KIN6005 Statistical Analysis Studio

t Tests & ANOVA

Compare a numeric outcome with a reference value, between independent groups, or before and after a condition.

Which analysis should I use?

One-sample t test: Compare one sample mean with a hypothesized value.
Paired-samples t test: Compare two measurements from the same participants using their within-person differences.
Independent-samples t test (Welch): Compare two groups of different participants without assuming equal variances.
One-way ANOVA / Welch ANOVA: Compare means across independent groups. Welch ANOVA allows unequal variances.
Two-way ANOVA (2–4 levels per factor): Examine two categorical factors and their interaction. Each factor can have two to four levels; every cell needs at least two observations.

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

Analysis

How to use the selected analysis

Use one row per participant with two different measurement columns.
Select Before and After. Change is After minus Before; the null mean change is usually zero.
Choose simulation or upload/paste your data, then check the included sample size. Sliders change simulation only. Simulated outcome and factor roles are fixed; upload data to map your own columns.
Read Results at a glance first. Confidence level sets interval coverage; alpha is 1 minus confidence level. Use the difference confidence interval and the two-sided p value to evaluate the null hypothesis.

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 before and after 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) (24 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
17,Control,35.22607057195932,35.22607057195932,42.88149381886406,35.22607057195932,42.88149381886406,46.881392877769834
18,Control,39.593801436574154,39.593801436574154,50.18915438264751,39.593801436574154,50.18915438264751,54.08169147001256
19,Control,32.0954256855205,32.0954256855205,36.41983649835529,32.0954256855205,36.41983649835529,42.49143156606808
20,Control,39.82320217043025,39.82320217043025,49.82627254213385,39.82320217043025,49.82627254213385,55.35209213077865
21,Control,40.78095754824114,40.78095754824114,36.60624671647833,40.78095754824114,36.60624671647833,50.07453448577477
22,Control,43.45654050059303,43.45654050059303,46.676770130229244,43.45654050059303,46.676770130229244,54.93414837120239
23,Control,33.48029558231436,33.48029558231436,43.42583734450593,33.48029558231436,43.42583734450593,39.97910874956953
24,Control,41.96062089145532,41.96062089145532,51.08457995721662,41.96062089145532,51.08457995721662,44.63940158846475

Before column

After column

Null mean change

Confidence level

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.

One-sample and paired t tests. Report n, M and SD (of changes for paired data), the null value, t(df), p, difference and confidence interval, and d or dz with its definition.

Welch t test. Report group n/M/SD, difference direction, t with fractional df, p, and the Welch confidence interval. A pooled-SD effect interval has additional assumptions.

Classical and Welch ANOVA. Report F(df1, df2), p, and group summaries. Identify which ANOVA was used. Descriptive η² and classical ω² are not Welch-specific effects.

Factorial ANOVA. Specify factors, coding, cell sizes, interaction, and partial tests. Report both numerator and residual df with F, p, and partial η².

Contrasts. State weights and the comparison family. Distinguish raw and Holm-adjusted p values, and identify intervals as individual or simultaneous.

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

Data and design

Source: Simulated teaching data (draw 941). This analysis uses 24 of 24 rows; Excluded rows: 0 (unselected groups or missing/invalid selected values).

Inspect input rows

First 12 rows (before exclusions)

First 12 rows (before exclusions)
pre	post
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

One row represents one person measured twice. Analyze complete pairs; do not treat the two columns as independent groups.

Results at a glance

Selected analysis: Paired t test. Confidence level = 95%; significance level α = 0.050.

Change-score summary (After − Before)

Change-score summary (After − Before)
n	Mean	SD	SE	t	df	Two-sided p	Cohen’s d_z
24	6.05	4.22	0.86	7.01	23	< .001	1.43

95% confidence intervals

95% confidence intervals
Quantity	Estimate	Lower	Upper
Difference from null (0)	6.05	4.26	7.83
Cohen’s d_z	1.43	0.85	2.00

Within-person change

Paired t test: n = 24, M = 6.05, SD = 4.22; t(23) = 7.01, p < .001. Difference from null 0 = 6.05, 95% CI [4.26, 7.83]; dz = 1.43, 95% CI [0.85, 2.00].

Mean comparison view

Horizontal: Outcome. Vertical: Probability density.

Normal curves fitted to the observed group means and SDs

Before (pre)
After (post) (dashed)

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

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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 curve describes individual scores under a normal model. Its width is the SD. A curve does not establish that the observations are normally distributed. Groups with zero SD have no normal curve. Before and after measurements belong to the same people. Use the change-score interval for the paired test.

Distribution and mean summary

Distribution and mean summary
Index	Group	n	Mean	SD	SE	95% mean CI
1	Before (pre)	24	40.15	5.57	1.14	37.80 to 42.51
2	After (post)	24	46.20	6.32	1.29	43.53 to 48.87

Horizontal: Occasion: 0 = before, 1 = after. Vertical: Outcome.

First 40 participants; each line connects one person's measurements

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.

Horizontal: After minus before. Vertical: Count.

After minus before

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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.

Difference from null

6.05

95% difference CI

4.26 to 7.83

t (degrees of freedom)

7.01 (23)

Two-sided p

< .001

Cohen’s d_z

1.43

Standardized-effect CI

0.85 to 2.00

Try this: For paired data, compare the spread of before scores with the spread of changes. Which spread determines precision?

Explain what happens

The SD of within-person changes determines the paired standard error. Pairing removes stable between-person differences from that uncertainty.

Assumptions and method

Independent participants; correct pairing; normally distributed values for one-sample inference or differences for paired inference, especially with small samples. Outliers may strongly affect means. The standardized-effect interval inverts the noncentral t distribution.

Read the method reference

KIN6005 Statistical Analysis Studio

Credits & citation

Cite this studio

Methods and reporting

Data and design

First 12 rows (before exclusions)

Results at a glance

Change-score summary (After − Before)

95% confidence intervals

Within-person change

Distribution and mean summary