KIN6005 Statistical Analysis Studio

Nonparametric Tests & Resampling

Compare ranks or estimate uncertainty by repeatedly resampling observations. Choose a method that matches independent or paired data.

Which analysis should I use?

Bootstrap confidence intervals: Estimate uncertainty for a mean, median, trimmed mean, or group difference by sampling with replacement.
Permutation / sign-flip test: Build a null distribution by rearranging group labels or flipping paired differences.
Mann–Whitney U test: Compare the ranks of two independent groups.
Wilcoxon signed-rank test: Compare paired measurements using signed ranks of within-person differences.
Kruskal–Wallis H test: Compare ranks across independent groups.
Friedman test: Compare at least three measurements or conditions from the same participants.

Choose the method from your study design and research question. The question-mark buttons explain each setting and result.

Method

How to use the selected analysis

Use paired measurements on the same row. Select different Before and After columns; differences are After minus Before.
Bootstrap estimates uncertainty; permutation tests a null hypothesis. These answer different questions.
Results update automatically as simulation sliders change. Run is disabled because no manual refresh is needed.

Data source

Simulated data, draw 941. Sliders keep the same random seed. Simulate draws a new sample.

Simulated participants

Population mean

Population SD

Mean within-person change

Before–after correlation

0.6

Upload data or download a template

Upload instructions and data privacy

Use one row per participant, with both paired measurements in separate columns.

The template contains synthetic example rows. Replace them with your observations, then upload the CSV. Keep the headers or select your own column names below.

This page accepts up to 1,000 rows and 2 MB. Data stay in your browser; upload them separately on each tab.

Dataset: Simulated teaching data (draw 941) (16 rows).

How to format your CSV

Save your spreadsheet as CSV UTF-8 (comma delimited), not an Excel workbook. Put unique variable names in the first row, with no title or description above them. Spaces in variable names are allowed.

Put one observation on each row. Keep the same number of columns throughout the file.
Put numbers alone in measurement cells: use 42.5, not 42.5 cm. Put units in the header, such as Jump height (cm). Use a decimal point and omit thousands separators.
Use consistent group labels. Both text (Control, Training) and numeric codes (0, 1) work. Blank measurements are missing, not zero.
Select your outcome, grouping variable, and predictors after uploading. Suggested selections are not a substitute for checking your variables.
For paired tests, measurement agreement, and Friedman tests, use one row per participant with each occasion or device in its own column.
For repeated and mixed models, use one row per participant per occasion, with participant ID, time, and outcome columns. Use numeric time for mixed models.
For categorical analyses, use individual observations, not a summarized frequency table. Each row is one person or event.

Explore accepts up to 10,000 rows and 5 MB. Other CSV labs accept up to 1,000 rows and 2 MB. Use the example download on each page to see its data layout.

Variable types and graph colors (8 variables)

Review the suggested types. Numeric codes such as 0 and 1 can represent categories. A type describes the variable; it does not recode cells or choose a statistical test.

Use variable colors in graphs

Measurements color their plotted values. Category colors identify groups when that column is selected for grouping. Derived plots use the outcome’s color. Settings apply to this dataset on this page.

Presets repeat after seven colors. Use custom hex colors when needed, and check that groups remain distinguishable.

Paste or edit CSV

CSV data

id,group,outcome,pre,post,before,after,followup
1,Control,44.81856418173733,44.81856418173733,50.81855921419285,44.81856418173733,50.81855921419285,50.454797967765444
2,Control,34.93756292484065,34.93756292484065,38.846862569465515,34.93756292484065,38.846862569465515,47.24785811445401
3,Control,37.12318209811927,37.12318209811927,41.72669205852717,37.12318209811927,41.72669205852717,46.43228063697257
4,Control,43.80362500044896,43.80362500044896,53.592068847228475,43.80362500044896,53.592068847228475,49.667393726159716
5,Control,33.35655921721986,33.35655921721986,40.98762711426991,33.35655921721986,40.98762711426991,52.564572930459505
6,Control,38.417884880264396,38.417884880264396,40.60344847574147,38.417884880264396,40.60344847574147,53.37959343966286
7,Control,49.53396495134719,49.53396495134719,51.97898582470806,49.53396495134719,51.97898582470806,42.59944074152308
8,Control,42.72641283094211,42.72641283094211,49.29667327701861,42.72641283094211,49.29667327701861,47.82450639865447
9,Control,33.706269273832746,33.706269273832746,41.642923834157926,33.706269273832746,41.642923834157926,45.9889802231737
10,Control,37.506127331107315,37.506127331107315,48.35955535920448,37.506127331107315,48.35955535920448,51.15694181476427
11,Control,50.641639810716555,50.641639810716555,51.35442812185957,50.641639810716555,51.35442812185957,59.657881715341205
12,Control,46.18391887240976,46.18391887240976,56.77048940869426,46.18391887240976,56.77048940869426,59.14267310012181
13,Control,45.478736800883716,45.478736800883716,44.99492446009588,45.478736800883716,44.99492446009588,42.04982068435051
14,Control,33.99249458250232,33.99249458250232,44.55345241722484,33.99249458250232,44.55345241722484,46.042220610997255
15,Control,48.76039976394779,48.76039976394779,58.833037125552906,48.76039976394779,58.833037125552906,43.30837212349433
16,Control,36.25789264955062,36.25789264955062,37.292727066237916,36.25789264955062,37.292727066237916,48.90072887732463

