KIN6005 Statistical Analysis Studio

Sampling & Power

See how sample size affects estimates, confidence intervals, and statistical power. Use a simulated population or resample an uploaded numeric variable.

Which analysis should I use?

Sampling distributions and confidence intervals: Repeat a study and compare its sample means and intervals. CSV mode treats your observations as a reference population.
Power and sample size: Plan a one-sample, independent-samples, or paired-samples t test using an expected effect and variability.

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

How to use the selected analysis

Choose a simulated population or upload a numeric reference population. The population and null means are different concepts.
Set sample size, confidence and the alternative hypothesis. Inspected-study results and repeated-study percentages are separate outputs.
The quick power planner below uses separate effect, SD and sample-size assumptions, but shares alpha and test direction with the top controls. Use Power Studio for direct d/d_z planning.

Population source

Upload data or download a template

Upload instructions and data privacy

Use one row per observation and a numeric outcome column. This lab repeatedly samples the uploaded values with replacement to illustrate sampling uncertainty.

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 study 1, draw 2026 (25 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 (2 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

Population shape

Population mean

Population SD

Sample size

Number of studies

300

Confidence level

Null mean

Alternative hypothesis

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.

Sampling and coverage. State the simulated population, n, repetitions, seed, confidence level, and observed coverage. Simulated coverage is a teaching result.

t inference. State the null mean and one- or two-sided alternative, t(df), exact p, and the mean estimate with its confidence interval.

Power. State the study design, assumed effect and SD (or standardized effect), α, sidedness, target power, and planned n. Power is conditional on those assumptions.

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

Simulated normal population. Power planning below uses separately entered assumptions.

One sample and its uncertainty

Inspect study number

Horizontal: Observed outcome. Vertical: Count.

Observed outcome

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.

The dashed reference marks the reference population mean (40.00).

Sample mean

42.11

Sample SD

6.23

Estimated SE

1.25

95% interval

39.54 to 44.68

Try this: Quadruple sample size while keeping population SD fixed. Predict which quantity halves: SD or SE.

Explain what happens

The theoretical SE halves. Individual observations remain equally variable, so population SD stays fixed. Sample SD fluctuates around that population value.

Assumptions and method

Observations are independent. The t interval has exact coverage for normal populations; skewed small samples may not attain nominal coverage.

Read the method reference

Sampling distribution and interval coverage

Horizontal: Means across repeated studies. Vertical: Count.

Means across repeated studies

Export APA PNG

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.

Theoretical SE

1.20

Observed spread of means

1.20

Intervals covering the mean

95.7%

Horizontal: Population mean estimate and interval. Vertical: Study number.

First 60 confidence intervals; dashed intervals miss the reference mean

Export APA PNG

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.

Inspect or export all simulated studies

First 10 studies

First 10 studies
Study	Mean	SD	SE	Lower	Upper	Covers mean
1	42.11	6.23	1.25	39.54	44.68	Yes
2	41.86	5.25	1.05	39.69	44.03	Yes
3	39.80	7.08	1.42	36.88	42.72	Yes
4	39.24	5.95	1.19	36.79	41.70	Yes
5	40.61	6.80	1.36	37.80	43.42	Yes
6	38.52	6.15	1.23	35.98	41.06	Yes
7	40.18	5.20	1.04	38.04	42.33	Yes
8	38.78	6.12	1.22	36.25	41.31	Yes
9	39.37	6.66	1.33	36.62	42.12	Yes
10	40.42	6.41	1.28	37.77	43.06	Yes

Try this: Use a strongly skewed population and a small sample. Increase sample size and compare the distribution of means.

Explain what happens

Averages become less skewed as sample size grows under these finite-variance populations. This is the central limit theorem. It does not say that the individual observations become normal.

Assumptions and method

Independent observations, finite population variance, and repeated random samples. The displayed coverage estimates are Monte Carlo results, not guarantees for every population.

Null distribution and decision errors

Study 1: t(24) = 1.69, p = .104 (two-sided alternative). M = 42.11, SD = 6.23, n = 25; 95% two-sided CI [39.54, 44.68]. Null mean = 40.

Horizontal: t statistic under the null. Vertical: Density.

Null t distribution; dashed lines mark rejection boundaries

Export APA PNG

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.

Inspected study t

1.69

Inspected study p

.104

Simulated Type I error

4.3%

Alpha

0.05

Selected study: do not reject the null at α = 0.05.

Try this: Set the true mean equal to the null mean and repeat the experiment. Then move the true mean away from the null.

Explain what happens

Rejections are Type I errors when the null is true. When the mean differs, rejections estimate power for that effect. Failing to reject does not establish equivalence.

Assumptions and method

The null reference is Student's t distribution. Exact normal-theory inference requires independent normal observations. The simulation intentionally lets you explore departures from normality.

Plan a study before collecting data

Planning α = 0.050; test direction = two-sided. These come from Confidence level and Alternative hypothesis above. Open Power Studio for direct effect-size planning.

Planning design

Planned mean difference (outcome units)

Planning SD

Participants per group

Target power

Planning uses α = 0.05 and the selected two-sided alternative. The simulated shape or uploaded CSV does not alter this normal-theory planning calculation. Enter the expected effect and SD deliberately.

Planned Cohen’s d

0.50

Planning alpha

0.050

Prospective power

47.8%

Required sample size

64 per group

Horizontal: Participants per group. Vertical: Probability of rejection.

Power as sample size changes (2–200)

Export APA PNG

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.

Try this: Compare independent and paired designs at the same marginal SD and participant count. Increase the paired correlation.

Explain what happens

The paired design gains precision when pre/post measurements are positively correlated. Independent groups require twice the per-group count in total. The designs answer different questions and must match how data are collected.

Assumptions and method

Normal-theory t tests. Independent power assumes equal group sizes and variances; paired power uses SD(change) = SD × √[2(1 − correlation)]. Numerical integration uses the noncentral t representation. This is not post-hoc observed power.

Read the method reference

KIN6005 Statistical Analysis Studio

Credits & citation

Cite this studio

Methods and reporting

One sample and its uncertainty

Sampling distribution and interval coverage

First 10 studies

Null distribution and decision errors

Plan a study before collecting data