should still inspect the actual median difference and IQR difference before drawing practical conclusions.

8. Can I download the results?

Yes. Use the CSV button for spreadsheet friendly output or the PDF button for a quick printable report of the summary table.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.