Study design

Before column

After column

Summary statistic

Confidence level

Resamples

Random seed

APA reporting guide

Use the results as parts of a report. Explain the study design, variables, units, missing data, and assumptions. Include effect estimates and confidence intervals where available. Do not invent an interval that this tool does not estimate.

Bootstrap. Name the statistic, resampling unit, sample sizes, replicates, seed, and percentile confidence level. Report the estimate and interval; this is not a BCa interval.

Permutation and sign-flip. State the null, exchangeability or symmetry assumption, statistic direction, exact versus Monte Carlo method, repetitions, seed, two-sided p, and Monte Carlo SE.

Mann–Whitney and Wilcoxon. Report U (and which group it refers to) or the smaller signed-rank sum, n, p, exact or approximate method, ties/zero handling, and the named rank-biserial effect. These are not universally tests of medians.

Kruskal–Wallis and Friedman. Report H or Friedman χ² with df, n, p, tie correction, and ε² or Kendall’s W. Friedman n counts complete participants.

Report exact p values to three decimals, or p < .001. Omit leading zeros for probabilities and correlations. Use italics for Latin statistical symbols; keep Greek symbols upright. Precision should suit the measurement scale.

APA numbers and statistics guide · APA reporting standards

Observed estimate and resampled distribution

Source: Simulated teaching data (draw 941). This analysis uses 16 of 16 rows; Excluded rows: 0 (unselected groups or missing/invalid selected values).

Inspect input rows

First 12 rows (before exclusions)

First 12 rows (before exclusions)
before	after
44.81856418173733	50.81855921419285
34.93756292484065	38.846862569465515
37.12318209811927	41.72669205852717
43.80362500044896	53.592068847228475
33.35655921721986	40.98762711426991
38.417884880264396	40.60344847574147
49.53396495134719	51.97898582470806
42.72641283094211	49.29667327701861
33.706269273832746	41.642923834157926
37.506127331107315	48.35955535920448
50.641639810716555	51.35442812185957
46.18391887240976	56.77048940869426

Differences are after − before; n = 16 matched rows.

Observed statistic

5.90

Percentile interval

4.01 to 7.71

Bootstrap SE

0.95

Estimated bootstrap bias

-0.01

Horizontal: Bootstrap estimates. Vertical: Count.

Bootstrap estimates

Export APA PNG

The export uses your selected graph colors and Arial, with 10-point graph labels and an 11-point caption at 6.5 inches wide (300 dpi). Check variable units, title case, and the note before downloading. Custom captions persist until you reset them.

Figure number

Custom figure title

Custom note below the figure

Export in black and white (grayscale)

Export background

Transparent exports keep dark text and are intended for light backgrounds. Grayscale removes color from the entire figure, including the legend. Check group labels and line styles.

Include figure number, title, and note

Turn this off if you will add the caption in your manuscript. Match your manuscript’s figure numbering and caption font. A figure does not replace a complete statistical report.

Each resample preserves the original sample size. Paired data resample whole within-person differences. Actual resamples: 2000.

Inspect the first 12 replicate values

Resampled statistics

Resampled statistics
Replicate	Statistic
1	5.32
2	6.56
3	7.02
4	5.61
5	4.92
6	6.11
7	6.80
8	4.89
9	5.46
10	5.31
11	5.87
12	6.37

Try this: Keep the settings fixed and change the random seed. Then increase the resample count.

Explain what happens

Monte Carlo results vary with the seed. Increasing the resample count reduces this variation. The original dataset still determines the underlying uncertainty; resampling does not create new information.

Assumptions and method

The observed sample should represent the target population. Resampling units must be independent; clustered data require cluster resampling. This lab resamples individual observations or paired differences and uses percentile intervals, which are approximate.

Read the method reference

KIN6005 Statistical Analysis Studio

Credits & citation

Cite this studio

Methods and reporting

Observed estimate and resampled distribution

First 12 rows (before exclusions)

Resampled statistics